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Figure 3. Various cutoff frequencies with respect to the changes of Zeq ((a) 33 O, (b) 41 O, (c) 56 O and (d) 90 ©) and Leg used to examine the stopband characteristics and verify the closed-form expressions for fy, and fy. Figure 3 depicts the f, and fy; values of the stopband characteristics with the aforementioned Zeq and Le, values, as acquired from the FEM simulations (blue lines) and the proposed equations (red lines). The results for Zeq of 33, 41, 56, and 90 Q, are shown in Figure 3a—d, respectively. The closed-form expressions for f;, and fy exhibit good correlations with the FEM-based full-wave simulations, as shown in all the figures. The discrepancies associated with f}; may result from the first-order approximation of the Taylor series expansion of the tangent function. However, the differences between the FEM simulation and the closed-form expressions are approximately uniform for all the Leq values. Thus, the tendencies among these results are in close agreement. Even though the closed-form expressions for ft and fy derived herein are verified using a limited number of test cases, these equations can be extended and applied to other DP-EBG structures, including the different dimensions of geometrical parameters.

Figure 3 Various cutoff frequencies with respect to the changes of Zeq ((a) 33 O, (b) 41 O, (c) 56 O and (d) 90 ©) and Leg used to examine the stopband characteristics and verify the closed-form expressions for fy, and fy. Figure 3 depicts the f, and fy; values of the stopband characteristics with the aforementioned Zeq and Le, values, as acquired from the FEM simulations (blue lines) and the proposed equations (red lines). The results for Zeq of 33, 41, 56, and 90 Q, are shown in Figure 3a—d, respectively. The closed-form expressions for f;, and fy exhibit good correlations with the FEM-based full-wave simulations, as shown in all the figures. The discrepancies associated with f}; may result from the first-order approximation of the Taylor series expansion of the tangent function. However, the differences between the FEM simulation and the closed-form expressions are approximately uniform for all the Leq values. Thus, the tendencies among these results are in close agreement. Even though the closed-form expressions for ft and fy derived herein are verified using a limited number of test cases, these equations can be extended and applied to other DP-EBG structures, including the different dimensions of geometrical parameters.

Related Figures (183)

Figure 1. Effects of resonant coupling mechanisms on non-modulated and SS-modulated EMI.
Figure 1. Effects of resonant coupling mechanisms on non-modulated and SS-modulated EMI.
Figure 2. Digital communication channel with EMI resonant coupling: Block Diagram.
Figure 2. Digital communication channel with EMI resonant coupling: Block Diagram.
Figure 3. EMI resonant coupling in the frequency domain: power spectral densities of nominal signals, EMI, background noise and resonant coupling transfer function.
Figure 3. EMI resonant coupling in the frequency domain: power spectral densities of nominal signals, EMI, background noise and resonant coupling transfer function.
and where a is the signal-to-noise ratio as in (1) and 6 = Pgmi/ Ps is the overall EMI-to-signal power ratio. Since the integral in (7) can be calculated analytically in closed form in terms of:
and where a is the signal-to-noise ratio as in (1) and 6 = Pgmi/ Ps is the overall EMI-to-signal power ratio. Since the integral in (7) can be calculated analytically in closed form in terms of:
Figure 4. Normalized capacity versus resonant frequency fr/B for a communication channel with bandwidth B = (f1, fz) in the presence of EMI. The same analysis is repeated in Figure 5 for different values of the quality factor Q ranging from 1 to 1,000,000 to discuss the effects of SS-modulations on signal capacity under different resonant coupling quality factors.
Figure 4. Normalized capacity versus resonant frequency fr/B for a communication channel with bandwidth B = (f1, fz) in the presence of EMI. The same analysis is repeated in Figure 5 for different values of the quality factor Q ranging from 1 to 1,000,000 to discuss the effects of SS-modulations on signal capacity under different resonant coupling quality factors.
Figure 5. Normalized capacity versus resonant frequency fp /B for the channel in Figure 3 for different values of the resonant coupling quality factor Q under constant peak coupling, reported in each plot for different SS-modulation depth 6 ranging from 0 (no SS) to 30%.
Figure 5. Normalized capacity versus resonant frequency fp /B for the channel in Figure 3 for different values of the resonant coupling quality factor Q under constant peak coupling, reported in each plot for different SS-modulation depth 6 ranging from 0 (no SS) to 30%.
Figure 6. Worst case normalized capacity loss over different resonant frequencies fr versus SS-modulation depth 6 ranging from 0 (no SS) to 30% for different values of the resonant coupling quality factor Q under constant peak coupling. A detail of the top figure is reported in the bottom figure.
Figure 6. Worst case normalized capacity loss over different resonant frequencies fr versus SS-modulation depth 6 ranging from 0 (no SS) to 30% for different values of the resonant coupling quality factor Q under constant peak coupling. A detail of the top figure is reported in the bottom figure.
Figure 7. Average normalized capacity for resonant frequencies fr ranging from 2B to 7B versus SS-modulation depth 6 ranging from 0 (no SS) to 30% for different values of the resonant coupling quality factor Q under constant peak coupling. A detail of the top figure is reported in the bottom figure.
Figure 7. Average normalized capacity for resonant frequencies fr ranging from 2B to 7B versus SS-modulation depth 6 ranging from 0 (no SS) to 30% for different values of the resonant coupling quality factor Q under constant peak coupling. A detail of the top figure is reported in the bottom figure.
Figure 8. Worst case and average normalized capacity loss over different resonant frequencies fr versus SS-modulation depth 6 ranging from 0 (no SS) to 25% for different values of the resonant coupling quality factor Q under constant coupling integral.
Figure 8. Worst case and average normalized capacity loss over different resonant frequencies fr versus SS-modulation depth 6 ranging from 0 (no SS) to 25% for different values of the resonant coupling quality factor Q under constant coupling integral.
Figure 9. Schematic view of the test setup. different modulation depth 5. The EMI voltage v, at the receiver input without SS-modulation and with random SS-modulation at different modulation depth 6 is acquired by a digital scope at 125 MS/s during the DC-DC converter operation and is stored in a database. The power spectral density of the measured waveform for periodic and random SS-modulated (6 = 6%) is reported in Figure 10.
Figure 9. Schematic view of the test setup. different modulation depth 5. The EMI voltage v, at the receiver input without SS-modulation and with random SS-modulation at different modulation depth 6 is acquired by a digital scope at 125 MS/s during the DC-DC converter operation and is stored in a database. The power spectral density of the measured waveform for periodic and random SS-modulated (6 = 6%) is reported in Figure 10.
Figure 10. Measured power spectral density of periodic and random SS-modulated (6 = 6%) EMI For this purpose, a 4-QAM communication scheme over an AWGN channel with B = 600 kHz bandwidth is considered and the effects of non-modulated and SS-modulated EMI coupled to the channel bandwidth with a resonant transfer function with Q = 1 and with Q = 100 have been simulated in the Matlab environment, adding the measured non-modulated and SS-modulated EMI waveforms generated by the power converter to the received input signal.
Figure 10. Measured power spectral density of periodic and random SS-modulated (6 = 6%) EMI For this purpose, a 4-QAM communication scheme over an AWGN channel with B = 600 kHz bandwidth is considered and the effects of non-modulated and SS-modulated EMI coupled to the channel bandwidth with a resonant transfer function with Q = 1 and with Q = 100 have been simulated in the Matlab environment, adding the measured non-modulated and SS-modulated EMI waveforms generated by the power converter to the received input signal.
Figure 11. Bit error rate of a communication channel corrupted by SS-modulated EMI under weakly resonant coupling (Q = 1) vs. EMI normalized r.m.s. amplitude at different modulation depth 6. to the same measured EMI waveforms) for different values of the modulation depth 6. From the figure, it can be observed that the EMI amplitude at which BER starts increasing in a significant way is lower for a larger SS-modulation depth and higher in the non-modulated case or for small values of 6.
Figure 11. Bit error rate of a communication channel corrupted by SS-modulated EMI under weakly resonant coupling (Q = 1) vs. EMI normalized r.m.s. amplitude at different modulation depth 6. to the same measured EMI waveforms) for different values of the modulation depth 6. From the figure, it can be observed that the EMI amplitude at which BER starts increasing in a significant way is lower for a larger SS-modulation depth and higher in the non-modulated case or for small values of 6.
Figure 12. Bit error rate of a communication channel corrupted by SS-modulated EMI under strongly resonant coupling (Q = 100) vs. EMI normalized r.m.s. amplitude at different modulation depth 6. Comparing non-modulated EMI with SS-modulated EMI, a similar BER is achieved for a 20% higher EMI amplitude in the non-modulated case. In Figure 12, the same analysis is performed under resonant EMI coupling with quality factor Q = 100. In this case, a similar BER is achieved for a 3.4X higher EMI amplitude than in the non-modulated cases, revealing an even worse impact of SS-modulations on the BER when an EMI resonant coupling with a higher Q factor is introduced.
Figure 12. Bit error rate of a communication channel corrupted by SS-modulated EMI under strongly resonant coupling (Q = 100) vs. EMI normalized r.m.s. amplitude at different modulation depth 6. Comparing non-modulated EMI with SS-modulated EMI, a similar BER is achieved for a 20% higher EMI amplitude in the non-modulated case. In Figure 12, the same analysis is performed under resonant EMI coupling with quality factor Q = 100. In this case, a similar BER is achieved for a 3.4X higher EMI amplitude than in the non-modulated cases, revealing an even worse impact of SS-modulations on the BER when an EMI resonant coupling with a higher Q factor is introduced.
Figure 13. Bit error rate of a communication channel corrupted by SS-modulated EMI under weakly resonant coupling (Q = 1) vs. different modulation depth 6 at different EMI normalized rm.s. amplitude values.
Figure 13. Bit error rate of a communication channel corrupted by SS-modulated EMI under weakly resonant coupling (Q = 1) vs. different modulation depth 6 at different EMI normalized rm.s. amplitude values.
Figure 14. Bit error rate of a communication channel corrupted by SS-modulated EMI under strongly resonant coupling (Q = 100) vs. different modulation depth 6 at different EMI normalized rm.s. amplitude values.
Figure 14. Bit error rate of a communication channel corrupted by SS-modulated EMI under strongly resonant coupling (Q = 100) vs. different modulation depth 6 at different EMI normalized rm.s. amplitude values.
Figure 1. Scheme of the experimental setup: SMPS under test and its de variable load, LISN (Line Impedance Stabilization Network), 50 O. impedance matching, high-pass filter (1 kHz cutoff) and low-pass filter (2 MHz cutoff), Digital Storage Oscilloscope (DSO) and EMI Receiver.
Figure 1. Scheme of the experimental setup: SMPS under test and its de variable load, LISN (Line Impedance Stabilization Network), 50 O. impedance matching, high-pass filter (1 kHz cutoff) and low-pass filter (2 MHz cutoff), Digital Storage Oscilloscope (DSO) and EMI Receiver.
Figure 2. Typical time-domain waveform of an SMPS at the high-pass filtered LISN output measured as DSO input signal yj. The switching byproducts responsible for the conducted emissions are superimposed to the mains sinusoidal voltage, located at its zero crossings. The signal y; at the DSO input (qualitatively similar to the signal yo as provided at the LISN output) is an intermittent waveform, deprived of the 50 Hz mains voltage component and of its low-order harmonics, also to improve the dynamic range. The zero-mean high-pass filtered signal is characterized by steep transients and rapid oscillations, as shown in Figure 2. The instantaneous frequency of oscillations is in the order of 20-30 kHz and is in relation to the internal switching frequency; the repetition rate is 100 Hz, twice the mains frequency.
Figure 2. Typical time-domain waveform of an SMPS at the high-pass filtered LISN output measured as DSO input signal yj. The switching byproducts responsible for the conducted emissions are superimposed to the mains sinusoidal voltage, located at its zero crossings. The signal y; at the DSO input (qualitatively similar to the signal yo as provided at the LISN output) is an intermittent waveform, deprived of the 50 Hz mains voltage component and of its low-order harmonics, also to improve the dynamic range. The zero-mean high-pass filtered signal is characterized by steep transients and rapid oscillations, as shown in Figure 2. The instantaneous frequency of oscillations is in the order of 20-30 kHz and is in relation to the internal switching frequency; the repetition rate is 100 Hz, twice the mains frequency.
Figure 3. WPT (Wavelet Packet Transform) tree structure, indicating levels, ordinal indices at each level and terminal nodes. The down arrow “|n” indicates a down sampling (or decimation) by a factor of n (in our case, n = 2).
Figure 3. WPT (Wavelet Packet Transform) tree structure, indicating levels, ordinal indices at each level and terminal nodes. The down arrow “|n” indicates a down sampling (or decimation) by a factor of n (in our case, n = 2).
Figure 4. EMI receiver spectra with variable RBW (200 Hz, black; 1 kHz, blue; 2 kHz, light blue; 3 kHz, magenta; 5 kHz, red) for a SMPS featuring fixed switching frequency (type Black at 90% of rated power). of the switching peaks at 43.3 kHz and 87 kHz and above, and a variable estimated amplitude for the low-frequency nonstationary components (with a behavior similar to that of background noise). The result with 1 kHz RBW is retained for further analysis as a good compromise, also in view of the necessary time resolution settings in STFT and WPT.
Figure 4. EMI receiver spectra with variable RBW (200 Hz, black; 1 kHz, blue; 2 kHz, light blue; 3 kHz, magenta; 5 kHz, red) for a SMPS featuring fixed switching frequency (type Black at 90% of rated power). of the switching peaks at 43.3 kHz and 87 kHz and above, and a variable estimated amplitude for the low-frequency nonstationary components (with a behavior similar to that of background noise). The result with 1 kHz RBW is retained for further analysis as a good compromise, also in view of the necessary time resolution settings in STFT and WPT.
Figure 6. (a) Zoom on the frequency axis of Figure 5b for the frequency resolution of 976 Hz, where the change of the instantaneous frequency between 4 and 6 ms is well visible; and (b) additional spectrum obtained by replacing symlet1 with bior1.3. The case of two different wavelets is shown in Figure 6, applied to the signal using the same scaling: the amplitude estimates are quite similar, with the bior1.3 in Figure 6b, showing slightly smoother amplitude profile than the symlet1. Quantitatively, the average difference for the bins with the largest amplitude (those in Figure 6 with amplitude above 50 dB) is only 1.3 dB; the peaks, which are the most relevant for compliance to limits, are reproduced quite reliably with almost identical values (average difference of less than 0.25 dB). Thus, at least for the considered case, the choice of wavelets with “similar” characteristics and of suitable order for the observed time support gives repeatable results, although it represents a source of systematic error and the contribution to the uncertainty of the estimate of spectrum amplitude is not negligible (0.25 dB on average for the considered case).
Figure 6. (a) Zoom on the frequency axis of Figure 5b for the frequency resolution of 976 Hz, where the change of the instantaneous frequency between 4 and 6 ms is well visible; and (b) additional spectrum obtained by replacing symlet1 with bior1.3. The case of two different wavelets is shown in Figure 6, applied to the signal using the same scaling: the amplitude estimates are quite similar, with the bior1.3 in Figure 6b, showing slightly smoother amplitude profile than the symlet1. Quantitatively, the average difference for the bins with the largest amplitude (those in Figure 6 with amplitude above 50 dB) is only 1.3 dB; the peaks, which are the most relevant for compliance to limits, are reproduced quite reliably with almost identical values (average difference of less than 0.25 dB). Thus, at least for the considered case, the choice of wavelets with “similar” characteristics and of suitable order for the observed time support gives repeatable results, although it represents a source of systematic error and the contribution to the uncertainty of the estimate of spectrum amplitude is not negligible (0.25 dB on average for the considered case).
Figure 7. Comparison of two different wavelets in relation to localization on the time axis and spread to adjacent frequency bins; frequency resolution Af = 976 Hz, number of levels L = 9: (a) db15; and (b) sym8. SMPS type Black at 90% of rated power. for 2 ms giving yield then to fourth bin, with a return around 4 ms. Behavior of sym8 instead is more chaotic with no definite bin prevailing for at least some ms.
