provement of the stopband in H-plane bandpass filters w8x investigated the inductive iris-coupled resonator filters with increased-width waveguide sections. In this paper, H-plane waveguide structures with increased-width waveguide sections and mixed adjacent resonator widths are designed and their stopband behavior is studied.

2. FILTER SYNTHESIS PROCEDURE

The synthesis procedure determines the geometrical dimension of each coupling iris and the distance between two consecutive irises in the waveguide filter structure. The synthesis method uses the analysis method for obtaining the dataS-matrix of the discontinuities involved in the filter structure. required for the determination of the opening of each coupling iris.

The synthesis method is based on a formulation proposed by Rhodes for a distributed stepimpedance bandpass prototype w4x. Chebyshev type of response is considered in the design method. The generalized lumped element prototype for the bandpass filter is shown in Figure 1a and the equivalent distributed prototype containing impedance inverters is shown in Figure 1b.

CAD of Tapered Wa¨eguide Bandpass Filters 15

The distributed prototype consists of a cascade of impedance inverters connected by transmis- sion-line sections. Parallel-resonant circuits of the bandpass filter in Figure 1a are replaced by impedance inverters Ki j as shown in Figure 1b. An impedance inverter of impedance K can be defined as a two port network which, looking into its input port, inverts and scales to impedance K any impedance Z connected to its output port. Because, in waveguides an arrangement consisting of series and parallel resonators is difficult to realize, the use of impedance inverters in the synthesis method is a quite practical approach.

The procedure for designing H-plane corrugated waveguide bandpass filters is as follows w4x:

1.The midband guide wavelength lg0 is determined by solving:

lg L sin pllg Lg 0 / q lg H sin pllg Hg 0 / s 0, 1.

where lg L and lg H are the guide wavelengths in the resonator section at the lower fL and upper fH cutoff frequencies. For a narrow-band case:

lg 0 f	lg L q lg H	.	2.
2

Figure 1. Equivalent models of the corrugated waveguide filter including impedance inverters: a. bandpass filter prototype, b. bandpass filter containing impedance inverters.

16 Balasubramanian and Pramanick

A suitable numerical method such as the Newton]Raphson method w9x is applied for solving eq. 1..

2. Scaling parameter a is obtained from

	a s	lg 0			.	3.
		lg L sin	plg 0	/
			lg L

3. The number of resonators N is determined

by w10x,
	LA q RL q 6
N G				. 4.
	20 log g q 'g 2 y 1 /

4.The impedance of the distributed element Z and impedance inverter values K are determined by

	2 a sin		2 n y 1.p
Zn s			2 N
			y

¡ 2

2

np ¦

y

1

~

y

q sin

N

/

¥

4 ya

¢sin

2 n q 1.p

§

2 N

¡ 2

2

n y 1.p

¦

y

1

~

y

q sin

N

¥,

2 N

¢

§

4 ya

sin

2 n y 3.p

5.

n s 1, 2, . . . , N,

and

(y2 q sin2

np

kXn ,nq1 s

/

N

,

y

n s 0, . . . , N,

6.

where

1

sinhy1

1

.

7.

y s sinh

N

«

5.In uniform corrugated waveguide filters, the characteristic impedance of the resonator sections are identical and hence by scaling the impedance Zn to unity, the K-inverters

are normalized by

		kX
Kn , nq1 s		n , nq1		,	n s 0, . . . , N, 8.
	'
		Zn Znq1
Z0 s Znq1 s 1.					9.

6.In tapered corrugated waveguide filters, the characteristic impedance of the resonator sections are not identical, and hence normalization of the K-inverter values with the characteristic impedance is done so that the

quantity Kr 'Zn Znq1					is made invariant
when matching a practical network to a
prototype. Thus:
X	Kn , nq1				n s 0, . . . , N, 10.
Kn , nq1 s				,
	'
		ZnX ZnX q1
Z0X s ZnX q1 s 1,					11.

where, ZnX is the characteristic impedance of the resonator section n.

7.The filter structure can be represented by using the asymmetrical impedance inverter as shown in Figure 2. The width of the iris is determined so that the required impedance

Figure 2. a. Equivalent circuit of an asymmetrical iris, b. Equivalent impedance inverter representation.