Phase Adjustment of S-Parameters from Coupled Resonator Filters

da Silva, L. M.; de Melo, M. T.; Santos, M. G. A. R.; Serres, A. J. R.

doi:10.1590/2179-10742022v21i1255112

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Journal of Microwaves, Optoelectronics and Electromagnetic Applications

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Article • J. Microw. Optoelectron. Electromagn. Appl. 21 (1) • Mar 2022 • https://doi.org/10.1590/2179-10742022v21i1255112 copy

Phase Adjustment of S-Parameters from Coupled Resonator Filters

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This paper presents a method to cancel the constant phase loading and transmission line that are added to the S-parameters of coupled resonant networks. Thus, the phase-corrected S-parameters may be used to obtain a rational model together with its representative coupling matrix. This method is applicable to lossy and lossless coupled resonator networks with two ports, such as microwave filters. In addition, it has the advantage of not requiring S-parameters with wide frequency ranges, and offers less computational effort than other approaches. Examples including simulations of microwaves passband filters are provided in order to demonstrate the effectiveness of this new technique.

Index Terms
Coupling matrix; filters; rational approximation; vector fitting

Mij	j=1	j=2	j=3	j=4
i=1	-0.0042 (exr)	0.0187(exr)	0.0000(exr)	-0.0072(exr)
	-0.0041 (ext)	0.0187(ext)	0.0000(ext)	-0.0072(ext)
	0.0000 (id)	0.0192(id)	0.0000(exr)	-0.0068 (id)
i=2	0.0187 (exr)	-0.0018(exr)	0.0181(exr)	0.0035(exr)
	0.0187 (ext)	-0.0017(ext)	0.0181(ext)	0.0035(ext)
	0.0192 (id)	0.0000(id)	0.0188(exr)	-0.0000 (id)
i=3	0.0000 (exr)	0.0181(exr)	-0.0089(exr)	0.0184(exr)
	0.0000 (ext)	0.0181(ext)	-0.0089(ext)	0.0184(ext)
	0.0000 (id)	0.0188(id)	0.0000(exr)	0.0192 (id)
i=4	-0.0072 (exr)	0.0035(exr)	0.0184(exr)	-0.0041(exr)
	-0.0072 (ext)	0.0035(ext)	0.0184(ext)	-0.0040(ext)
	-0.0068 (id)	0.0000(id)	0.0192(exr)	0.0000 (id)
Q₁	41.9920(exr)		Q₂	42.0191(exr)
	41.0130(ext)			41.9964(ext)
	41.9170(id)			41.9170(id)

Mij	j=1	j=2	j=3	j=4
i=1	-0.0014-j0.0038(exr)	0.0187(exr)	0.0000(exr)	-0.0072(exr)
i=1	-0.0013-j0.0037(ext)	0.0186(ext)	0.0000(ext)	-0.0072(ext)
i=2	0.0187(exr)	-0.0010-j0.0037(exr)	0.0181(exr)	0.0035(exr)
i=2	0.0186(ext)	-0.0010-j0.0037(ext)	0.0180(ext)	0.0035(ext)
i=3	0.0000(exr)	0.0181(exr)	-0.0062-j0.0036(exr)	0.0184(exr)
i=3	0.0000(ext)	0.0180(ext)	-0.0061-j0.0035(ext)	0.0184(ext)
i=4	-0.0072(exr)	0.0035(exr)	0.0184(exr)	-0.0014-j0.0037(exr)
i=4	-0.0072(ext)	0.0035(ext)	0.0184(ext)	-0.0012-j0.0039(ext)
Q₁	42.2120(exr)		Q₂	41.8725(exl)
Q₁	42.3960(ext)		Q₂	41.8232(ext)

Mij	i=1	i=2	i=3	i=4	i=5	i=6
j=1	53-j42(exl)	249(exl)	0(exl)	0(exl)	0(exl)	-9 (exl)
	58-j46(exh)	248(exh)	0(exh)	0(exh)	0(exh)	-9 (exh)
	0(id)	229(id)	0(id)	0(id)	0(id)	-9(id)
j=2	249(exl)	17-j42(exl)	151(exl)	0(exl)	62(exl)	6(exl)
	248(exh)	16-j42(exh)	152(exh)	0(exh)	63(exh)	6(exh)
	229(id)	0(id)	155(id)	0(id)	61 (id)	0(id)
j=3	0(exl)	151(exl)	26-j42(exl)	-224(exl)	20(exl)	0(exl)
	0(exh)	152(exh)	26-j42(exh)	-226(exh)	22(exh)	0(exh)
	0(id)	155(id)	0(id)	-206(id)	0(id)	0(id)
j=4	0(exl)	0(exl)	-224(exl)	-22-j44(exl)	151(0X1)	0(exl)
	0(exh)	0(exh)	-226(exh)	-26-j40(exh)	150(exh)	0(exh)
	0(id)	0(id)	-206(id)	0(id)	155(id)	0(id)
j=5	0(exl)	62(exl)	20(exl)	151(exl)	14-j43(exl)	249(exl)
	0(exh)	63(exh)	22(exh)	150(exh)	15-j42(exh)	248(exh)
	0(id)	61(id)	0(id)	155(id)	0(id)	229(id)
j=6	-9 (exl)	6(exl)	0(exl)	0(exl)	249(exl)	52-j43(exl)
	-9 (exh)	6(exh)	0(exh)	0(exh)	248(exh)	54-j44(exh)
	-9(id)	0(id)	0(id)	0(id)	229(id)	0(id)
Q₁	32.4602(exl)			Q₂	32.6213(exl)
	32.9904(exh)				32.9268(exh)
	36.5880(id)				36.5880(id)

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