Figure 7. Comparison of two different wavelets in relation to localization on the time axis and spread to adjacent frequency bins; frequency resolution Af = 976 Hz, number of levels L = 9: (a) db15; and (b) sym8. SMPS type Black at 90% of rated power. for 2 ms giving yield then to fourth bin, with a return around 4 ms. Behavior of sym8 instead is more chaotic with no definite bin prevailing for at least some ms.
Figure 8. Black SMPS tested at 90% of rated power: (a) WPT spectrum obtained with db15, L = 9, Af = 976 Hz; and (b) STFT spectrum with Af = 1 kHz and time step At = 1 ms.
Figure 8. Black SMPS tested at 90% of rated power: (a) WPT spectrum obtained with db15, L = 9, Af = 976 Hz; and (b) STFT spectrum with Af = 1 kHz and time step At = 1 ms.
Figure 9. IMFs extracted with the EMD procedure. Figure 10. Comparison of the FFT spectra obtained from IMFs 2 and 3 extracted with EMD (red) and from the original signal (blue).
Figure 9. IMFs extracted with the EMD procedure. Figure 10. Comparison of the FFT spectra obtained from IMFs 2 and 3 extracted with EMD (red) and from the original signal (blue).
Figure 11. Comparison of the FFT spectra obtained from IMFs 2-5 extracted with EMD (red) and from the original signal (blue). a CY Yr Oe The results of comparison with STFT with 1 kHz frequency resolution, a 1 ms time step and a Flat Top window are shown in Figures 15 and 16. The former figure refers to the application of STFT to the signal obtained composing IMFs 2 and 3 extracted with EMD; the latter to the application of STFT to the signal obtained composing IMFs 2-4 extracted with EEMD. The amplitudes are the maximum values obtained by the successive FFTs that compose the STFT, as it would be with a spectrum analyzer set to max hold. It can be noticed that the amplitudes of the first peak (at 44 kHz, with 68.27 dBuV and 69.97 dBuV, respectively) and of the second peak (at 88 kHz, with 57.59 dBuV and 58.51 dBuV, respectively) are in agreement with those shown in Table 1 for WPT and EMI receiver data, thus confirming the suitability of the approach in the analysis of EMI.
Figure 11. Comparison of the FFT spectra obtained from IMFs 2-5 extracted with EMD (red) and from the original signal (blue). a CY Yr Oe The results of comparison with STFT with 1 kHz frequency resolution, a 1 ms time step and a Flat Top window are shown in Figures 15 and 16. The former figure refers to the application of STFT to the signal obtained composing IMFs 2 and 3 extracted with EMD; the latter to the application of STFT to the signal obtained composing IMFs 2-4 extracted with EEMD. The amplitudes are the maximum values obtained by the successive FFTs that compose the STFT, as it would be with a spectrum analyzer set to max hold. It can be noticed that the amplitudes of the first peak (at 44 kHz, with 68.27 dBuV and 69.97 dBuV, respectively) and of the second peak (at 88 kHz, with 57.59 dBuV and 58.51 dBuV, respectively) are in agreement with those shown in Table 1 for WPT and EMI receiver data, thus confirming the suitability of the approach in the analysis of EMI.
Figure 12. IMFs extracted with the EEMD procedure.
Figure 12. IMFs extracted with the EEMD procedure.
Figure 13. Comparison of the FFT spectra obtained from IMFs 2-4 extracted with EEMD (red) and from the original signal (blue).
Figure 13. Comparison of the FFT spectra obtained from IMFs 2-4 extracted with EEMD (red) and from the original signal (blue).
Figure 14. Comparison of the FFT spectra obtained from IMFs 2-7 extracted with EEMD (red) and from the original signal (blue).
Figure 14. Comparison of the FFT spectra obtained from IMFs 2-7 extracted with EEMD (red) and from the original signal (blue).
Figure 15. STFT spectrum with Af = 1 kHz and time step At = 1 ms of the signal resulting from the composition of IMFs 2 and 3 extracted with EMD.
Figure 15. STFT spectrum with Af = 1 kHz and time step At = 1 ms of the signal resulting from the composition of IMFs 2 and 3 extracted with EMD.
Figure 16. STFT spectrum with Af = 1 kHz and time step At = 1 ms of the signal resulting from the composition of IMFs 2 to 4 extracted with EEMD. 4. Conclusions
Figure 16. STFT spectrum with Af = 1 kHz and time step At = 1 ms of the signal resulting from the composition of IMFs 2 to 4 extracted with EEMD. 4. Conclusions
Figure 1. Configuration of the conventional boost circuit (CBC) and LISN setup.
Figure 1. Configuration of the conventional boost circuit (CBC) and LISN setup.
Figure 2. Common mode (CM) noise model of the conventional boost circuit. calculation. Vy is the noise source, represents the voltage between drain and source of the switch (namely V qs). Zcg is the impedance of Cg. According to the EMI measurement specification, the length of the connecting wire between EUT and LISN should be equal to 80 cm. Here, to improve the accuracy of the noise model, the impedance of the connecting wire is considered and represented as Zw.
Figure 2. Common mode (CM) noise model of the conventional boost circuit. calculation. Vy is the noise source, represents the voltage between drain and source of the switch (namely V qs). Zcg is the impedance of Cg. According to the EMI measurement specification, the length of the connecting wire between EUT and LISN should be equal to 80 cm. Here, to improve the accuracy of the noise model, the impedance of the connecting wire is considered and represented as Zw.
Figure 3. The experimental voltage waveform of switch measured by oscilloscope. Figure 3 shows the voltage waveform of switch measured by oscilloscope. The ringing caused by turn-on and turn-off could be seen clearly from the following magnified images. Note that the turn-on ringing is quite limited and thus, its effectiveness could be ignored.
Figure 3. The experimental voltage waveform of switch measured by oscilloscope. Figure 3 shows the voltage waveform of switch measured by oscilloscope. The ringing caused by turn-on and turn-off could be seen clearly from the following magnified images. Note that the turn-on ringing is quite limited and thus, its effectiveness could be ignored.
Figure 4. Decomposition diagram of the switch voltage waveform. As the real voltage waveform is an irregular shape, it is difficult to calculate its spectrum directly. This paper decomposed the switch voltage waveform and the Fourier series could be done in steps. The corresponding decomposition process of the overall waveform is shown in Figure 4. The overall waveform is shown at the top of the figure, and it can be divided into the trapezoid component and the ringing component. This decomposition has reduced the complexity of Fourier transformation and improved the precision at the same time. The relative parameters are also marked in Figure 4, which could help to identify the corresponding symbols listed in Table 2.
Figure 4. Decomposition diagram of the switch voltage waveform. As the real voltage waveform is an irregular shape, it is difficult to calculate its spectrum directly. This paper decomposed the switch voltage waveform and the Fourier series could be done in steps. The corresponding decomposition process of the overall waveform is shown in Figure 4. The overall waveform is shown at the top of the figure, and it can be divided into the trapezoid component and the ringing component. This decomposition has reduced the complexity of Fourier transformation and improved the precision at the same time. The relative parameters are also marked in Figure 4, which could help to identify the corresponding symbols listed in Table 2.
Table 2. Characteristic parameters of the switch voltage waveform. According to the mathematical definition [14], the formula for calculating the Fourier series corresponding to trapezoid could be expressed in Equation (2).
Table 2. Characteristic parameters of the switch voltage waveform. According to the mathematical definition [14], the formula for calculating the Fourier series corresponding to trapezoid could be expressed in Equation (2).
Figure 5. The experimental setup of conducted noise measurement.
Figure 5. The experimental setup of conducted noise measurement.
Figure 6. The frequency spectra of switch voltage (noise source) comparison between calculation and measured results. According to Equations (2)-(5) and the measured data, the Fourier series calculation was completed with Matlab 2015b. Figure 6 shows the noise source spectra comparison between experimental and calculation results. The calculation results are plotted in the blue line, and the red experimental results refer to Fast Fourier Transformation (FFT) computed by the oscilloscope. The comparison shows that the calculation results match the experimental result in all frequency ranges. The high-frequency peak is caused by the ringing, and this frequency (around 23.5 MHz) agrees with the frequency of ringing waveform in Figure 3 (Ty = 42.3 ns). The effectiveness of this frequency domain modeling method and the obtained parameters was well verified.
Figure 6. The frequency spectra of switch voltage (noise source) comparison between calculation and measured results. According to Equations (2)-(5) and the measured data, the Fourier series calculation was completed with Matlab 2015b. Figure 6 shows the noise source spectra comparison between experimental and calculation results. The calculation results are plotted in the blue line, and the red experimental results refer to Fast Fourier Transformation (FFT) computed by the oscilloscope. The comparison shows that the calculation results match the experimental result in all frequency ranges. The high-frequency peak is caused by the ringing, and this frequency (around 23.5 MHz) agrees with the frequency of ringing waveform in Figure 3 (Ty = 42.3 ns). The effectiveness of this frequency domain modeling method and the obtained parameters was well verified.
Figure 7. CM noise spectra comparison of a conventional boost converter (CBC) between prediction and measured results. observed that the prediction result matches the measurement in the whole frequency band, and this model is able to predict CM noise with good accuracy.
Figure 7. CM noise spectra comparison of a conventional boost converter (CBC) between prediction and measured results. observed that the prediction result matches the measurement in the whole frequency band, and this model is able to predict CM noise with good accuracy.
Figure 8. Configuration of the balanced boost converter and LISN. Instead of adding conventional passive or active EMI filters, the impedance balancing technique could reduce the conducted noise by changing the topology of CBC. The configuration of balanced boost converter along with LISN is shown in Figure 8. Compared with Figure 1, the power inductor L was split into two parts (Ly and Lz) and another capacitor Cy was placed between the N phase and the ground. This action changes the path of the noise current without affecting the efficiency of the circuit.
Figure 8. Configuration of the balanced boost converter and LISN. Instead of adding conventional passive or active EMI filters, the impedance balancing technique could reduce the conducted noise by changing the topology of CBC. The configuration of balanced boost converter along with LISN is shown in Figure 8. Compared with Figure 1, the power inductor L was split into two parts (Ly and Lz) and another capacitor Cy was placed between the N phase and the ground. This action changes the path of the noise current without affecting the efficiency of the circuit.
Figure 9. (a) CM noise model of the impedance balanced boost circuit; (b) simplified CM noise model by the Thevenin theorem. The corresponding CM noise model of balanced boost circuit is shown in Figure 9a. The model includes the equivalent parallel capacitor (EPC) and equivalent parallel resistor (EPR) of each inductor, as well asthe equivalent series inductor (ESL) and equivalent series resistor (ESR) of each capacitor. These parameters may affect the self-resonant frequency and cause impedance unbalancing as well. In addition, a more simplified model obtained according to the Thevenin theorem is shown in Figure 9b. Vx and Zg in the figure are the equivalent noise source and the equivalent impedance, respectively. Vn is the same with CBC since the driver circuit of the switch is the same with CBC, and the implement of balancing impedance would not affect the efficiency of the circuit. The relationships between Vz, Zr, Vn, and the impedance bridge arms are shown in Equations (6) and (7).
Figure 9. (a) CM noise model of the impedance balanced boost circuit; (b) simplified CM noise model by the Thevenin theorem. The corresponding CM noise model of balanced boost circuit is shown in Figure 9a. The model includes the equivalent parallel capacitor (EPC) and equivalent parallel resistor (EPR) of each inductor, as well asthe equivalent series inductor (ESL) and equivalent series resistor (ESR) of each capacitor. These parameters may affect the self-resonant frequency and cause impedance unbalancing as well. In addition, a more simplified model obtained according to the Thevenin theorem is shown in Figure 9b. Vx and Zg in the figure are the equivalent noise source and the equivalent impedance, respectively. Vn is the same with CBC since the driver circuit of the switch is the same with CBC, and the implement of balancing impedance would not affect the efficiency of the circuit. The relationships between Vz, Zr, Vn, and the impedance bridge arms are shown in Equations (6) and (7).
Figure 10. Magnitude comparison of bridge arms impedance (Zc; VS. Zc and Z, VS. Zj2).
Figure 10. Magnitude comparison of bridge arms impedance (Zc; VS. Zc and Z, VS. Zj2).
Figure 11. CM noise spectra comparison of balanced impedance circuit. Figure 11 shows the experimental CM noise spectrum of balanced boost circuit, which is plotted in red. Meanwhile, the green envelope is the CM noise of CBC (same as in Figure 7). By utilizing the balanced technique, the noise level was well attenuated from 0.5 MHz and upwards. The effect of this technique is obvious, as much as 40 dB reduction was done at some frequency points. Nevertheless, the noise peak at low frequency bands degraded the performance. The relative analysis and solution are given in the following sections.
Figure 11. CM noise spectra comparison of balanced impedance circuit. Figure 11 shows the experimental CM noise spectrum of balanced boost circuit, which is plotted in red. Meanwhile, the green envelope is the CM noise of CBC (same as in Figure 7). By utilizing the balanced technique, the noise level was well attenuated from 0.5 MHz and upwards. The effect of this technique is obvious, as much as 40 dB reduction was done at some frequency points. Nevertheless, the noise peak at low frequency bands degraded the performance. The relative analysis and solution are given in the following sections.
Figure 12. Magnitude spectra comparison between Zgo (250 pH and 1 nF) and Zcg. The equivalent impedance of balanced boost circuit Zp could be calculated by Equations (6), or measured directly. The error between the two results is small. Referring to Equation (6), Zgo represents the entire impedance of 250 1H inductors (L1, Lz) paralleled with 1 nF capacitors (Cj, C2). Figure 12 shows the impedance variation of Zcg and Zgo through frequency. The Zcg is larger than Zgo from 0.15 MHz to 0.69 MHz, and then the Zg9 becomes larger from 0.69 MHz. According to Figure 12, it should be noted that Zcg equals Zxo at the point of 0.69 MHz, where the noise of balanced circuit is 80 dBuV and the CBC is about 100 dBuV. This spectra difference equals to 20 dBuV, which means that Vy is about 10 times of Vg according to the definition. Therefore, this paper assumed that Vg is one-tenth of Vx and then substituted other measured impedance values into Equations (8) for calculation.
Figure 12. Magnitude spectra comparison between Zgo (250 pH and 1 nF) and Zcg. The equivalent impedance of balanced boost circuit Zp could be calculated by Equations (6), or measured directly. The error between the two results is small. Referring to Equation (6), Zgo represents the entire impedance of 250 1H inductors (L1, Lz) paralleled with 1 nF capacitors (Cj, C2). Figure 12 shows the impedance variation of Zcg and Zgo through frequency. The Zcg is larger than Zgo from 0.15 MHz to 0.69 MHz, and then the Zg9 becomes larger from 0.69 MHz. According to Figure 12, it should be noted that Zcg equals Zxo at the point of 0.69 MHz, where the noise of balanced circuit is 80 dBuV and the CBC is about 100 dBuV. This spectra difference equals to 20 dBuV, which means that Vy is about 10 times of Vg according to the definition. Therefore, this paper assumed that Vg is one-tenth of Vx and then substituted other measured impedance values into Equations (8) for calculation.
Figure 13. CM noise comparison after replacing the 250 uH inductors with 1.4 mH inductors. After calculation using Equations (10), the inductance should be larger than 1.3 mH if the capacitors C, and Cy are kept constant. Here, two1.4mH inductors were utilized to replace the 250 uH inductors. The experimental results were recorded and drawn with black in Figure 13, compared with the former balanced boost circuit in red and the green envelope of CBC. These experimental results show that the proposed balanced scheme with 1.4 mH inductors and 1nF capacitors could attenuate noise level over all frequency range compared with CBC. Furthermore, the spike at 0.37 MHz was effectively suppressed. However, the noise at high frequency increased in contrast with the former balanced boost circuit (250 wH and 1 nF). The valley at 0.8 MHz is due to the self-resonance between the 1.4 mH inductor and its EPCs.
Figure 13. CM noise comparison after replacing the 250 uH inductors with 1.4 mH inductors. After calculation using Equations (10), the inductance should be larger than 1.3 mH if the capacitors C, and Cy are kept constant. Here, two1.4mH inductors were utilized to replace the 250 uH inductors. The experimental results were recorded and drawn with black in Figure 13, compared with the former balanced boost circuit in red and the green envelope of CBC. These experimental results show that the proposed balanced scheme with 1.4 mH inductors and 1nF capacitors could attenuate noise level over all frequency range compared with CBC. Furthermore, the spike at 0.37 MHz was effectively suppressed. However, the noise at high frequency increased in contrast with the former balanced boost circuit (250 wH and 1 nF). The valley at 0.8 MHz is due to the self-resonance between the 1.4 mH inductor and its EPCs.
