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A triplet (trisection) is a section that consists of three nodes or asynchronously tuned shunt LC resonators mutually cou- pled. Each triplet is entirely responsible for the synthesis of only one finite non—equalization transmission zero.

Figure 3 A triplet (trisection) is a section that consists of three nodes or asynchronously tuned shunt LC resonators mutually cou- pled. Each triplet is entirely responsible for the synthesis of only one finite non—equalization transmission zero.

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Each resonator is modeled by one capacitance C’; shunted by one non realizable invariant susceptance jB; (fig. 1), which represents the offset of each resonator frequency. Low—pass to band-pass transformation leads to shunt LC (realizable) resonators. Admittance inverters represent magnetic or elec- tric frequency invariant couplings between resonators. Sym- metric response filters are characterized by ABC'D matrix polynomials that have real coefficients. This leads to By = 0, Vi = 1...n (synchronously tuned resonators) and to fewer number of non-zero cross couplings (e.g., the diago- nal couplings of fig. 1 will not exist). B. Atia & Williams Synthesis
Each resonator is modeled by one capacitance C’; shunted by one non realizable invariant susceptance jB; (fig. 1), which represents the offset of each resonator frequency. Low—pass to band-pass transformation leads to shunt LC (realizable) resonators. Admittance inverters represent magnetic or elec- tric frequency invariant couplings between resonators. Sym- metric response filters are characterized by ABC'D matrix polynomials that have real coefficients. This leads to By = 0, Vi = 1...n (synchronously tuned resonators) and to fewer number of non-zero cross couplings (e.g., the diago- nal couplings of fig. 1 will not exist). B. Atia & Williams Synthesis
A filter can be built by cascading such circuit sections. Two consecutive triplets share one common node (fig. 3(a)). T his kind of filter has the advantage that the location of each zero can be independently modified, making the filter easier tune. The program performs the synthesis of structures t to hat consist entirely of cascaded triplets (n = 2n, +1), and struc- tures with some triplets at input and/or output. In this case (fig. 3(b)) the remaining network is synthesized through a canonical topology, that may be transformed, if desired, in any other topology (e.g., in-line). This type of synthesis is very well suited for predistortion techniques in order to c rect the effect of non desired modes propagation. or-
A filter can be built by cascading such circuit sections. Two consecutive triplets share one common node (fig. 3(a)). T his kind of filter has the advantage that the location of each zero can be independently modified, making the filter easier tune. The program performs the synthesis of structures t to hat consist entirely of cascaded triplets (n = 2n, +1), and struc- tures with some triplets at input and/or output. In this case (fig. 3(b)) the remaining network is synthesized through a canonical topology, that may be transformed, if desired, in any other topology (e.g., in-line). This type of synthesis is very well suited for predistortion techniques in order to c rect the effect of non desired modes propagation. or-
Cascaded quadruplets may be used just like cascaded triplets, (in this case, consecutive quadruplets do not share any node, fig. 5(a)). They are limited to symmetric response filters. Structures consisting of one or more quadruplets and a net- work with different topology are possible (fig. 5(b)). The position of each pair of zeros can be independently modified.
Cascaded quadruplets may be used just like cascaded triplets, (in this case, consecutive quadruplets do not share any node, fig. 5(a)). They are limited to symmetric response filters. Structures consisting of one or more quadruplets and a net- work with different topology are possible (fig. 5(b)). The position of each pair of zeros can be independently modified.
function presents a pair of symmetric transmission zeros on either the real (equalization zeros) or imaginary axis.
function presents a pair of symmetric transmission zeros on either the real (equalization zeros) or imaginary axis.
Fig. 7. Coupling matrix rotation for an in-line 9*” order filter.
Fig. 7. Coupling matrix rotation for an in-line 9*” order filter.
Fig. 8. Comparison of several |S21(f)| plots. Mask is shown.
Fig. 8. Comparison of several |S21(f)| plots. Mask is shown.
Fig. 9. Asymmetric response filter, n = 5.
Fig. 9. Asymmetric response filter, n = 5.
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EngineeringComputer ScienceBand Pass FilterInsertion LossChebyshev ApproximationChebyshev filterBand pass filters
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