By A Matsumoto
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Additional resources for Microwave Filters and Circuits: Contributions from Japan
In the above examples any number of unit elements can be added to the front and to the rear of the prototype filters. But by adding UE's only to the rear, the driving-point impedance is kept unchanged. Therefore the method can be applied to the synthesis of one-ports or of filter groups with specified driving-point admittances (14). In the example of Fig. 16 one can reduce all the series inductances to shunt stubs, and if the prototype filter is symmetrical, the resulting Kazuyuki Kuroda 28 τΧ Ci Öl ^Γο (a)prototype Ω| , C 2| , , _Ω1„ r-^ ^ 2 ^ ' ^ ^ ί .
14) Substitution of these expressions into Eq. 4) shows that the two net works have the same matrices, hence the sufficiency of the left-hand, and consequently the right-hand, groups of the above equations. From Eq. 13) the necessary conditions for Y3 > 0 are n < 1 and ri < 1, which lead to two cases: (i) m > 1, rri > 1 (Ω02 > 0) and (ii) m < 0, m' < 0 (fi02 < 0). In case (i) they are sufficient, since one obtains Y0 > Υτ > 0 and Y0' > Υλ > 0 from Eq. 9), so that Y2 > 0 and F4 > 0 from Eq. 10).
14) The new zeros (other than λ = co) are given by Υλ(λ) — λΥ0 = 0, and are the same as those one obtains when a capacitance C = Y0 is removed from Y1. 15) and are the same as those obtained when an inductance L = 1/Y0 is removed from Zt= 1/Y1. Both zeros and poles move to the right but do not go beyond the nearest poles or zeros, respectively, of Yx, lying to the right. When Y1 has a pole or zero at λ = co, Eq. 14) shows that Y/ has a zero or a pole, respectively, at A = co; that is, the greatest zero or pole of Y1 will go to λ = co in y/.