Figure 14. Impedance comparison between Zg) (1.4 mH and 1 nF) and Zcg. the equivalent noise source Vg in the optimized scheme was attenuated well compared with CBC. However, a drawback of this approach is the increased weight and volume of the circuit.
Figure 14. Impedance comparison between Zg) (1.4 mH and 1 nF) and Zcg. the equivalent noise source Vg in the optimized scheme was attenuated well compared with CBC. However, a drawback of this approach is the increased weight and volume of the circuit.
Figure 15. CM noise comparison after replacing the 1 nF Y-capacitors with 4.7 nF Y-capacitors. * The CM noise spectra comparison is shown in Figure 15. The purple curve is for the case of an optimized solution after replacing the 1 nF Y-capacitors with 4.7 nF, the green one is the noise envelope of CBC, and the red one is for the former balanced circuit boost (250 wH and 1 nF). The comparison shows that after utilizing the scheme with 4.7 nF capacitors, a low-frequency spike was also moved out from the frequency band of interest and the CM noise was significantly attenuated. Meanwhile, at a high frequency, the noise after adopting 4.7 nF capacitors is lower than the former case using 1 nF capacitors. out from the frequency band of interest and the CM noise was significantly attenuated. Meanwhile,
Figure 15. CM noise comparison after replacing the 1 nF Y-capacitors with 4.7 nF Y-capacitors. * The CM noise spectra comparison is shown in Figure 15. The purple curve is for the case of an optimized solution after replacing the 1 nF Y-capacitors with 4.7 nF, the green one is the noise envelope of CBC, and the red one is for the former balanced circuit boost (250 wH and 1 nF). The comparison shows that after utilizing the scheme with 4.7 nF capacitors, a low-frequency spike was also moved out from the frequency band of interest and the CM noise was significantly attenuated. Meanwhile, at a high frequency, the noise after adopting 4.7 nF capacitors is lower than the former case using 1 nF capacitors. out from the frequency band of interest and the CM noise was significantly attenuated. Meanwhile,
Figure 16. Impedance comparison between Zgz (250 wH and 4.7 nF) and Zcg. Similarly to Zg;, Zp2 represents the whole bridge impedance of 250 uH inductors and 4.7 nl capacitors. The comparison between Zp (purple) and Zc, (red) is shown in Figure 16. The resonan equency of optimized impedance Zg2 was removed to around 0.16 MHz and the performance a igh frequency is almost the same compared to that in Figure 12. At 0.68 MHz, where Zp equal: Ce about 30 dB reduction was achieved according to Figure 15. Compared with the former balancex dost circuit (250 uH and 1 nF), the noise source was significantly attenuated and the performance wa: nproved over the entire frequency range.
Figure 16. Impedance comparison between Zgz (250 wH and 4.7 nF) and Zcg. Similarly to Zg;, Zp2 represents the whole bridge impedance of 250 uH inductors and 4.7 nl capacitors. The comparison between Zp (purple) and Zc, (red) is shown in Figure 16. The resonan equency of optimized impedance Zg2 was removed to around 0.16 MHz and the performance a igh frequency is almost the same compared to that in Figure 12. At 0.68 MHz, where Zp equal: Ce about 30 dB reduction was achieved according to Figure 15. Compared with the former balancex dost circuit (250 uH and 1 nF), the noise source was significantly attenuated and the performance wa: nproved over the entire frequency range.
Figure 17. Experimental CM current waveforms comparison between CBC and optimized impedance balancing boost converter (250 uH and 4.7 nF). There may be some concerns that the greater capacitor may increase the CM current and exceed relative standards. Figure 17 shows the CM currents comparison between CBC and the optimized balanced boost circuit (250 1H and 4.7 nF). The results show that with optimized schemes, the CM current becomes even smaller because the noise source has been effectively attenuated.
Figure 17. Experimental CM current waveforms comparison between CBC and optimized impedance balancing boost converter (250 uH and 4.7 nF). There may be some concerns that the greater capacitor may increase the CM current and exceed relative standards. Figure 17 shows the CM currents comparison between CBC and the optimized balanced boost circuit (250 1H and 4.7 nF). The results show that with optimized schemes, the CM current becomes even smaller because the noise source has been effectively attenuated.
Table 3. Comparison of noise optimization effects. 5. Conclusions A comparative investigation between the proposed work and the previously published relevant arts was carried out and is addressed in Table 3. The comparison reveals the effectiveness and practicability of the proposed schemes.
Table 3. Comparison of noise optimization effects. 5. Conclusions A comparative investigation between the proposed work and the previously published relevant arts was carried out and is addressed in Table 3. The comparison reveals the effectiveness and practicability of the proposed schemes.
Figure 1. Architecture of a battery management system (BMS) for EV/HEV applications. other more conventional electrochemical accumulators, Li-ion and LiPo cells can be permanently damaged and can also originate life-threatening hazards such as fires and explosions in the event of overdischarging, overcharging and/or overtemperature operation [21-23]. An electronic battery management system (BMS), which quickly detects the onset of dangerous conditions and takes the appropriate countermeasures to avoid hazards, is therefore necessary to safely operate Li-ion and LiPo cells in vehicles [21-23]. A BMS, which is schematically depicted in Figure 1, typically includes several front-end modules that acquire critical cell information, such as terminal voltages and temperatures, and a digital control unit that runs specific control and management algorithms.
Figure 1. Architecture of a battery management system (BMS) for EV/HEV applications. other more conventional electrochemical accumulators, Li-ion and LiPo cells can be permanently damaged and can also originate life-threatening hazards such as fires and explosions in the event of overdischarging, overcharging and/or overtemperature operation [21-23]. An electronic battery management system (BMS), which quickly detects the onset of dangerous conditions and takes the appropriate countermeasures to avoid hazards, is therefore necessary to safely operate Li-ion and LiPo cells in vehicles [21-23]. A BMS, which is schematically depicted in Figure 1, typically includes several front-end modules that acquire critical cell information, such as terminal voltages and temperatures, and a digital control unit that runs specific control and management algorithms.
Figure 2. Simplified schematic diagram of the BMS integrated circuit (IC) direct power injection (DPI) test board. The simplified block diagram of the BMS front-end IC, which is considered in what follows as the device under test (DUT), is reported in the pink box of Figure 2. Such an IC is designed to monitor the terminal voltages of up to twelve series-connected electrochemical cells using a 12-bit analog-to-digital converter (ADC). To that end, the IC includes 12 cell input pins, internally connected to the ADC’s differential input by a 12-channel, isolated, high-voltage analog multiplexer to measure the (differential) voltages across each of twelve series-connected cells, whose common-mode voltage can be up to 50 V with respect to the IC reference.
Figure 2. Simplified schematic diagram of the BMS integrated circuit (IC) direct power injection (DPI) test board. The simplified block diagram of the BMS front-end IC, which is considered in what follows as the device under test (DUT), is reported in the pink box of Figure 2. Such an IC is designed to monitor the terminal voltages of up to twelve series-connected electrochemical cells using a 12-bit analog-to-digital converter (ADC). To that end, the IC includes 12 cell input pins, internally connected to the ADC’s differential input by a 12-channel, isolated, high-voltage analog multiplexer to measure the (differential) voltages across each of twelve series-connected cells, whose common-mode voltage can be up to 50 V with respect to the IC reference.
Figure 3. Direct power injection. Experimental test setup.
Figure 3. Direct power injection. Experimental test setup.
Figure 4. Measured immunity level (expressed in terms of RF incident power) for DPI on the cell input pins: differential (DM) and common-mode (CM) injection, with and without RC 100 O, 100 nF RC filters in Figure 2.
Figure 4. Measured immunity level (expressed in terms of RF incident power) for DPI on the cell input pins: differential (DM) and common-mode (CM) injection, with and without RC 100 O, 100 nF RC filters in Figure 2.
Figure 5. Total RF voltage induced at the DPI injection port corresponding to the DPI immunity levels in Figure 4.
Figure 5. Total RF voltage induced at the DPI injection port corresponding to the DPI immunity levels in Figure 4.
Figure 6. EMI-induced offset in the cell voltage readings obtained in accordance with DPI failure levels of Figure 4 (DM injection performed on the 6th cell positive terminal, without RC filters).
Figure 6. EMI-induced offset in the cell voltage readings obtained in accordance with DPI failure levels of Figure 4 (DM injection performed on the 6th cell positive terminal, without RC filters).
Figure 7. EMI-induced offset in the cell voltage readings obtained in accordance with DPI failures level of Figure 4 (DM injection performed on the 6th cell positive terminal, with RC filters).
Figure 7. EMI-induced offset in the cell voltage readings obtained in accordance with DPI failures level of Figure 4 (DM injection performed on the 6th cell positive terminal, with RC filters).
a Finally, the DC current delivered by the battery pack and measured by the DC amper meter (see Figure 3) in accordance with the DPI failure levels shown in Figure 4, is plotted in Figure 8 for DM DPI performed without (a) and with (b) the RC input filters in Figure 2. Notice that such a current does not include the DC current sunk by the IC for its operation, and no external load is connected to the cells. Figure 8 shows how such a DC current delivered by the battery pack in accordance with the DPI failure levels, (whose measured value without EMI is about 170 A), can be significative of being affected by the injected disturbances if the RC filters are not included, reaching 6 mA for a 40 MHz EMI injection frequency. It is interesting to observe that the measured DC current is negative (current delivered to the battery pack) for most EMI injection frequencies. Figure 8. DC current absorbed from the battery pack by the BMS IC cell inputs in accordance with DPI failures levels in Figure 4 for DM injection performed on the 6th, without (a) and with (b) the RC filters.
a Finally, the DC current delivered by the battery pack and measured by the DC amper meter (see Figure 3) in accordance with the DPI failure levels shown in Figure 4, is plotted in Figure 8 for DM DPI performed without (a) and with (b) the RC input filters in Figure 2. Notice that such a current does not include the DC current sunk by the IC for its operation, and no external load is connected to the cells. Figure 8 shows how such a DC current delivered by the battery pack in accordance with the DPI failure levels, (whose measured value without EMI is about 170 A), can be significative of being affected by the injected disturbances if the RC filters are not included, reaching 6 mA for a 40 MHz EMI injection frequency. It is interesting to observe that the measured DC current is negative (current delivered to the battery pack) for most EMI injection frequencies. Figure 8. DC current absorbed from the battery pack by the BMS IC cell inputs in accordance with DPI failures levels in Figure 4 for DM injection performed on the 6th, without (a) and with (b) the RC filters.
Figure 9. Measured immunity level for DPI on the SPI input pins: simultaneous injection on the four SPI lines and injection on the single SCLK line.
Figure 9. Measured immunity level for DPI on the SPI input pins: simultaneous injection on the four SPI lines and injection on the single SCLK line.
Figure 10. Total RF voltage induced at the SPI input pins: simultaneous injection on the four SPI lines and injection on the single SCLK line.
Figure 10. Total RF voltage induced at the SPI input pins: simultaneous injection on the four SPI lines and injection on the single SCLK line.
Figure 11. EMI-induced offset in the cell voltage readings obtained in accordance with failure levels of Bjiore 9 ahove 50 MH7 (cimiuiltaneoie iniection on the four SPT nine). EE eee ee An analysis of the mechanisms giving rise to EMI-induced failures when DPI is performed on >I lines has been carried out on the basis of the data retrieved during the DPI tests, in analogy to hat was discussed in Section 4.1.2. Based on these data, failures below 100 MHz are related, as one yuld expect, to errors in the SPI transmission detected by checking the PEC code. At higher frequency »wever, EMI failures for SPI injection are related to an offset in the acquired cell voltages, equal for | the six cells, as shown in Figure 11. Such a behavior, which is similar to what was highlighted for PI on the cell inputs in the high frequency range (Figure 6), can be related to EMI propagation inside e DUT to the internal ADC and/or to its reference voltage source. —e——————————— saad 5. Discussion: DPI Tests
Figure 11. EMI-induced offset in the cell voltage readings obtained in accordance with failure levels of Bjiore 9 ahove 50 MH7 (cimiuiltaneoie iniection on the four SPT nine). EE eee ee An analysis of the mechanisms giving rise to EMI-induced failures when DPI is performed on >I lines has been carried out on the basis of the data retrieved during the DPI tests, in analogy to hat was discussed in Section 4.1.2. Based on these data, failures below 100 MHz are related, as one yuld expect, to errors in the SPI transmission detected by checking the PEC code. At higher frequency »wever, EMI failures for SPI injection are related to an offset in the acquired cell voltages, equal for | the six cells, as shown in Figure 11. Such a behavior, which is similar to what was highlighted for PI on the cell inputs in the high frequency range (Figure 6), can be related to EMI propagation inside e DUT to the internal ADC and/or to its reference voltage source. —e——————————— saad 5. Discussion: DPI Tests
Figure 12. Radiated susceptibility test setup. Antenna in front of the equipment under test (EUT).
Figure 12. Radiated susceptibility test setup. Antenna in front of the equipment under test (EUT).
Figure 13. EMI-induced offset in the cell voltage readings. Antenna in front of the EUT (Figure 12). Vertical polarization.
Figure 13. EMI-induced offset in the cell voltage readings. Antenna in front of the EUT (Figure 12). Vertical polarization.
Figure 14. EMI-induced offset in the cell voltage readings. Antenna in front of the EUT (Figure 12). Horizontal polarization.
Figure 14. EMI-induced offset in the cell voltage readings. Antenna in front of the EUT (Figure 12). Horizontal polarization.
Figure 15. EMI-induced offset in the cell voltage readings. Antenna in front of the cable. Vertical polarization. The same measurements have been repeated by moving the antenna in front of the cable, obtaining a similar phenomena. The respective wrong readings and EMI-induced offsets in the cell voltage readings in the anechoic chamber for vertical and horizontal polarizations are reported respectively in Figures 15 and 16.
Figure 15. EMI-induced offset in the cell voltage readings. Antenna in front of the cable. Vertical polarization. The same measurements have been repeated by moving the antenna in front of the cable, obtaining a similar phenomena. The respective wrong readings and EMI-induced offsets in the cell voltage readings in the anechoic chamber for vertical and horizontal polarizations are reported respectively in Figures 15 and 16.
Figure 16. EMI-induced offset in the cell voltage readings. Antenna in front of the cable. Horizontal polarization.
Figure 16. EMI-induced offset in the cell voltage readings. Antenna in front of the cable. Horizontal polarization.
Figure 17. (a) Measured immunity level for DPI on the cell input pins: differential (DM) and common-mode (CM) injection, with 100 ©, 100 nF RC filters in Figure 2, and (b) respective EMI peak amplitudes. (c) Measured immunity level for DPI on the four SPI lines. (d) EMI-induced offset in the acquired cell voltages, E = 200 V/m. Vertical polarization. (e) EMI]-induced offset in the acquired cell voltages, E = 200 V/m, horizontal polarization.
Figure 17. (a) Measured immunity level for DPI on the cell input pins: differential (DM) and common-mode (CM) injection, with 100 ©, 100 nF RC filters in Figure 2, and (b) respective EMI peak amplitudes. (c) Measured immunity level for DPI on the four SPI lines. (d) EMI-induced offset in the acquired cell voltages, E = 200 V/m. Vertical polarization. (e) EMI]-induced offset in the acquired cell voltages, E = 200 V/m, horizontal polarization.
Figure 2. Possible coupling mechanisms for EMI attack.
Figure 2. Possible coupling mechanisms for EMI attack.
Figure 1. EMC issues.
Figure 1. EMC issues.
Figure 3. EMI induced offset in ua741: interferences coupled to the output pin.
Figure 3. EMI induced offset in ua741: interferences coupled to the output pin.
Figure 4. EMI induced offset in OPA705: interferences coupled to the output pin.
Figure 4. EMI induced offset in OPA705: interferences coupled to the output pin.
Figure 5. EMI induced offset in NE5534: interferences coupled to the output pin.
Figure 5. EMI induced offset in NE5534: interferences coupled to the output pin.
Figure 6. EMI induced offset in ICL7611: interferences coupled to the output pin.
