inverter value is realized via ref. 11:

L s 1 q 1 a y d.2 q b y c.24 , 13.

where a, b, c and d are normalized elements of the ABCD matrix, and Z1 and Z2 are normalized guide impedances of the tapered waveguide resonator sections. The reference planes are obtained from the equations:

where the angles f1 and f2 are expressed in radians.

The K-values can also be obtained directly from the scattering matrix S without converting the S matrix into the ABCD matrix. The voltage standing wave ratioVSWR. seen at one port of the inverter when the other port is terminated in its characteristic impedance is given by

where <S11 < is the absolute value of the reflection coefficient seen at one port when the other is terminated in its characteristic impedance. The reference plane locations are given by the following equations:

CAD of Tapered Wa¨eguide Bandpass Filters 17

A root-seeking program is implemented to find the value of the iris width. The Newton]Raphson method using the derivative w9x is implemented for faster convergence to the solution. Because the method uses gradient information, it is very efficient in converging toward the solution. The gradient is calculated using the perturbation method as the function is unknown in analytical form.

8.Finally, the physical length of the resonator formed by the ith and i q 1.th iris is found by

where lg 0 is the guide wavelength. The guide wavelength remains a constant for the E-plane structures as the guide wavelength for the dominant TE10 mode does not depend on the height of the guide. However, in H-plane tapered corrugated waveguide filter structures the change in width of the cavities between any two iris types of discontinuities changes the guide wavelength. Hence, the appropriate guide wavelength for each of the cavities should be substituted in place of lg 0r2 when calculating the length of the cavity or resonator. In practice, f1 and f2 may be realized as negative values and by absorbing such a negative value into the positive adjacent length, the length of the filter structure can be shortened.

3. RESULTS

The method described was used to design an H-plane filter with the passband extending from 10 to 10.2 GHz and a 16-dB return loss. Waveguide dimensions of 22.86-mm width and 10.16mm height were used. A 2-mm iris thickness was used in the calculations. Figures 3 and 4 show the simulated performance characteristics of a 4-pole conventional H-plane uniform corrugated waveguide structure in the passband and stopband region, respectively. The simulated response compares very well with the desired frequency response characteristics. However, at 16.5 GHz a spurious passband appears in the stopband.

In order to improve the stopband performance, the filter structure with increased-width wave-

18 Balasubramanian and Pramanick

Figure 3. Simulated passband characteristics of the uniform corrugated pass filter; w1 s w5 s 10.055, w2 s w4 s 6.206 mm, w3 s 5.790 mm, l mm, lR2 s lR 3 s 18.365 mm, a1 s a4 s a2 s a3 s 22.86 mm.

waveguide band- R1 s lR 4 s 16.933

guide resonator sections as shown in Figure 5 was designed. Figure 6 shows the comparison of stopband characteristics between the filters with uniform and increased-width cosine tapered resonator sections. The harmonic which appears at 16.5 GHz in the uniform case is shifted to 17.5 GHz when tapered corrugated waveguide filter structure with increased-width resonator sections are used. The resonator length of the tapered increased-width structure is smaller in compari-

Figure 5. H-plane tapered increased-width corrugated waveguide bandpass filter.

son with the resonator length obtained for a uniform waveguide structure. Hence, the overall length of the filter is decreased.

Another structure is formed by making the widths of the waveguide resonator sections all equal to 25 mm while the input and output waveguides of the filter structure are 22.86 mm wide. Figure 7 shows the comparison of stopband characteristics between the uniform and 25 mm through tapered filters designed. The harmonic which appears at 16.5 GHz in the uniform case is shifted to 17.0 GHz for the through tapered filters.

Instead of increasing the widths of the waveguide resonators following a particular tapering

profile, a structure with resonators having widths which are alternately increased and decreasedmixed-width. was designed. Same design parameters were used for the design and Figure 8 shows the comparison of stopband characteristics between the uniform and the filters designed with 25 and 19 mm tapering and 25 and 20 mm mixed tapering. The 25 and 19 mm tapering structure stopband response is very poor while the 25 and 20 mm tapering structure stopband response is extended compared with the uniform tapering. There are many possible tapering profiles which would give a satisfactory performance in both the passband and stopband region. Hence, several designing and redesigning parameters may be re-