IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, VOL. CAS-27, No. 4, APRIL 1980

A Special Case of the Achieser-Zolotarev Filter                   G. F. NUDD

Abstract - Achieser-Zolotarev filters are similar to the familiar Chebyschev filters except that the first ripple (DC end for low pass, HF end for high pass) is larger than the others, Iimiting the use ot these filters to applications where only the upper part (low pass), (lower part, high pass), of the passband will be used. The advantages of these filters are a slightly increased attenuation in the stopband and the ability to choose the impedance level within the filter. [1]

In this letter it is pointed out that the impedance level may be chosen to produce filters with all even numbered elements equal in value giving a simpler filter. Tables for design of these filters are provided.

As can be deduced from the tabulated element values of Achieser-Zolotarev filters provided by Levy [1], it is possible to design these filters with all even numbered elements (for example, all inductances) equal. Such a filter can be useful when a low- (or high-) pass filter is only needed to function in the upper (lower) part of the passband, the design giving a simpler and, therefore, cheaper filter with reduced documentation and reduced number of different components. Other advantages are that a production error of switching two inductances no longer has any effect, and further that the stopband attenuation is slightly better than the equivalent Chebyshev filter. In the case of filters using transmission lines instead of inductances the design allows the lines to be all of the same length. Tables of values are presented for quick use.

A Short Summary of the A-Z Filter

The Zolotarev filter is similar to the Chebyshev except that the one ripple nearest the zero-frequency end (low pass case) is allowed to become greater than the other ripples in the passband, (Fig. 1). The Zolotarev filter has, therefore, an extra design parameter l that specifies the useful part of the passband. This parameter can be used to vary the impedance level (and thus the element values) through the filter. By selecting the correct value for l , seven and nine element filters can be designed with all even numbered elements equal in value (see Tables I and II). With eleven element filters (Table III) it is possible to make elements E2, E6, and EI0 equal leaving E4 and E8 between 2 and 5 per cent different. Table III for 11 element filters is thus included although the even numbered elements are not all exactly equal, because in some filters differences of a few per cent can be adjusted out, still using nominally equal elements. The tables cover filters to the 11 th order, because these are the ones most used, although a filter of 13th order may be designed (being similar to the 11th) and still higher orders are probably possible.

Fig.1. Amplitude / frequency response of N=9 0.25dB ripple low pass filter.

The filter values are tabulated in the usual manner 1) normalized 2) the value is an impedance for series elements and an admittance for parallel elements. Five filters for each order are tabulated, with values of return loss of around 12.5,17.5,- - - 32.5 dB intended to be specified as better than 10,15,20,25,30 dB. These values equate to a ripple of 0.25, 0.08... 0.0025 dB (better than 0.3,0.1 ... 0.003 dB) and a v.s.w.r. of 1.62,1.312... 1.049 (better than 2,1.5,1.2,1.1,1.05). The filter passband extends from the corner down to the frequency X which varies from 0.246 to 0.6556 according to the filter order and return loss needed, and it is of course necessary to check that this passband is large enough for the application in mind. In the high-pass case the passband extends from the corner to a frequency of 1/l . The tables also give the amplitude response in decibels of each filter.

REFERENCES

[l] R. Levy, "Characteristics and element values of equally terminated Achieser-Zolotarev quasi low pass filters," IEEE Trans. Circuit Theory, vol. CT-18, pp. 538-544, Sept. 1971. Manuscript received February 20; revised May 29, 1979. The author is with AEG Telefunken, Department N12 E21, D7900 Ulm, Germany.
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