Figure 6. EMI induced offset in ICL7611: interferences coupled to the output pin.
Figure 7. EMI induced offset in series voltage references: interferences coupled to the output pin.
Figure 7. EMI induced offset in series voltage references: interferences coupled to the output pin.
Figure 8. EMI induced offset in shunt voltage references: interferences coupled to the output pin.
Figure 8. EMI induced offset in shunt voltage references: interferences coupled to the output pin.
Table 1. DC and AC parameters and Transistor Sizing of the Common Source Stage. Table 2. DC and AC parameters and Transistor Sizing of the Common Drain Stage.
Table 1. DC and AC parameters and Transistor Sizing of the Common Source Stage. Table 2. DC and AC parameters and Transistor Sizing of the Common Drain Stage.
Table 3. DC and AC parameters and Transistor Sizing of the Cascode Stage.
Table 3. DC and AC parameters and Transistor Sizing of the Cascode Stage.
Figure 9. Schematics of the common source stage, with passive (A) and active (B) load respectively
Figure 9. Schematics of the common source stage, with passive (A) and active (B) load respectively
Figure 10. Schematics of the common drain stage, with passive (A) and active (B) load respectively.
Figure 10. Schematics of the common drain stage, with passive (A) and active (B) load respectively.
Figure 11. Schematics of the cascode stage, with passive (A) and active (B) load respectively.
Figure 11. Schematics of the cascode stage, with passive (A) and active (B) load respectively.
Figure 12. EMI induced offset in the common source stage.
Figure 12. EMI induced offset in the common source stage.
Figure 13. Schematics of the common gate stage, with passive (A) and active (B) load respectively.
Figure 13. Schematics of the common gate stage, with passive (A) and active (B) load respectively.
Figure 14. EMI induced offset in the common drain stage.
Figure 14. EMI induced offset in the common drain stage.
Figure 15. EMI induced offset in the cascode stage.
Figure 15. EMI induced offset in the cascode stage.
Table 4. DC and AC parameters and Transistor Sizing of the Two Stages Amplifier. The offset induced by the interfering signals capacitively coupled to the output pin is shown in Figure 17: the blue line represents the Miller amplifier with active load (A circuit in Figure 16) and the red one represents the amplifier with the passive load (B circuit in Figure 16). The output stage of the amplifier in the open loop configuration is exactly a common source stage and a similar EMI susceptibility could be expected. Instead, as shown by the simulation results plotted in Figure 17, the EMI induced offset has two main differences. The first one is the susceptibility of the amplifier with passive load: although it is much less than the amplifier with active load, it is rather high, much higher than the susceptibility of the simple common source stage with passive load (which is negligible). The maximum offset is indeed 600 mV and the critical frequencies range from tens of MHz up to Ghz. The second difference is that the susceptibility of the amplifier with active low decreases at very high frequencies. It does not happen in the simple stages (common source, gate, drain and cascode).
Table 4. DC and AC parameters and Transistor Sizing of the Two Stages Amplifier. The offset induced by the interfering signals capacitively coupled to the output pin is shown in Figure 17: the blue line represents the Miller amplifier with active load (A circuit in Figure 16) and the red one represents the amplifier with the passive load (B circuit in Figure 16). The output stage of the amplifier in the open loop configuration is exactly a common source stage and a similar EMI susceptibility could be expected. Instead, as shown by the simulation results plotted in Figure 17, the EMI induced offset has two main differences. The first one is the susceptibility of the amplifier with passive load: although it is much less than the amplifier with active load, it is rather high, much higher than the susceptibility of the simple common source stage with passive load (which is negligible). The maximum offset is indeed 600 mV and the critical frequencies range from tens of MHz up to Ghz. The second difference is that the susceptibility of the amplifier with active low decreases at very high frequencies. It does not happen in the simple stages (common source, gate, drain and cascode).
Figure 16. Schematic ofthe Miller amplifier: (A) with active load, (B) with resistive load.
Figure 16. Schematic ofthe Miller amplifier: (A) with active load, (B) with resistive load.
Figure 17. EMI induced offset in the Miller amplifier, open loop configuration. Finally, another huge difference is the value of the offset, which is much larger than that of the single stage: indeed, the maximum offset is above 1 V in the Miller amplifier, while it is less than 200 mV in the common source stage. One of the possible reason of the different behavior could be the RC network for the frequency compensation. It is indeed in the amplifier schematic, even if it is used in an open loop. The sizing of the RC network is: 3 kO, for the resistor and 1 pF for the capacitor. The RC network is directly connected to the output pin, it is across the first and the second stage and it may cause a typical phenomenon, Ref. [25-27], called EMI charge pumping, which leads to a severe DC shift of the biasing point. To investigate this, a schematic without the RC network (see Figure 18) has been simulated and the simulation results are plotted in Figure 19.
Figure 17. EMI induced offset in the Miller amplifier, open loop configuration. Finally, another huge difference is the value of the offset, which is much larger than that of the single stage: indeed, the maximum offset is above 1 V in the Miller amplifier, while it is less than 200 mV in the common source stage. One of the possible reason of the different behavior could be the RC network for the frequency compensation. It is indeed in the amplifier schematic, even if it is used in an open loop. The sizing of the RC network is: 3 kO, for the resistor and 1 pF for the capacitor. The RC network is directly connected to the output pin, it is across the first and the second stage and it may cause a typical phenomenon, Ref. [25-27], called EMI charge pumping, which leads to a severe DC shift of the biasing point. To investigate this, a schematic without the RC network (see Figure 18) has been simulated and the simulation results are plotted in Figure 19.
Figure 18. Schematic ofthe Miller amplifier without the RC network for the frequency compensation: (A) with active load, (B) with resistive load.
Figure 18. Schematic ofthe Miller amplifier without the RC network for the frequency compensation: (A) with active load, (B) with resistive load.
Figure 19. EMI induced offset in the Miller amplifier without RC network, open loop configuration.
Figure 19. EMI induced offset in the Miller amplifier without RC network, open loop configuration.
Figure 20. EMI induced offset in the Miller amplifier with RC network, closed loop configuration.
Figure 20. EMI induced offset in the Miller amplifier with RC network, closed loop configuration.
Figure 1. Schematic view of the current sensing setup for: (a) resistive approach, and (b) the Hall sensor. esigned. Whenever the Power MOS is switched-on by a driver, the current to be detected flows nrough the power trace on the PCB. When the setup aims to test a resistive current sensing unde ne effect of EMI, the Hall sensor output is floating and the voltage across the sense resistor Reense in eries with the Power MOS is properly amplified and processed by a detection block (as sketched in igure la). On the contrary, to evaluate the EMI robustness of the Hall sensor, the resistor Rsense is horted and the output voltage of the Hall sensor is elaborated by a properly-modified detection block is sketched in Figure 1b).
Figure 1. Schematic view of the current sensing setup for: (a) resistive approach, and (b) the Hall sensor. esigned. Whenever the Power MOS is switched-on by a driver, the current to be detected flows nrough the power trace on the PCB. When the setup aims to test a resistive current sensing unde ne effect of EMI, the Hall sensor output is floating and the voltage across the sense resistor Reense in eries with the Power MOS is properly amplified and processed by a detection block (as sketched in igure la). On the contrary, to evaluate the EMI robustness of the Hall sensor, the resistor Rsense is horted and the output voltage of the Hall sensor is elaborated by a properly-modified detection block is sketched in Figure 1b).
Figure 2. Layout representation of the testing board. A schematic layout representation of the the test PCB that can address both the current sensing methods is reported in Figure 2. A power MOS transistor, which is remotely driven by an optical fiber link, is employed to switch on and off the power circuit. The power supplies to the MOS and to the analog front-end are obtained from a line of the wiring harness and reach the PCB trough an automotive connector.
Figure 2. Layout representation of the testing board. A schematic layout representation of the the test PCB that can address both the current sensing methods is reported in Figure 2. A power MOS transistor, which is remotely driven by an optical fiber link, is employed to switch on and off the power circuit. The power supplies to the MOS and to the analog front-end are obtained from a line of the wiring harness and reach the PCB trough an automotive connector.
Figure 3. Processing chain of the Hall sensor output voltage.
Figure 3. Processing chain of the Hall sensor output voltage.
Figure 4. Hysteresis window of the output comparator for: (a) resistive current sensing; and (b) the Hall-effect sensor.
Figure 4. Hysteresis window of the output comparator for: (a) resistive current sensing; and (b) the Hall-effect sensor.
Figure 5. Overall schematic view of the current detection setup. To assess the susceptibility of the testing board introduced in Section 2, BCI tests were performed on the overall current detection system in Figure 5 by the setup in Figure 6 [11].
Figure 5. Overall schematic view of the current detection setup. To assess the susceptibility of the testing board introduced in Section 2, BCI tests were performed on the overall current detection system in Figure 5 by the setup in Figure 6 [11].
Figure 6. Pictorial representation of BCI test setup [11].
Figure 6. Pictorial representation of BCI test setup [11].
Figure 7. BCI immunity measurement for different current values. To highlight the susceptibility of the Hall-effect sensors, BCI immunity tests were performed the on different configurations of the EUT introduced in Section 2.
Figure 7. BCI immunity measurement for different current values. To highlight the susceptibility of the Hall-effect sensors, BCI immunity tests were performed the on different configurations of the EUT introduced in Section 2.
Figure 8. BCI immunity measurement for different caps presence in layout in Figure 2: Meas0 = no caps; Meas] = C,, C_; and Meas2 = C,, C_, CH yout, Cu_vpp-
Figure 8. BCI immunity measurement for different caps presence in layout in Figure 2: Meas0 = no caps; Meas] = C,, C_; and Meas2 = C,, C_, CH yout, Cu_vpp-
Figure 10. (a) Hall sensor inclination considered in BCI tests; and (b) respective BCI immunity measurements. Other EMI investigations were performed for different Hall sensor inclination with respect to th PCB surface, as represented in Figure 10a. In all cases, the distance beetween the wire and the Hal sensor has not been changed. The experimental results obtained with such configurations are reportec in Figure 10b and show a significant dependence of the susceptibility level on the inclination of ths sensor.
Figure 10. (a) Hall sensor inclination considered in BCI tests; and (b) respective BCI immunity measurements. Other EMI investigations were performed for different Hall sensor inclination with respect to th PCB surface, as represented in Figure 10a. In all cases, the distance beetween the wire and the Hal sensor has not been changed. The experimental results obtained with such configurations are reportec in Figure 10b and show a significant dependence of the susceptibility level on the inclination of ths sensor.
Figure 11. TEM cell testing setup. The radiated EMI susceptibility tests highlight that electromagnetic field distribution inside the TEM cell induces a negative offset in the Hall sensor output voltage. In Figure 13, the magnitude of the induced offset voltage in the range from 500 kHz to 1 GHz for an RF incident power applied to the TEM cell equal to 34 dBm. This implies a vertical electric field magnitude of 250 V/m and a transversal magnetic field magnitude of 0.66 A/m where the Hall sensor under test is placed [17-19].
Figure 11. TEM cell testing setup. The radiated EMI susceptibility tests highlight that electromagnetic field distribution inside the TEM cell induces a negative offset in the Hall sensor output voltage. In Figure 13, the magnitude of the induced offset voltage in the range from 500 kHz to 1 GHz for an RF incident power applied to the TEM cell equal to 34 dBm. This implies a vertical electric field magnitude of 250 V/m and a transversal magnetic field magnitude of 0.66 A/m where the Hall sensor under test is placed [17-19].
Figure 12. Magnetic and electric field orientation for different Hall sensor setup.
Figure 12. Magnetic and electric field orientation for different Hall sensor setup.
Figure 13. TEM cell immunity measurements at 34 dBm RF power amplitude for different setup.
Figure 13. TEM cell immunity measurements at 34 dBm RF power amplitude for different setup.
Figure 14. DPI on Hall sensor VDD Test setup [13]. As a further EMI investigation, direct power injection tests [13] on the employed Hall sensor were performed. RF power was injected on the supply voltage of the Hall sensor by means of an RF generator, an RF amplifier and a bias tee, as represented in Figure 14. The employed bias tee has a lower bandwidth limit equal to 30 MHz. Therefore, in the following figure, the measurement results are not reliable for a frequency lower that 30 MHz. At the end of the power amplifier a —3 dB attenuator was placed for the safety of the RF amplifier. In fact, if the RF amplifier were accidentally not totally connected (open circuit condition) during the measurement operation, a reflection coefficient |[| = 1 could damage the RF amplifier.
Figure 14. DPI on Hall sensor VDD Test setup [13]. As a further EMI investigation, direct power injection tests [13] on the employed Hall sensor were performed. RF power was injected on the supply voltage of the Hall sensor by means of an RF generator, an RF amplifier and a bias tee, as represented in Figure 14. The employed bias tee has a lower bandwidth limit equal to 30 MHz. Therefore, in the following figure, the measurement results are not reliable for a frequency lower that 30 MHz. At the end of the power amplifier a —3 dB attenuator was placed for the safety of the RF amplifier. In fact, if the RF amplifier were accidentally not totally connected (open circuit condition) during the measurement operation, a reflection coefficient |[| = 1 could damage the RF amplifier.
Figure 15. DPI on VDD immunity measurements (|AVour| vs. frequency) for different RF power amplitudes.
Figure 15. DPI on VDD immunity measurements (|AVour| vs. frequency) for different RF power amplitudes.
Figure 16. DPI on VDD immunity measurements (|AVour| vs. RF power amplitude) for different frequencies.
Figure 16. DPI on VDD immunity measurements (|AVour| vs. RF power amplitude) for different frequencies.
Figure 1. Printed circuit boards with two kinds of split gap adopted. The dotted line is on the bottom side. (a) Two signal lines cross over a straight split gap on the ground plane. (b) A meander DGS split gap. (c) Detailed structure.
Figure 1. Printed circuit boards with two kinds of split gap adopted. The dotted line is on the bottom side. (a) Two signal lines cross over a straight split gap on the ground plane. (b) A meander DGS split gap. (c) Detailed structure.
Figure 2. Measured reflection, transmission and crosstalk of the signal line with a complete homogeneous ground, straight and meander split power or ground plane. (a) S11. (b) S21. (¢) S31 (near-end crosstalk). (d) S4; (far-end crosstalk). We measured the scattering parameters of the two samples with a complete homogeneous ground plane in Figure 2. As shown in the figure, the reflections occur due to the split gaps, and the scattering parameters show resonant behavior. Compared with the complete homogeneous ground plane, the two split ground planes degrade the signal integrity and increase crosstalk. However, the meander split improves the signal integrity and decreases 30 dB of crosstalk up to 9 GHz more than the straight split ground plane, like a rectangular DGS [30,31]. This difference comes from the enhanced coupling due to the meander structure on the split plane.
Figure 2. Measured reflection, transmission and crosstalk of the signal line with a complete homogeneous ground, straight and meander split power or ground plane. (a) S11. (b) S21. (¢) S31 (near-end crosstalk). (d) S4; (far-end crosstalk). We measured the scattering parameters of the two samples with a complete homogeneous ground plane in Figure 2. As shown in the figure, the reflections occur due to the split gaps, and the scattering parameters show resonant behavior. Compared with the complete homogeneous ground plane, the two split ground planes degrade the signal integrity and increase crosstalk. However, the meander split improves the signal integrity and decreases 30 dB of crosstalk up to 9 GHz more than the straight split ground plane, like a rectangular DGS [30,31]. This difference comes from the enhanced coupling due to the meander structure on the split plane.
Table 1. Characteristic impedances and relative dielectric constants of the meander slot line.
Table 1. Characteristic impedances and relative dielectric constants of the meander slot line.
Figure 3. Equivalent circuit of the meander gap.
Figure 3. Equivalent circuit of the meander gap.
Figure 4. Transmission line equivalent circuit of the meander gap.
Figure 4. Transmission line equivalent circuit of the meander gap.
Figure 5. S3; (near-end crosstalk) and S4; (far-end crosstalk) of the meander split plane with length 13 and w, changed. (a) S31; (b) S41.
Figure 5. S3; (near-end crosstalk) and S4; (far-end crosstalk) of the meander split plane with length 13 and w, changed. (a) S31; (b) S41.
Figure 6. Crosstalk equivalent circuit of the meander split on the ground plane.
