SOME USEFUL DESIGN PARAMETERS OF NON-UNIFORM INTEGRATED BAND-PASS FILTERS

Important design parameters for a two-port three-terminal band-pass filter configuration of the integrated thin-film exponential distributed parameter R–C–KR microstructure are presented. The circuit exhibits load independent characteristics. The changes in the value of design parameters under varying loading conditions are given. Various plots illustrating the inter-relationship of the different parameters with each other that can serve as guidelines for a system designer to obtain a pre-assigned pattern of the performance characteristics of the microstructure are included.


INTRODUCTION
The paper presents a set of performance characteristics suitable for use as design curves for a two-port three terminal subnetwork configuration of the non-uniform distributed parameter (n.u.d.p) R-C-KR microsystem.The study is also extended to show the behaviour of the band-pass characteristics under varying loading conditions.The R-C-KR microstructure, which forms the mathematical model of a thin-film microsystem (Figure 1), consists of two thin-film resistors whose per-unit length (p.u.1) series impe- dances are R Ro exp (kx) and KR respectively, separated from each other by a dielec- tric film of p.u.1 shunt capacitance C Co exp (-kx), where the constants Ro and Co are resistive and capacitive constant respectively, k is the exponential taper constant and K is the ratio of the resistivity of one layer to that of another layer.Here is the length of the f'flms (represented by distance variable x).

DISCUSSION
The open circuit and loaded voltage ratio transfer functions (Tvo and Tvl)of Figure 2 obtained from the four-terminal exponential R-C-KR microstructure, are given in terms of their matrix parameter functions (m.p.f's) as'-    The normalised frequency ut is given by:- U wR tC whereCt =L Co exp(-kx) (1-e-k') Various design parameters of the above subnetwork have been computed for different combinations of 1, k and K under varying loading conditions as shown in the following figures (Figs. 3 7).The results show that the pass-band may be shifted from a higher to a lower frequency region by increasing K.The centre frequency Uco and bandwidth (b.w.)of the pass-band can be controlled according to the system designer's requirement by properly selecting the value of k and K as shown in Figure 3(a).The quality factor, Q, for both the loaded and unloaded configuration has been calculated and shown on the figures (Figures 3(a poor, almost negligible, characteristic for negative values of k. Figure 4 presents the design curves that show the effect of load on such a filter.It is observed that for given values of k and K and with varying load Rl, the pass-band remains the same.This means that the subnetwork is independent of load (which can be seen from Figure 6).The phase angle, , is minimum (in the vicinity of zero) for the centre frequency Uco of the pass- band in both loaded and unloaded conditions (Figures 3(b) and 4(b).
Figure 5 gives the variations in Tvoi and ut versus K for k 8.0 and 1.0.It is clear that there is a small increase in Tv as K decreases from 10 to 6, while Tvl increases rapidly for values of K, less than 2. Similarly the normalised frequency, ut, increases rapidly from 500 to 1000 for 0.1 < K < 1.The most important observation here is that there is a slow variation in the lower 3 db cut-off frequency, Ucl, for 0.1 < K < 1. However the upper 3 db cut-off frequency, Uc2, moves rapidly towards the higher fre- quency region for the same change in value of K. Variations of the centre frequency of the pass-band as a function of K for a given value of k are shown in Figure 7.It is found that there is a sharp variation in Uco for 0.1 < K < 1, while for higher K, it shows a smooth variation.These design data are equally applicable to other subnetworks of similar transfer func- tions in the C-R-KC microsystem. 2Another subnetwork of similar characteristics has already been reported. 3Important design parameters of the same subnetwork in a uniform configuration are to be reported shortly. FIGURE

FIGURE 4
FIGURE 4 Characteristics of the subnetwork with load for various values of k, K and R L.

FIGURE 5 FIGURE 7
FIGURE 5 Variation of u and ITvl vs. K.