Figure 6. Crosstalk equivalent circuit of the meander split on the ground plane.
Figure 7 shows the effectiveness of the equivalent circuit of Figures 4 and 5. The crosstalk behaviors of the circuit model simulated using Agilent ADS and measurement show good overall agreement about the peak and zero. At low frequencies below about 3 GHz, the LC equivalent circuit model of Figure 4 was closer to the measured result than the transmission line equivalent model of Figure 5. At high frequencies, the transmission line model was close to the measured result. The mutual inductance effect is proportional to the vertical length of the meander split and their relationship is calculated by the linear interpolation from the simulation and measured result. The crosstalk simulation result of the circuit model is slightly overestimated compared to the measured result because of the interpolation residual error of the mutual inductance value.
Figure 7 shows the effectiveness of the equivalent circuit of Figures 4 and 5. The crosstalk behaviors of the circuit model simulated using Agilent ADS and measurement show good overall agreement about the peak and zero. At low frequencies below about 3 GHz, the LC equivalent circuit model of Figure 4 was closer to the measured result than the transmission line equivalent model of Figure 5. At high frequencies, the transmission line model was close to the measured result. The mutual inductance effect is proportional to the vertical length of the meander split and their relationship is calculated by the linear interpolation from the simulation and measured result. The crosstalk simulation result of the circuit model is slightly overestimated compared to the measured result because of the interpolation residual error of the mutual inductance value.
Figure 8. Lateral wave attenuation of the unit cell of the meander slot line obtained by Figure 4. (a) Split gap width w2 changed (when |; = 0.25 mm, /y = 0.4 mm, /3 = 30 mm, w; = 2.1 mm, w2 = w3); (b) length Iz changed (when 1; = 0.25 mm, J) = 0.4 mm, w, = 2.1 mm, w7 = w3 = 0.2 mm); (c) length J) changed (when |; = 0.25 mm, /3 = 2 mm, w, = 2.1 mm, w = w3 = 0.2 mm); (d) number of cells changed (when |; = 0.25 mm, Ip = 0.4mm, /3 = 30 mm, wy =2.1 mm, w2 = w3 = 0.2 mm.
Figure 8. Lateral wave attenuation of the unit cell of the meander slot line obtained by Figure 4. (a) Split gap width w2 changed (when |; = 0.25 mm, /y = 0.4 mm, /3 = 30 mm, w; = 2.1 mm, w2 = w3); (b) length Iz changed (when 1; = 0.25 mm, J) = 0.4 mm, w, = 2.1 mm, w7 = w3 = 0.2 mm); (c) length J) changed (when |; = 0.25 mm, /3 = 2 mm, w, = 2.1 mm, w = w3 = 0.2 mm); (d) number of cells changed (when |; = 0.25 mm, Ip = 0.4mm, /3 = 30 mm, wy =2.1 mm, w2 = w3 = 0.2 mm.
Figure 9. Current distributions on the straight and meander split power or ground plane at 2 GHz. (a Straight split plane; (b) meander split plane.
Figure 9. Current distributions on the straight and meander split power or ground plane at 2 GHz. (a Straight split plane; (b) meander split plane.
Figure 10. Time simulation of the crosstalk signal of the straight and meander split ground plane.
Figure 10. Time simulation of the crosstalk signal of the straight and meander split ground plane.
Figure 11. Time domain simulation result of Figure 10.
Figure 11. Time domain simulation result of Figure 10.
Figure 12. Comparison of the transmission and crosstalk signal with the straight and meander split power or ground plane. (a) Transmission signal measured at port #2; (b) near-end crosstalk signal measured at port #3; (c) far-end crosstalk signal measured at port #4.
Figure 12. Comparison of the transmission and crosstalk signal with the straight and meander split power or ground plane. (a) Transmission signal measured at port #2; (b) near-end crosstalk signal measured at port #3; (c) far-end crosstalk signal measured at port #4.
Figure 1. A unit cell of a dual-perforation electromagnetic bandgap dual-perforation—electromagnetic bandgap (DP-EBG) structure consisting of perforated dual planes and its design parameters. The proposed dual-perforation EBG (DP-EBG) structure is developed to suppress parallel-plate noise in multilayer PCBs, including thin dielectrics. The DP-EBG structure is a periodic structure in which a unit cell comprises a perforated power plane, a perforated patch, and a ground plane embedded in a thin dielectric, as shown in Figure 1. The power plane is perforated by four square apertures, while the resonant patch is perforated by an L-shape slot. These perforations are simple to implement with conventional PCB manufacturing techniques without requiring additional, costly processes. The perforated power plane and patch are connected through a short-length via owing to the thin dielectric. The apertures in the power plane electrically enhance the characteristic impedance of the EBG unit cell, while the L-shape slot in the resonant patch effectively increases the inductance of the EBG unit cell. The unit cell size and square aperture of the DP-EBG structure are represented as d,—by-d, and d,—by-d, structures, respectively. Therefore, the width of the remaining conductor is the same and equal to d.-2d,. Regarding the L-shape slot, the conductor width etched on the patch is denoted by wg and the width of the remaining conductor is denoted by wy. The sum of dp/2 and dg is the total length of the L-shape slot. The design parameter dg is adjustable to obtain a desired patch inductance. The dielectric thickness between the dual perforated planes is hy. The distance between the perforated patch and the ground plane is hp.
Figure 1. A unit cell of a dual-perforation electromagnetic bandgap dual-perforation—electromagnetic bandgap (DP-EBG) structure consisting of perforated dual planes and its design parameters. The proposed dual-perforation EBG (DP-EBG) structure is developed to suppress parallel-plate noise in multilayer PCBs, including thin dielectrics. The DP-EBG structure is a periodic structure in which a unit cell comprises a perforated power plane, a perforated patch, and a ground plane embedded in a thin dielectric, as shown in Figure 1. The power plane is perforated by four square apertures, while the resonant patch is perforated by an L-shape slot. These perforations are simple to implement with conventional PCB manufacturing techniques without requiring additional, costly processes. The perforated power plane and patch are connected through a short-length via owing to the thin dielectric. The apertures in the power plane electrically enhance the characteristic impedance of the EBG unit cell, while the L-shape slot in the resonant patch effectively increases the inductance of the EBG unit cell. The unit cell size and square aperture of the DP-EBG structure are represented as d,—by-d, and d,—by-d, structures, respectively. Therefore, the width of the remaining conductor is the same and equal to d.-2d,. Regarding the L-shape slot, the conductor width etched on the patch is denoted by wg and the width of the remaining conductor is denoted by wy. The sum of dp/2 and dg is the total length of the L-shape slot. The design parameter dg is adjustable to obtain a desired patch inductance. The dielectric thickness between the dual perforated planes is hy. The distance between the perforated patch and the ground plane is hp.
Figure 2. Equivalent circuit model of the DP—EBG unit cell based on transmission line theory for the extraction of the dispersion equation. f parallel-plate noise. The transmission line is the circuital representation of electromagnetic waves ropagating through the parallel plate waveguide, which is formed by the perforated power and he ground planes. In the DP-EBG circuit model, Zq and £,- respectively denote the characteristic mpedance and propagation constant of this parallel plate waveguide or transmission line. Its length s d-/2. In the transmission line model, Zeq is significantly enhanced by the square perforation aperture yecause the width of the remaining conductor perpendicular to the direction of wave propagation s narrowed. In the resonator circuit, the capacitance Cy is attributed to the capacitor between the esonant patch and the corresponding ground plane, while the inductance is attributed to the patch nd the via inductances. For the DP-EBG structure in the thin PCBs, the inductance of the via can be snored compared to the patch inductance which substantially increases due to the L-shape slot. Thus, he value of Leg in the DP-EBG circuit model is mainly determined by the L-shape slot on the perforated esonant patch. Hence, the equivalent circuit of the proposed DP-EBG structure is expressed with a ‘o-enhanced transmission line and an L-enhanced resonator.
Figure 2. Equivalent circuit model of the DP—EBG unit cell based on transmission line theory for the extraction of the dispersion equation. f parallel-plate noise. The transmission line is the circuital representation of electromagnetic waves ropagating through the parallel plate waveguide, which is formed by the perforated power and he ground planes. In the DP-EBG circuit model, Zq and £,- respectively denote the characteristic mpedance and propagation constant of this parallel plate waveguide or transmission line. Its length s d-/2. In the transmission line model, Zeq is significantly enhanced by the square perforation aperture yecause the width of the remaining conductor perpendicular to the direction of wave propagation s narrowed. In the resonator circuit, the capacitance Cy is attributed to the capacitor between the esonant patch and the corresponding ground plane, while the inductance is attributed to the patch nd the via inductances. For the DP-EBG structure in the thin PCBs, the inductance of the via can be snored compared to the patch inductance which substantially increases due to the L-shape slot. Thus, he value of Leg in the DP-EBG circuit model is mainly determined by the L-shape slot on the perforated esonant patch. Hence, the equivalent circuit of the proposed DP-EBG structure is expressed with a ‘o-enhanced transmission line and an L-enhanced resonator.
From the equations listed above, an effective phase constant Buc of the DP-EBG unit cell is Using the ABCD parameters of the microwave theory, the voltage/current relationships between ports 1 and 2 of the DP-EBG unit cell are described by [22]
From the equations listed above, an effective phase constant Buc of the DP-EBG unit cell is Using the ABCD parameters of the microwave theory, the voltage/current relationships between ports 1 and 2 of the DP-EBG unit cell are described by [22]
Table 1. Dimensions of geometrical parameters of the DP-EBG structure.
Table 1. Dimensions of geometrical parameters of the DP-EBG structure.
Figure 4. Variations of (a) f, and (b) fy for various Zeq and Leq values obtained using the closed-form expressions. the minimum f,, value is 0.85 GHz when Zeqg and Leg are 95 O. and 3.0 nH, respectively. The maximum value of f, is 1.63 GHz and results from Zeq = 5 O.and Leg = 1.0 nH. As shown in Figure 4b, the minimum value of f} is 1.10 GHz and is observed when Zeq = 5 O.and Leg = 3.0 nH, while the DP-EBG structure has a maximum value of fy is 8.34 GHz when Zeq = 95 O. and Leq = 1.0 nH. The conditions for the minimum and maximum f,, and fy values are different.
Figure 4. Variations of (a) f, and (b) fy for various Zeq and Leq values obtained using the closed-form expressions. the minimum f,, value is 0.85 GHz when Zeqg and Leg are 95 O. and 3.0 nH, respectively. The maximum value of f, is 1.63 GHz and results from Zeq = 5 O.and Leg = 1.0 nH. As shown in Figure 4b, the minimum value of f} is 1.10 GHz and is observed when Zeq = 5 O.and Leg = 3.0 nH, while the DP-EBG structure has a maximum value of fy is 8.34 GHz when Zeq = 95 O. and Leq = 1.0 nH. The conditions for the minimum and maximum f,, and fy values are different.
Figure 5. Contour plots of f, and fy used for the design and analyses of DP-EBG structures. To gain insight into the efficient design of the DP-EBG structure, the variations of f, and fy ar resented graphically. Figure 5 depicts the contour lines of both f;, (black dashed lines) and fy (blu olid lines) when Leq changes from 5 O to 95 O. and when Leq changes from 1.0 nH to 3.0 nH. Point . n Figure 5 shows that f, and fy are equal to 1.23 GHz and 4.42 GHz when Zeg and Le, are 40 O an .5 nH, respectively. However, the suppression region of the parallel-plate noise given at point A need 9 be extended in the low-frequency range. To achieve this, Leg can increase. For instance, fi change rom 1.23 GHz to 1.0 GHz as Leq increases from 1.5 nH (point A) to 2.42 nH (point B) by maintainin eq to 40 Q. In this approach, both fi. and fy are lowered, thus reducing the stopband bandwidt! o compensate for this drawback, other approaches can be considered, namely, by moving point . oC. Zeq increases from 40 O to 60 O and Leg increases from 1.5 nH to 2.42 nH, thus resulting in an j alue of 1.0 GHz and an fy value of 4.42 GHz. The f,, reduction is successfully achieved by maintainin 4 to 4.42 GHz. Consequently, the suppression region of the parallel plate noise is broadened as is f;, 1 educed. As it has been observed in the proposed analysis, the contour plots, which were extracte vith the use of the closed-form expressions for f;, and fy, provided a simple and systematic approac 9 design the DP-EBG structure in thin and cost-effective PCBs.
Figure 5. Contour plots of f, and fy used for the design and analyses of DP-EBG structures. To gain insight into the efficient design of the DP-EBG structure, the variations of f, and fy ar resented graphically. Figure 5 depicts the contour lines of both f;, (black dashed lines) and fy (blu olid lines) when Leq changes from 5 O to 95 O. and when Leq changes from 1.0 nH to 3.0 nH. Point . n Figure 5 shows that f, and fy are equal to 1.23 GHz and 4.42 GHz when Zeg and Le, are 40 O an .5 nH, respectively. However, the suppression region of the parallel-plate noise given at point A need 9 be extended in the low-frequency range. To achieve this, Leg can increase. For instance, fi change rom 1.23 GHz to 1.0 GHz as Leq increases from 1.5 nH (point A) to 2.42 nH (point B) by maintainin eq to 40 Q. In this approach, both fi. and fy are lowered, thus reducing the stopband bandwidt! o compensate for this drawback, other approaches can be considered, namely, by moving point . oC. Zeq increases from 40 O to 60 O and Leg increases from 1.5 nH to 2.42 nH, thus resulting in an j alue of 1.0 GHz and an fy value of 4.42 GHz. The f,, reduction is successfully achieved by maintainin 4 to 4.42 GHz. Consequently, the suppression region of the parallel plate noise is broadened as is f;, 1 educed. As it has been observed in the proposed analysis, the contour plots, which were extracte vith the use of the closed-form expressions for f;, and fy, provided a simple and systematic approac 9 design the DP-EBG structure in thin and cost-effective PCBs.
Figure 6. Unit cells of (a) mushroom-type (MT)-, (b) defected ground structure (DGS)-, (c) inductance-enhanced patch (IEP)—, and (d) DP-EBG structures for stopband comparisons.
Figure 6. Unit cells of (a) mushroom-type (MT)-, (b) defected ground structure (DGS)-, (c) inductance-enhanced patch (IEP)—, and (d) DP-EBG structures for stopband comparisons.
Figure 7. Dispersion diagrams of (a) MT-, (b) DGS-, (c) IEP-, and (d) DP-EBG structures.
Figure 7. Dispersion diagrams of (a) MT-, (b) DGS-, (c) IEP-, and (d) DP-EBG structures.
Figure 8. Comparison of unit-cell miniaturization between previous MT- and proposed DP-EBG structures.
Figure 8. Comparison of unit-cell miniaturization between previous MT- and proposed DP-EBG structures.
Figure 9. Finite difference method (FEM)-based simulation model of the DP—EBG structure with a 7 X 7 array. A full-wave simulation model of the DP-EBG structure with a 7 x 7 array is depicted in Figure 9 The array size is determined to implement the quasiperiodic condition of the DP-EBG structure Two-port simulation is performed with waveguide ports renormalized to 50 O. The boundaries are set to perfect magnetic conductors and a perfect matched layer, as shown in Figure 9. To compare the noise suppression performance, the simulated S-parameters of the previous EBG structures with the 7 x 7 array and the parallel plate waveguide (PPW) without any EBG structure are also obtained The dimensions of the geometrical parameters were described in the previous section. The port locations and the boundary conditions are identical for all EBG structures and the PPW.
Figure 9. Finite difference method (FEM)-based simulation model of the DP—EBG structure with a 7 X 7 array. A full-wave simulation model of the DP-EBG structure with a 7 x 7 array is depicted in Figure 9 The array size is determined to implement the quasiperiodic condition of the DP-EBG structure Two-port simulation is performed with waveguide ports renormalized to 50 O. The boundaries are set to perfect magnetic conductors and a perfect matched layer, as shown in Figure 9. To compare the noise suppression performance, the simulated S-parameters of the previous EBG structures with the 7 x 7 array and the parallel plate waveguide (PPW) without any EBG structure are also obtained The dimensions of the geometrical parameters were described in the previous section. The port locations and the boundary conditions are identical for all EBG structures and the PPW.
Figure 10. Comparison of S-parameters between (a) the ppw, IEP-EBG and proposed EBG structures and (b) MT-EBG, DGS-EBG, and proposed EBG structures to demonstrate a broad stopband bandwidth and miniaturization. level of the IEP—EBG structure forms in the frequency range from 1.01 GHz to 1.36 GHz, while that o: the DP-EBG structure ranges from 0.98 GHz to 3.32 GHz. For the same size of the EBG structures the stopband bandwidth of the DP-EBG structure is approximately 6.7 times wider than that of the IEP-EBG structure. Moreover, the stopband of the proposed DP-EBG structure is significantly lowered compared to those of the MT-EBG and DGS-EBG structures, as shown in Figure 10b. The f,, values ot the MT-EBG, DGS-EBG, and DP-EBG structures are 4.6, 3.33, and 0.98 GHz, respectively. The DP-EBC structure substantially reduces the fj, value up to 78.7% without adding costly materials and processes The stopband estimation based on the S-parameter exhibits a good correlation with dispersion analysis results. The f, and ft predicted from the dispersion analysis are 1.0 and 3.75 GHz, respectively.
Figure 10. Comparison of S-parameters between (a) the ppw, IEP-EBG and proposed EBG structures and (b) MT-EBG, DGS-EBG, and proposed EBG structures to demonstrate a broad stopband bandwidth and miniaturization. level of the IEP—EBG structure forms in the frequency range from 1.01 GHz to 1.36 GHz, while that o: the DP-EBG structure ranges from 0.98 GHz to 3.32 GHz. For the same size of the EBG structures the stopband bandwidth of the DP-EBG structure is approximately 6.7 times wider than that of the IEP-EBG structure. Moreover, the stopband of the proposed DP-EBG structure is significantly lowered compared to those of the MT-EBG and DGS-EBG structures, as shown in Figure 10b. The f,, values ot the MT-EBG, DGS-EBG, and DP-EBG structures are 4.6, 3.33, and 0.98 GHz, respectively. The DP-EBC structure substantially reduces the fj, value up to 78.7% without adding costly materials and processes The stopband estimation based on the S-parameter exhibits a good correlation with dispersion analysis results. The f, and ft predicted from the dispersion analysis are 1.0 and 3.75 GHz, respectively.
Figure 11. Measurement setup for DP-EBG structure with a 7 x 7 array.
Figure 11. Measurement setup for DP-EBG structure with a 7 x 7 array.
Figure 12. Measured and simulated Sj; parameters of the DP—EBG structure.
Figure 12. Measured and simulated Sj; parameters of the DP—EBG structure.
* Shielding effectiveness measurement (SE meas.) Table 1. Fabrication and measurements of the cement composites.
* Shielding effectiveness measurement (SE meas.) Table 1. Fabrication and measurements of the cement composites.
Figure 1. Three-dimensional (3D) printed master mold with silicone mold and an example of a composite sample. in a three-dimensional (3D) printed master mold of specific dimensions (see Figure 1). The reusable and flexible silicone molds helped with easy extraction of composite samples once they were cured.
Figure 1. Three-dimensional (3D) printed master mold with silicone mold and an example of a composite sample. in a three-dimensional (3D) printed master mold of specific dimensions (see Figure 1). The reusable and flexible silicone molds helped with easy extraction of composite samples once they were cured.
Figure 2. WR90 waveguide measurement set-up. The scattering parameters of the composites were measured in a WR90 (Sivers IMA, Holding AB (HQ), Sweden) rectangular waveguide from 8 GHz to 12 GHz using a set-up similar to that in Reference [33]. The samples were fabricated in order to fit the rectangular waveguide cross-section (a = 22.86 mm, b = 10.16 mm). The thickness of the samples was 4 mm. The set-up is shown in Figure 2. It consisted of a two-port vector network analyzer (VNA) (Agilent E8361A: Keysight, Santa Rosa, CA 81841, USA), two coaxial cables connected to the two ports of the network analyzer, two coaxial-to-waveguide adapters, and two rectangular waveguides. Between the waveguide flanges, a spacer holding the sample was inserted. Before the measurements, a two-port calibration (short, matched load, thru) was performed. The reference planes were at the ends of the spacer. 2.4. Finite Element Simulations A commercial finite element modeling tool, Ansys HFSS, was used to simulate the waveguide with the composite sample as shown in Figure 3. The material properties of the composite inserted in the waveguide were chosen by fitting the simulated shielding effectiveness values to the measured shielding effectiveness values. The composite dimensions and thickness were varied to analyze the impact of fabrication tolerances and thickness on the values of shielding effectiveness.
Figure 2. WR90 waveguide measurement set-up. The scattering parameters of the composites were measured in a WR90 (Sivers IMA, Holding AB (HQ), Sweden) rectangular waveguide from 8 GHz to 12 GHz using a set-up similar to that in Reference [33]. The samples were fabricated in order to fit the rectangular waveguide cross-section (a = 22.86 mm, b = 10.16 mm). The thickness of the samples was 4 mm. The set-up is shown in Figure 2. It consisted of a two-port vector network analyzer (VNA) (Agilent E8361A: Keysight, Santa Rosa, CA 81841, USA), two coaxial cables connected to the two ports of the network analyzer, two coaxial-to-waveguide adapters, and two rectangular waveguides. Between the waveguide flanges, a spacer holding the sample was inserted. Before the measurements, a two-port calibration (short, matched load, thru) was performed. The reference planes were at the ends of the spacer. 2.4. Finite Element Simulations A commercial finite element modeling tool, Ansys HFSS, was used to simulate the waveguide with the composite sample as shown in Figure 3. The material properties of the composite inserted in the waveguide were chosen by fitting the simulated shielding effectiveness values to the measured shielding effectiveness values. The composite dimensions and thickness were varied to analyze the impact of fabrication tolerances and thickness on the values of shielding effectiveness.
Figure 3. Geometrical configuration of the waveguide: (a) geometry of the simulated waveguide with composite. (b) Cross-section of the waveguide for the dimensional analysis.
Figure 3. Geometrical configuration of the waveguide: (a) geometry of the simulated waveguide with composite. (b) Cross-section of the waveguide for the dimensional analysis.
Figure 4. Analysis of fabrication tolerances of the plain cement composites. In order to take into account the dimensional tolerance of the cement composite, simulations were performed based on varying the two dimensions along the x-axis and y-axis (see Figure 3). In the case of plain cement composites, it was found that there was negligible variation of the transmission properties by varying the a; dimension of the sample, while the impact of the variation of by was significant. A variation of 0.5 mm in by, resulted in a variation of almost 1 dB in the transmission coefficient, as shown in Figure 4. It was ensured that the tolerance in the dimensions of the cement composites was below this value.
Figure 4. Analysis of fabrication tolerances of the plain cement composites. In order to take into account the dimensional tolerance of the cement composite, simulations were performed based on varying the two dimensions along the x-axis and y-axis (see Figure 3). In the case of plain cement composites, it was found that there was negligible variation of the transmission properties by varying the a; dimension of the sample, while the impact of the variation of by was significant. A variation of 0.5 mm in by, resulted in a variation of almost 1 dB in the transmission coefficient, as shown in Figure 4. It was ensured that the tolerance in the dimensions of the cement composites was below this value.
Figure 5. Thermogravimetric analysis (TGA) curve of biochar filler.
Figure 5. Thermogravimetric analysis (TGA) curve of biochar filler.
Figure 6. SEM micrograph of cement containing biochar 18% at 1000x magnification. Figure 6 illustrates the SEM image of composites with the highest content of biochar (18 wt.%) recorded with secondary electrons. The black structures shown in the SEM image are the carbonaceous particles. The expected elongated structure of the particles was due to the fiber origin of the biochar. The particles showed a good dispersion in the matrix.
Figure 6. SEM micrograph of cement containing biochar 18% at 1000x magnification. Figure 6 illustrates the SEM image of composites with the highest content of biochar (18 wt.%) recorded with secondary electrons. The black structures shown in the SEM image are the carbonaceous particles. The expected elongated structure of the particles was due to the fiber origin of the biochar. The particles showed a good dispersion in the matrix.
Figure 7. Measured and simulated shielding effectiveness values for plain cement, as well as the sample with 14 wt.% biochar and the sample with 18 wt.%. Samples were cured for seven days in water. Measurements were performed after 10 weeks of aging.
Figure 7. Measured and simulated shielding effectiveness values for plain cement, as well as the sample with 14 wt.% biochar and the sample with 18 wt.%. Samples were cured for seven days in water. Measurements were performed after 10 weeks of aging.
Figure 8. Measured shielding effectiveness of cement sample with 18 wt.% biochar: (a) cured in water for seven days; (b) cured in water for 28 days. Measurements were performed after two weeks and 10 weeks. There is a strong correlation between the curing period in water and the mechanical strength of cement composites [30]. In order to evaluate the effect of the curing period in water on the shielding offectiveness values, samples with 18 wt.% biochar cured in water for a period of seven days and 28 days were analyzed. The shielding effectiveness of the cement composite with 18 wt.% biochar cured in water for seven days and 28 days, measured after two weeks and 10 weeks, are shown in Figure 8. [t can be seen that the sample cured in water for 28 days had higher shielding effectiveness when measured both after two weeks and after 10 weeks. The variation of the shielding effectiveness over time of the cement composite cured for 28 days was also higher than that cured in water for seven days. This shows that the shielding effectiveness increased due to the presence of water, whereby the loss of water from the sample over time resulted in a reduced value of the shielding effectiveness.
Figure 8. Measured shielding effectiveness of cement sample with 18 wt.% biochar: (a) cured in water for seven days; (b) cured in water for 28 days. Measurements were performed after two weeks and 10 weeks. There is a strong correlation between the curing period in water and the mechanical strength of cement composites [30]. In order to evaluate the effect of the curing period in water on the shielding offectiveness values, samples with 18 wt.% biochar cured in water for a period of seven days and 28 days were analyzed. The shielding effectiveness of the cement composite with 18 wt.% biochar cured in water for seven days and 28 days, measured after two weeks and 10 weeks, are shown in Figure 8. [t can be seen that the sample cured in water for 28 days had higher shielding effectiveness when measured both after two weeks and after 10 weeks. The variation of the shielding effectiveness over time of the cement composite cured for 28 days was also higher than that cured in water for seven days. This shows that the shielding effectiveness increased due to the presence of water, whereby the loss of water from the sample over time resulted in a reduced value of the shielding effectiveness.
Figure 1. The view of the obtained samples: (a) the polyaniline (PANI) film on a polyethylene substrate; (b) the gelatin film; and (c) the gelatin-PANI composite film. The views of the obtained PANI film sample on a polyethylene substrate, the sample of gelatin film, and the sample of the gelatin-PANI composite film are given in Figure 1. The minimal binding radius of the gelatin-PANI composite film with a thickness of 200-400 um was about 5 cm. SEM images of the PANI film on a polyethylene substrate are given in Figure 2. As can be seen from the images, the film consists of PANI grains of 100-1000 nm, which presumably may be due to the fact that the film was directly obtained from an aniline solution with subsequent polymerization.
Figure 1. The view of the obtained samples: (a) the polyaniline (PANI) film on a polyethylene substrate; (b) the gelatin film; and (c) the gelatin-PANI composite film. The views of the obtained PANI film sample on a polyethylene substrate, the sample of gelatin film, and the sample of the gelatin-PANI composite film are given in Figure 1. The minimal binding radius of the gelatin-PANI composite film with a thickness of 200-400 um was about 5 cm. SEM images of the PANI film on a polyethylene substrate are given in Figure 2. As can be seen from the images, the film consists of PANI grains of 100-1000 nm, which presumably may be due to the fact that the film was directly obtained from an aniline solution with subsequent polymerization.
Figure 2. SEM images of the PANI film on a polyethylene substrate: (a) low magnification and (b) high magnification.
Figure 2. SEM images of the PANI film on a polyethylene substrate: (a) low magnification and (b) high magnification.
The optical microscopy images of PANI film on a polyethylene substrate and gelatin-PANI samples are given in Figure 3.
The optical microscopy images of PANI film on a polyethylene substrate and gelatin-PANI samples are given in Figure 3.
Figure 4. Thickness dependence of the electrical resistivity of the PANI films on a polyethylene substrate The results of the electrical resistivity of the PANI films on a polyethylene substrate are shown in
Figure 4. Thickness dependence of the electrical resistivity of the PANI films on a polyethylene substrate The results of the electrical resistivity of the PANI films on a polyethylene substrate are shown in
Figure 5. Frequency dependence of the complex dielectric permittivity of the gelatin-PANI composite films: (a) real part of dielectric permittivity; (b) imaginary part of dielectric permittivity; 1—gelatin; 2—22%-PANI-GEL; 3—36%-PANI-GEL; and 4—59%-PANI-GEL.
Figure 5. Frequency dependence of the complex dielectric permittivity of the gelatin-PANI composite films: (a) real part of dielectric permittivity; (b) imaginary part of dielectric permittivity; 1—gelatin; 2—22%-PANI-GEL; 3—36%-PANI-GEL; and 4—59%-PANI-GEL.
Figure 6. Frequency dependence of the electromagnetic radiation (EMR) absorption coefficient of the PANI films on a polyethylene substrate: 1—110 um, 2—120 um, 3—140 um, and 4—160 um.
Figure 6. Frequency dependence of the electromagnetic radiation (EMR) absorption coefficient of the PANI films on a polyethylene substrate: 1—110 um, 2—120 um, 3—140 um, and 4—160 um.
Figure 7. Frequency dependence of the EMR absorption coefficient of the gelatin-PANI composite films: 1—2%-PANI-GEL; 2—36%-PANI-GEL; 3—46%-PANI-GEL; 4—53%-PANI-GEL; and 5—22%-PANI-GEL.
Figure 7. Frequency dependence of the EMR absorption coefficient of the gelatin-PANI composite films: 1—2%-PANI-GEL; 2—36%-PANI-GEL; 3—46%-PANI-GEL; 4—53%-PANI-GEL; and 5—22%-PANI-GEL.
Figure 1. Diagram of common mode (CM) and differential mode (DM) currents passing through a cable ferrite with two adjacent conductors (signal and return paths). a tat i a hie aaa ee eee i” ‘el A cable ferrite’s effectiveness to reduce EMI in cables is defined by its capability to increase the flux density of a specific field strength created around a conductor. The presence of noise current in a conductor generates an undesired magnetic field around it that can result in EMI problems. When a cable ferrite is applied in the conductor, the magnetic field is concentrated into magnetic flux inside the cable ferrite because it provides a higher magnetic permeability than air. As a result, the flowing noise current in the conductor is reduced and, thus, the EMI is attenuated. Currents that flow in cables (with two or more conductors) can be divided into differential mode (DM) and common mode (CM) depending on the directions of propagation. Although DM currents are usually significantly higher than CM currents, one of the most common radiated EMI problems is originated by CM currents flowing through the cables of the system [5]. CM currents, despite not having a high value, have a much greater interfering potential. This fact is because only a few microamps are required to flow through a cable to fail radiated emission requirements [4]. The use of a cable ferrite is an efficient solution to filter the CM currents in cables because, if a pair of adjacent conductors is considered, when the cable ferrite is placed over both signal and ground wires, the CM noise is reduced. As shown in Figure 1, the CM currents in both wires flow in the same direction, so the two magnetic fluxes in the cable ferrite are added together, and the filtering action occurs. The intended (DM) current is not affected by the presence of the cable ferrite because the DM current travels in opposite directions and it is transmitted through the signal and returns. Thus, the currents of the two conductors are opposing, meaning they cancel out and the cable ferrite has no effect [6]. This ability to attenuate only the undesirable CM disturbances is a very interesting feature of this kind of component [7-9].
Figure 1. Diagram of common mode (CM) and differential mode (DM) currents passing through a cable ferrite with two adjacent conductors (signal and return paths). a tat i a hie aaa ee eee i” ‘el A cable ferrite’s effectiveness to reduce EMI in cables is defined by its capability to increase the flux density of a specific field strength created around a conductor. The presence of noise current in a conductor generates an undesired magnetic field around it that can result in EMI problems. When a cable ferrite is applied in the conductor, the magnetic field is concentrated into magnetic flux inside the cable ferrite because it provides a higher magnetic permeability than air. As a result, the flowing noise current in the conductor is reduced and, thus, the EMI is attenuated. Currents that flow in cables (with two or more conductors) can be divided into differential mode (DM) and common mode (CM) depending on the directions of propagation. Although DM currents are usually significantly higher than CM currents, one of the most common radiated EMI problems is originated by CM currents flowing through the cables of the system [5]. CM currents, despite not having a high value, have a much greater interfering potential. This fact is because only a few microamps are required to flow through a cable to fail radiated emission requirements [4]. The use of a cable ferrite is an efficient solution to filter the CM currents in cables because, if a pair of adjacent conductors is considered, when the cable ferrite is placed over both signal and ground wires, the CM noise is reduced. As shown in Figure 1, the CM currents in both wires flow in the same direction, so the two magnetic fluxes in the cable ferrite are added together, and the filtering action occurs. The intended (DM) current is not affected by the presence of the cable ferrite because the DM current travels in opposite directions and it is transmitted through the signal and returns. Thus, the currents of the two conductors are opposing, meaning they cancel out and the cable ferrite has no effect [6]. This ability to attenuate only the undesirable CM disturbances is a very interesting feature of this kind of component [7-9].
Figure 2. Nanocrystalline manufacturing procedure diagram and nanocrystalline (NC) final core sample without the protective coating.
Figure 2. Nanocrystalline manufacturing procedure diagram and nanocrystalline (NC) final core sample without the protective coating.
Figure 3. Non-split NC and split-core sample (left) and non-split ceramic and split-core sample (right) Table 1. List of cable ferrite samples used in this research.
Figure 3. Non-split NC and split-core sample (left) and non-split ceramic and split-core sample (right) Table 1. List of cable ferrite samples used in this research.
Figure 4. Split-core with air gaps: (a) Magnetic flux distribution diagram and (b) the magnetic circuit of a split-core with two air gaps. When the two parts of the split-core are joined, a certain air gap remains between them that results in a magnetic reluctance (R) increase, since the gap represents an opposition to the magnetic flux (P) normal flow [15,30]. As shown in Figure 4, this effect is analogous to adding a series resistor in an electronic circuit to reduce the magnitude of the current. In Figure 4, R- represents the reluctance of the core, Rg the reluctance of the gap, ® the magnetic flux that flows through the magnetic path length of the core (/,), Ie the length of the air gap, i the current that flows through the conductor and N the number of turns. The general expression to obtain the magnetic reluctance is given by [15]:
Figure 4. Split-core with air gaps: (a) Magnetic flux distribution diagram and (b) the magnetic circuit of a split-core with two air gaps. When the two parts of the split-core are joined, a certain air gap remains between them that results in a magnetic reluctance (R) increase, since the gap represents an opposition to the magnetic flux (P) normal flow [15,30]. As shown in Figure 4, this effect is analogous to adding a series resistor in an electronic circuit to reduce the magnitude of the current. In Figure 4, R- represents the reluctance of the core, Rg the reluctance of the gap, ® the magnetic flux that flows through the magnetic path length of the core (/,), Ie the length of the air gap, i the current that flows through the conductor and N the number of turns. The general expression to obtain the magnetic reluctance is given by [15]:
Figure 5. Comparison between experimental (solid traces) and estimated (dotted traces) effective permeability considering different gaps for NiZn, MnZn and NC samples: (a) NiZn non-split (red trace) and split cases; (b) MnZn non-split (red trace) and split cases and (c) NC non-split (red trace) and split cases.
Figure 5. Comparison between experimental (solid traces) and estimated (dotted traces) effective permeability considering different gaps for NiZn, MnZn and NC samples: (a) NiZn non-split (red trace) and split cases; (b) MnZn non-split (red trace) and split cases and (c) NC non-split (red trace) and split cases.
Figure 6. Impedance measurement setup with the DC bias test fixture connected: (a) Photograph of the measurement setup and (b) diagram blocks of the measurement setup. The experimental magnitude of the impedance of each sample is obtained by using the E4991A RF Impedance/Material Analyzer (Keysight, Santa Rosa, CA, USA) connected to the Terminal Adapter 16201A (Keysight, Santa Rosa, CA, USA). This adapter makes it possible to introduce into the measurement setup the 16200B External DC Bias (Keysight, Santa Rosa, CA, USA) that allows for supplying a bias current through the cable ferrite of up to 5 A using a 7 mm port and an external DC current source. Finally, the cable ferrite is connected by means of the Spring Clip Fixture 16092A (Keysight, Santa Rosa, CA, USA) that is connected to the 16200B test fixture [33]. After it is properly calibrated, this measurement setup is able to characterize cable ferrites from 1 MHz to 500 MHz since the E4991A equipment can operate from 1 MHz and the 16200B test fixture up to 500 MHz. Figure 6 shows the described experimental measurement setup.
Figure 6. Impedance measurement setup with the DC bias test fixture connected: (a) Photograph of the measurement setup and (b) diagram blocks of the measurement setup. The experimental magnitude of the impedance of each sample is obtained by using the E4991A RF Impedance/Material Analyzer (Keysight, Santa Rosa, CA, USA) connected to the Terminal Adapter 16201A (Keysight, Santa Rosa, CA, USA). This adapter makes it possible to introduce into the measurement setup the 16200B External DC Bias (Keysight, Santa Rosa, CA, USA) that allows for supplying a bias current through the cable ferrite of up to 5 A using a 7 mm port and an external DC current source. Finally, the cable ferrite is connected by means of the Spring Clip Fixture 16092A (Keysight, Santa Rosa, CA, USA) that is connected to the 16200B test fixture [33]. After it is properly calibrated, this measurement setup is able to characterize cable ferrites from 1 MHz to 500 MHz since the E4991A equipment can operate from 1 MHz and the 16200B test fixture up to 500 MHz. Figure 6 shows the described experimental measurement setup.
Figure 7. Cable ferrite simulation model. to two ports (input and output) referenced to a perfect electrical plane located at a certain distance under it. This simulation setup represents a transmission line based on a parallel line (or single wire) considering a single wire over a ground plane that allows for designing a system with a characteristic impedance of Zp = 150 ©. This parameter is fixed by selecting the distance from the plane to the center of the conductor H = 15 mm, the diameter of the conductor d = 4.9 mm and considering that it is surrounded by air [34-36]. By setting the ports’ impedance to 150 Q, it is possible to extract the cable ferrite’s impedance under test without the characterization system influencing the results obtained. This value is a reference value adopted in different EMC standards to characterize and calibrate devices such as common mode absorption devices (CMADs) intended for measuring EMI disturbances in cables [11]. These fixtures are characterized using the through-reflect-line (TRL) calibration method based on measuring the S-parameters of CMADs, as described in CISPR 16-1-4 [11]. Therefore, this simulation model provides a reference system that can extract the impedance introduced in the conductor by the cable ferrite. The procedure performed to emulate the different studied gap cases (g0, g1, g2 and g3) is based on a parametric gap sweep. This technique makes it possible to determine the sleeve core’s impedance when it is split into two parts and a specific gap is introduced. It is expected that this simulation model is able to provide the performance of the split samples from the original relative permeability (the values obtained for the non-split-core sample) by fixing the gaps described in Section 2. In the 90 case, the 0.01 mm distance value was introduced to differentiate it from the original non-split core.
Figure 7. Cable ferrite simulation model. to two ports (input and output) referenced to a perfect electrical plane located at a certain distance under it. This simulation setup represents a transmission line based on a parallel line (or single wire) considering a single wire over a ground plane that allows for designing a system with a characteristic impedance of Zp = 150 ©. This parameter is fixed by selecting the distance from the plane to the center of the conductor H = 15 mm, the diameter of the conductor d = 4.9 mm and considering that it is surrounded by air [34-36]. By setting the ports’ impedance to 150 Q, it is possible to extract the cable ferrite’s impedance under test without the characterization system influencing the results obtained. This value is a reference value adopted in different EMC standards to characterize and calibrate devices such as common mode absorption devices (CMADs) intended for measuring EMI disturbances in cables [11]. These fixtures are characterized using the through-reflect-line (TRL) calibration method based on measuring the S-parameters of CMADs, as described in CISPR 16-1-4 [11]. Therefore, this simulation model provides a reference system that can extract the impedance introduced in the conductor by the cable ferrite. The procedure performed to emulate the different studied gap cases (g0, g1, g2 and g3) is based on a parametric gap sweep. This technique makes it possible to determine the sleeve core’s impedance when it is split into two parts and a specific gap is introduced. It is expected that this simulation model is able to provide the performance of the split samples from the original relative permeability (the values obtained for the non-split-core sample) by fixing the gaps described in Section 2. In the 90 case, the 0.01 mm distance value was introduced to differentiate it from the original non-split core.
Figure 8. Comparison between experimental (solid traces) and simulated (dotted traces) impedance considering different gaps (non-split and split with gaps g0, ¢1, ¢2 and g3) for NiZn, MnZn and NC cable ferrites: (a) NiZn non-split (red trace) and split cases; (b) MnZn non-split (red trace) and split cases and (c) NC non-split (red trace) and split cases.
Figure 8. Comparison between experimental (solid traces) and simulated (dotted traces) impedance considering different gaps (non-split and split with gaps g0, ¢1, ¢2 and g3) for NiZn, MnZn and NC cable ferrites: (a) NiZn non-split (red trace) and split cases; (b) MnZn non-split (red trace) and split cases and (c) NC non-split (red trace) and split cases.
Figure 9. Comparison between experimental (solid traces) and new simulated (dotted traces) impedance, considering different gaps (non-split and split with gaps 90, ¢1, ¢2 and g3) for NC cable ferrites.
Figure 9. Comparison between experimental (solid traces) and new simulated (dotted traces) impedance, considering different gaps (non-split and split with gaps 90, ¢1, ¢2 and g3) for NC cable ferrites.
Additionally, the non-split NC core is able to yield a more stable response up to its maximum impedance value and it shows a better performance than ceramic cores to reduce EMI disturbances when they are distributed in a wideband frequency range (from the low-frequency region up to about 100 MHz). Figure 10b shows the impedance comparison when the cores are split into two parts and attached as closely as possible, emulating a snap ferrite’s function. In this case, NC has significantly reduced its performance and MnZn provides the best performance up to 8.4 MHz. From this frequency value, NiZn yields the highest impedance value. In the rest of the analyzed gaps (g1, g2 and 93), the NiZn sample mainly represents the most interesting solution because MnZn and NC cable ferrites offer a lower impedance response. Thus, when a significant gap is introduced, the material with lower permeability is able to yield the best EMI attenuation.
Additionally, the non-split NC core is able to yield a more stable response up to its maximum impedance value and it shows a better performance than ceramic cores to reduce EMI disturbances when they are distributed in a wideband frequency range (from the low-frequency region up to about 100 MHz). Figure 10b shows the impedance comparison when the cores are split into two parts and attached as closely as possible, emulating a snap ferrite’s function. In this case, NC has significantly reduced its performance and MnZn provides the best performance up to 8.4 MHz. From this frequency value, NiZn yields the highest impedance value. In the rest of the analyzed gaps (g1, g2 and 93), the NiZn sample mainly represents the most interesting solution because MnZn and NC cable ferrites offer a lower impedance response. Thus, when a significant gap is introduced, the material with lower permeability is able to yield the best EMI attenuation.
Figure 10. Comparison between the measured impedance of NiZn, MnZn and NC cable ferrites, considering five different gap cases: (a) NiZn, MnZn and NC non-split-cores; (b) NiZn, MnZn and NC g0 split-cores; (c) NiZn, MnZn and NC g1 split-cores; (d) NiZn, MnZn and NC g? split-cores and (e) NiZn, MnZn and NC g3 split-cores.
Figure 10. Comparison between the measured impedance of NiZn, MnZn and NC cable ferrites, considering five different gap cases: (a) NiZn, MnZn and NC non-split-cores; (b) NiZn, MnZn and NC g0 split-cores; (c) NiZn, MnZn and NC g1 split-cores; (d) NiZn, MnZn and NC g? split-cores and (e) NiZn, MnZn and NC g3 split-cores.
Figure 11. Impedance analysis considering different values of DC currents for the three different non-split samples: (a) NiZn; (b) MnZn and (c) NC.
Figure 11. Impedance analysis considering different values of DC currents for the three different non-split samples: (a) NiZn; (b) MnZn and (c) NC.
Figure 12. Impedance analysis considering different values of DC currents and gap conditions for the split samples: (a) NiZn g0 case; (b) NiZn g1, g2 and g3 cases; (c) MnZn g0 case; (d) MnZn g1, 92 and g3 cases; (e) NC g0 case and (f) NC g1, g2 and 3 cases. and the third to the split NC samples. The left column shows the behavior of each material when the g0 gap is considered, and the right column shows the results obtained when g1 (dotted traces), g2 (short dashed traces) and g3 (long dashed traces) gaps are introduced. When the effect on the impedance response of splitting the samples to be attached without an intended gap is observed, the g0 traces show quite similar behavior in the three materials. NC traces have the same behavior over most of the frequency range, whereas NiZn traces show the same match between traces except for the 5 A case. In the case of MnZn, there is a difference between traces in the low-frequency region, producing a shift of the resonance frequency when DC currents higher than 0.5 A are applied. When the rest of the gaps are analyzed, the three materials have the same response when DC currents up to 5 A are injected. Moreover, from a certain frequency value, the materials’ traces match independently of the DC current value and gap introduced.
Figure 12. Impedance analysis considering different values of DC currents and gap conditions for the split samples: (a) NiZn g0 case; (b) NiZn g1, g2 and g3 cases; (c) MnZn g0 case; (d) MnZn g1, 92 and g3 cases; (e) NC g0 case and (f) NC g1, g2 and 3 cases. and the third to the split NC samples. The left column shows the behavior of each material when the g0 gap is considered, and the right column shows the results obtained when g1 (dotted traces), g2 (short dashed traces) and g3 (long dashed traces) gaps are introduced. When the effect on the impedance response of splitting the samples to be attached without an intended gap is observed, the g0 traces show quite similar behavior in the three materials. NC traces have the same behavior over most of the frequency range, whereas NiZn traces show the same match between traces except for the 5 A case. In the case of MnZn, there is a difference between traces in the low-frequency region, producing a shift of the resonance frequency when DC currents higher than 0.5 A are applied. When the rest of the gaps are analyzed, the three materials have the same response when DC currents up to 5 A are injected. Moreover, from a certain frequency value, the materials’ traces match independently of the DC current value and gap introduced.
Figure 1. Representation and circuit model of a common mode choke made up of two equal coupled windings with self-inductance L and mutual inductance M. Figure 1 shows a simplified representation of a CMC along with a lumped-element circuit moc of the CMC. As shown in Figure la, a CMC is made up of two equal magnetically coupled windin, In [16] it has been demonstrated that a CMC can be conveniently modeled in a sufficiently bro: irequency range by using a lumped-elements circuit with two blocks, each one containing two perfec! coupled inductances as shown in Figure 1b. The first block in that figure (CM block) only affects CM noise, while the second block (DM block) contains inductors with opposite (perfect) couplit and therefore it only affects DM signals. In that circuit model parasitic intra-winding capacitanc C;) and inter-winding capacitances (Cj) have been added to account for the response of the CM throughout a sufficiently broad frequency range [16,17]. Also, losses within the magnetic material a accounted for in that model by resistors Rey and Rpm placed in parallel with the coupled inducto Finally, capacitances to ground, Cg, have been included in the circuit model to consider possible elect: coupling to nearby metallic surfaces, e.g., the ground plane on a printed circuit board (PCB).
Figure 1. Representation and circuit model of a common mode choke made up of two equal coupled windings with self-inductance L and mutual inductance M. Figure 1 shows a simplified representation of a CMC along with a lumped-element circuit moc of the CMC. As shown in Figure la, a CMC is made up of two equal magnetically coupled windin, In [16] it has been demonstrated that a CMC can be conveniently modeled in a sufficiently bro: irequency range by using a lumped-elements circuit with two blocks, each one containing two perfec! coupled inductances as shown in Figure 1b. The first block in that figure (CM block) only affects CM noise, while the second block (DM block) contains inductors with opposite (perfect) couplit and therefore it only affects DM signals. In that circuit model parasitic intra-winding capacitanc C;) and inter-winding capacitances (Cj) have been added to account for the response of the CM throughout a sufficiently broad frequency range [16,17]. Also, losses within the magnetic material a accounted for in that model by resistors Rey and Rpm placed in parallel with the coupled inducto Finally, capacitances to ground, Cg, have been included in the circuit model to consider possible elect: coupling to nearby metallic surfaces, e.g., the ground plane on a printed circuit board (PCB).
Figure 2. Equivalent circuits of the modes obtained for the high-frequency circuit of the CMC in Figure 1b. Normalized voltages at the four terminals of the CMC are indicated for each mode. In Figure 2 it can be seen that the admittances of the four modes of the CMC are either a capacitive admittance (modes C and V) or the admittance of a resistor, an inductor and a capacitor connected in parallel (parallel RLC circuit), where the inductive component is proportional to Lc = L + M for the CM (H mode) and to Lpy = L — M (the leakage inductance) for the DM (D mode). The admittances of the four modes of the CMC can be written as follows:
Figure 2. Equivalent circuits of the modes obtained for the high-frequency circuit of the CMC in Figure 1b. Normalized voltages at the four terminals of the CMC are indicated for each mode. In Figure 2 it can be seen that the admittances of the four modes of the CMC are either a capacitive admittance (modes C and V) or the admittance of a resistor, an inductor and a capacitor connected in parallel (parallel RLC circuit), where the inductive component is proportional to Lc = L + M for the CM (H mode) and to Lpy = L — M (the leakage inductance) for the DM (D mode). The admittances of the four modes of the CMC can be written as follows:
Table 1. Transmission coefficients and frequencies of resonance for a CMC measured in the setups of Figure 3, where Yoo = YHYp/(Yu + Yp). Approximated expressions assume Cg < C;,Cw and Yo < Yv, Yu, Yp- As an alternative to the DM setup, in Figure 3b we propose a simpler unbalanced setup (UDM setup) which dispenses with baluns and which at the same time is also able to provide information about the DM response of the CMC. The UDM setup in Figure 3b, like the DM setup in Figure 3a, involves the measurement of a transmission coefficient instead of the measurement of impedances of the CMC. This allows for avoiding additional measurements to account for the effect of cables and/or test fixtures (compensation measurements) [19]. To compare the UDM setup with the DM setup, it is useful to obtain also the transmission coefficient of the UDM setup (SYM) in terms of the admittances of the natural modes of the CMC. An analysis of the circuit in Figure 3b with the circuit model of the CMC in Figure 1b leads to: a a peer ke:
Table 1. Transmission coefficients and frequencies of resonance for a CMC measured in the setups of Figure 3, where Yoo = YHYp/(Yu + Yp). Approximated expressions assume Cg < C;,Cw and Yo < Yv, Yu, Yp- As an alternative to the DM setup, in Figure 3b we propose a simpler unbalanced setup (UDM setup) which dispenses with baluns and which at the same time is also able to provide information about the DM response of the CMC. The UDM setup in Figure 3b, like the DM setup in Figure 3a, involves the measurement of a transmission coefficient instead of the measurement of impedances of the CMC. This allows for avoiding additional measurements to account for the effect of cables and/or test fixtures (compensation measurements) [19]. To compare the UDM setup with the DM setup, it is useful to obtain also the transmission coefficient of the UDM setup (SYM) in terms of the admittances of the natural modes of the CMC. An analysis of the circuit in Figure 3b with the circuit model of the CMC in Figure 1b leads to: a a peer ke:
Figure 3. Balanced and unbalanced setups for measuring transmission coefficients conveying information about the attenuation provided by a CMC for a differential mode excitation. Measurements can be performed with a spectrum analyzer (SA) with tracking generator (TG) or a VNA. Since only Yp and Yy appear in the expression of SUM , we can conclude that only D (DM) and V modes of the CMC are excited in the DM setup. Also, from that expression it is possible to obtain the frequency of resonance of the CMC in that setup in terms of the elements of the circuit model of the CMC in Figure 1b. This frequency of resonance, fpm, is also given in Table 1 (Since in practice Rem, Rpm > R = 50Q the frequency of resonance can be calculated by taking Rom — © and Rpm — © in ge and imposing SUM = 0). At frequencies below fpm the response of the CMC is dominated by the inductive part of Yp, i.e., Lpqm. Above fom the CMC behaves capacitively and the magnitude of SDM increases with frequency. Please note that since fp does not depend on Cg, an electric coupling to ground will not alter the frequency of resonance of SPM.
Figure 3. Balanced and unbalanced setups for measuring transmission coefficients conveying information about the attenuation provided by a CMC for a differential mode excitation. Measurements can be performed with a spectrum analyzer (SA) with tracking generator (TG) or a VNA. Since only Yp and Yy appear in the expression of SUM , we can conclude that only D (DM) and V modes of the CMC are excited in the DM setup. Also, from that expression it is possible to obtain the frequency of resonance of the CMC in that setup in terms of the elements of the circuit model of the CMC in Figure 1b. This frequency of resonance, fpm, is also given in Table 1 (Since in practice Rem, Rpm > R = 50Q the frequency of resonance can be calculated by taking Rom — © and Rpm — © in ge and imposing SUM = 0). At frequencies below fpm the response of the CMC is dominated by the inductive part of Yp, i.e., Lpqm. Above fom the CMC behaves capacitively and the magnitude of SDM increases with frequency. Please note that since fp does not depend on Cg, an electric coupling to ground will not alter the frequency of resonance of SPM.
leading to terminals 1 and 3 of the CMC are not an issue. In fact, provided that they have the same 50, characteristic impedance as TLc lines, those traces will only introduce a phase shift in the transmission coefficient [19]. However, TLy lines attached at terminals 2 and 4 of the CMC create an asymmetric electric coupling of the CMC to ground whose effect is not negligible, as we will show here. To demonstrate that, consider the situation represented in Figure 4, where terminals 2 and 4 of the CMC are directly short-circuited to achieve an UDM configuration that circumvents the two TL lines attached to those terminals. Considering lengths of TLy lines in the order or centimeters, they will be electrically short at the frequencies of interest and, consequently, these open-circuited lines can be modeled as capacitances [20]. The two parasitic capacitances C, included in Figure 4 account for this effect. Since these C, capacitances correspond to the total capacitance of the trace lines, their values are typically in the order of units or tens of picofarads [20]. Consequently, C, capacitances cannot be disregarded by comparison with typical parasitic capacitances of the CMC, which are of the same order of magnitude. Figure 4. Schematic of a CMC mounted on a grounded PCB connected in UDM setup. Transmission lines labelled as TLc stand for the interconnecting cables. Transmission lines labelled as TLy represent the signal traces of the PCB. The signal traces terminated as open-circuits at terminals 2 and 4 are supposed to be electrically short and thereby modeled as two capacitances C,; to ground.
leading to terminals 1 and 3 of the CMC are not an issue. In fact, provided that they have the same 50, characteristic impedance as TLc lines, those traces will only introduce a phase shift in the transmission coefficient [19]. However, TLy lines attached at terminals 2 and 4 of the CMC create an asymmetric electric coupling of the CMC to ground whose effect is not negligible, as we will show here. To demonstrate that, consider the situation represented in Figure 4, where terminals 2 and 4 of the CMC are directly short-circuited to achieve an UDM configuration that circumvents the two TL lines attached to those terminals. Considering lengths of TLy lines in the order or centimeters, they will be electrically short at the frequencies of interest and, consequently, these open-circuited lines can be modeled as capacitances [20]. The two parasitic capacitances C, included in Figure 4 account for this effect. Since these C, capacitances correspond to the total capacitance of the trace lines, their values are typically in the order of units or tens of picofarads [20]. Consequently, C, capacitances cannot be disregarded by comparison with typical parasitic capacitances of the CMC, which are of the same order of magnitude. Figure 4. Schematic of a CMC mounted on a grounded PCB connected in UDM setup. Transmission lines labelled as TLc stand for the interconnecting cables. Transmission lines labelled as TLy represent the signal traces of the PCB. The signal traces terminated as open-circuits at terminals 2 and 4 are supposed to be electrically short and thereby modeled as two capacitances C,; to ground.
Figure 5. Equivalent circuit of the UDM setup for a CMC mounted on a PCB with an ungrounded return plane. Transmission lines labelled as TLc stand for the interconnecting cables. Transmission lines labelled as TLy represent the signal traces of the PCB. Since all the signal traces are terminated as open-circuits and they are supposed to be electrically short, they are actually modeled as capacitances C, to ground.
Figure 5. Equivalent circuit of the UDM setup for a CMC mounted on a PCB with an ungrounded return plane. Transmission lines labelled as TLc stand for the interconnecting cables. Transmission lines labelled as TLy represent the signal traces of the PCB. Since all the signal traces are terminated as open-circuits and they are supposed to be electrically short, they are actually modeled as capacitances C, to ground.
Figure 6. Star to triangle conversion for the parasitic capacitances C; that appear at the four terminals of the CMC in the circuit of Figure 5. 2.3. Effect of Magnetic Coupling to Metallic Surfaces
Figure 6. Star to triangle conversion for the parasitic capacitances C; that appear at the four terminals of the CMC in the circuit of Figure 5. 2.3. Effect of Magnetic Coupling to Metallic Surfaces
Table 2. Parameters extracted for the equivalent circuit of Figure 1b for several commercial common mode chokes. By comparing the frequencies of resonance in Table 1 it is apparent that for a given CMC we must have fupm < foc < fpm. We will use here this fact to verify the accuracy of our circuit model and to check the expressions for the transmission coefficients of the DM and UDM setups, spM and SYDM presented in Table 1.
Table 2. Parameters extracted for the equivalent circuit of Figure 1b for several commercial common mode chokes. By comparing the frequencies of resonance in Table 1 it is apparent that for a given CMC we must have fupm < foc < fpm. We will use here this fact to verify the accuracy of our circuit model and to check the expressions for the transmission coefficients of the DM and UDM setups, spM and SYDM presented in Table 1.
Figure 7. Open-circuit (OC) setup proposed in [16] for characterizing CMCs. setup (second resonance) and finally, for the DM, ie., fupm < foc < fpm. These results are consistent with our previous analysis. Similar results are obtained for all the CMCs in Table 2. An additional example is represented in Figure 9 for another CMC, identified in the caption of the figure and listed in Table 2.
Figure 7. Open-circuit (OC) setup proposed in [16] for characterizing CMCs. setup (second resonance) and finally, for the DM, ie., fupm < foc < fpm. These results are consistent with our previous analysis. Similar results are obtained for all the CMCs in Table 2. An additional example is represented in Figure 9 for another CMC, identified in the caption of the figure and listed in Table 2.
Figure 8. Magnitude |S;| for the CMC listed as Wiirth Elecktronik 744824622 (2.2 mH) in Table 2, using the setups in Figures 3 and 7.
Figure 8. Magnitude |S;| for the CMC listed as Wiirth Elecktronik 744824622 (2.2 mH) in Table 2, using the setups in Figures 3 and 7.
Figure 9. Magnitude |S ;| for the CMC listed as KEMET SC-02-30G (3 mH) in Table 2, using the setups in Figures 3 and 7.
Figure 9. Magnitude |S ;| for the CMC listed as KEMET SC-02-30G (3 mH) in Table 2, using the setups in Figures 3 and 7.
Figure 10. A 2.2mH CMC, listed in Table 2 as WURTH ELEKTRONIK 744824622, mounted on a PCB fabricated to check the impact on [syeM| of the capacitive coupling of the signal traces to the return plane. frequencies (well below resonance) is the same for these three situations. However, Figure 11 also reveals that at high frequencies there exists a shift in the frequency of resonance of SYPM. Compared to the isolated case, the frequency of resonance is slightly lower when the RP is not grounded and slightly higher when the RP is grounded. These results are consistent with the analysis presented in Section 2.2. We have obtained similar results for all the CMCs in Table 2.
Figure 10. A 2.2mH CMC, listed in Table 2 as WURTH ELEKTRONIK 744824622, mounted on a PCB fabricated to check the impact on [syeM| of the capacitive coupling of the signal traces to the return plane. frequencies (well below resonance) is the same for these three situations. However, Figure 11 also reveals that at high frequencies there exists a shift in the frequency of resonance of SYPM. Compared to the isolated case, the frequency of resonance is slightly lower when the RP is not grounded and slightly higher when the RP is grounded. These results are consistent with the analysis presented in Section 2.2. We have obtained similar results for all the CMCs in Table 2.
Figure 11. Measured and calculated |SyPM| curves for the CMC listed as WURTH ELEKTRONIK 744824220 (20 mH) in Table 2. We compare curves for three cases: standalone CMC, CMC mounted ona PCB with a floating return plane and CMC mounted on a PCB whose return plane is grounded (G label).
Figure 11. Measured and calculated |SyPM| curves for the CMC listed as WURTH ELEKTRONIK 744824220 (20 mH) in Table 2. We compare curves for three cases: standalone CMC, CMC mounted ona PCB with a floating return plane and CMC mounted on a PCB whose return plane is grounded (G label).
Table 3. Measured frequencies of resonance of SYM for three CMCs when isolated and when mounted on a PCB with an ungrounded return plane. Also, calculated fupm for the latter case. Table 4 compares the frequency of resonance of SYPM measured when the CMC is isolated with that measured when the CMC is mounted on a grounded PCB for the same three CMCs listed in Table 3. Results show that the grounded RP causes the frequency of resonance to increase in all the cases, as expected. This increase is up to 35% for the WE 2.2 mH CMC. Frequencies of resonance fp calculated by using (8) are also included in Table 4. The good agreement found in general between calculated and measured results confirms that the shift of the frequency of resonance of SYM is caused by the presence of the grounded RP and that this shift can be approximately predicted by using Equation (8).
Table 3. Measured frequencies of resonance of SYM for three CMCs when isolated and when mounted on a PCB with an ungrounded return plane. Also, calculated fupm for the latter case. Table 4 compares the frequency of resonance of SYPM measured when the CMC is isolated with that measured when the CMC is mounted on a grounded PCB for the same three CMCs listed in Table 3. Results show that the grounded RP causes the frequency of resonance to increase in all the cases, as expected. This increase is up to 35% for the WE 2.2 mH CMC. Frequencies of resonance fp calculated by using (8) are also included in Table 4. The good agreement found in general between calculated and measured results confirms that the shift of the frequency of resonance of SYM is caused by the presence of the grounded RP and that this shift can be approximately predicted by using Equation (8).
Table 4. Measured frequencies of resonance of SYM for three CMCs when isolated and when mounted on a PCB with a grounded return plane. Also, calculated fypm for the latter case. Summing up, results in this section show that when measured in the UDM setup, the capacitance between the signal traces and the RP of the PCB can modify the response of the CMC at high frequencies. Therefore, when accurate results are required, measuring a CMC mounted on a PCB with the UDM setup should be avoided unless the effect of the parasitic capacitances of the signal traces to the RP is accounted for. Table 4. Measured frequencies of resonance of sues for three CMCs when isolated and when mounted
Table 4. Measured frequencies of resonance of SYM for three CMCs when isolated and when mounted on a PCB with a grounded return plane. Also, calculated fypm for the latter case. Summing up, results in this section show that when measured in the UDM setup, the capacitance between the signal traces and the RP of the PCB can modify the response of the CMC at high frequencies. Therefore, when accurate results are required, measuring a CMC mounted on a PCB with the UDM setup should be avoided unless the effect of the parasitic capacitances of the signal traces to the RP is accounted for. Table 4. Measured frequencies of resonance of sues for three CMCs when isolated and when mounted
Table 5. Lp for different CMCs with and without the effect of a nearby conducting surface.
Table 5. Lp for different CMCs with and without the effect of a nearby conducting surface.
Figure 12. Measured and calculated |SDM| (a) and |SYPM| (b) for the CMC listed as WURTH ELEKTRONIK 744824310 (10 mH) in Table 2, whose picture is inserted in the figures. The CS acronym used in the legends indicates results corresponding to the case where a conducting surface is placed near the CMC.
Figure 12. Measured and calculated |SDM| (a) and |SYPM| (b) for the CMC listed as WURTH ELEKTRONIK 744824310 (10 mH) in Table 2, whose picture is inserted in the figures. The CS acronym used in the legends indicates results corresponding to the case where a conducting surface is placed near the CMC.
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