narrow band filter design

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TABLE 1. Chebyshev lowpass prototype. .036-dB Ripple, 20.8 dB Return Loss, 1.20 VSWR
N g0 g1 g2 g3 g4 g5 g6 g7 g8 g9 g10
N i =1
gi
2 3 4 5 6 7 8 9
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Narrow-Band Microwave Filter Design
Daniel G. Swanson, Jr.
A
s early as 1951, Dishal [1] recognized that any narrow-band, lumped-element, or distributed bandpass filter could be described by three fundamental vari ables: the synchronous tuning frequency of each resonator, f 0 ; the couplings between adjacent resonators, K r, r+1 ; and the singly loaded or external Q of the first and last resonators, Q e x . He also demonstrated that filter hardware could be tuned or aligned using knowledge of these fundamental parameters. For purposes of this discussion, “narrow band’’ is defined to be up to 10% relative bandwidth and perhaps as high as 20% relative bandwidth. In a later paper, Dishal [2] outlined a design procedure for tapped interdigital filters using the f 0 , 1.PHOTOCREDIT K r, r+1 , and Q e x parameters. Once the required K s and Q e x s are known, Dishal’s method uses measured experimental hardware to generate a design curve for each parameter. Almost 15 years later, after microstrip technology became more popular, Wong [3] demonstrated how Dishal’s method could be applied to the design of microstrip distributed filters with tapped inputs and outputs. Again, experimental data was used to generate design curves for coupling between resonators and external Q . Before electromagnetic (EM) field solvers became widely available, generating these two design curves required a rather tedious process of measuring, modify-
1.0000 0.8215 1.4615
1.1999 0.9921
1.1592 2.7265 4.4733 6.3831 8.2836 10.2739 12.2173 1.0000 14.2340
to several different planar filter topologies. The discussion of coupling concepts for planar filters in [7] is the most complete one currently available. In this article, we will combine Dishal’s concepts, EM simulation, and the port-tuning concept [8], [9] to outline a very general and powerful procedure for narrow-band filter design. When applied to an EM-based filter prototype, port tuning gives a direct indication of the magnitude and direction of the tunings needed to correct coupling errors and resonator frequency errors. An EM-based filter prototype potentially captures all the physics of the real hardware and includes secondorder effects that may be impossible to describe using analytical models. After iteratively reducing all the errors in the EM-based prototype, we can be confident that the first hardware prototype that we build will meet our performance goals. This design methodology can be applied to simple all-pole Chebyshev filters and to more complex cross-coupled filters that place transmission zeros in the stopbands.
0.6323 0.8185 0.8989 0.9393 0.9622 0.9763 0.9857 0.9921
0.5269 1.0895 1.2843 1.3677 1.4104 1.4353 1.4509 1.4615
1.1999 0.8185 1.5410 1.7691 1.8636 1.9115 1.9392 1.9568
mating filter order. Note that the graphs and equations assume an ideal, symmetrical Chebyshev response. Very few microwave filters have symmetrical stopband responses, so the required order may be higher or lower than what we originally estimate. With the ripple level and order N determined, we can go to the tables or equations for the normalized lowpass prototype values. Table 1 lists the normalized element values for a .036-dB ripple, Chebyshev lowpass prototype. At this point, we can estimate the midband filter loss using the expected average unloaded Q for the resonators Loss( f0 ) = 4.343 f0 f Qu
© ARTVILLE
ing, and remeasuring a set of experimental hardware. In the last few years, it has become more common to generate coupling and external Q curves using data from an EM field solver. Puglia [4], [5] and Rhea [6] have published excellent tutorials on combining Dishal’s concepts with EM simulation. Hong and Lancaster [7] also present examples of how these concepts can be applied
N i=1
gi (dB),
(1)
Dishal’s Method
A bandpass filter specification generally includes the desired center frequency, percentage bandwidth, maximum insertion loss in the passband, and several required rejection levels in the stopbands. There will also be a specification on the minimum return loss in the passband. A return loss of 26.4 dB (1.10 VSWR) corresponds to a prototype ripple level of .01 dB. A return loss of 20.8 dB (1.20 VSWR) corresponds to a prototype ripple level of .036 dB. Many mechanical filters with tuning screws can eventually be tuned to their designed return loss level. In printed filters, which are much harder to tune, we might design for 20-dB return loss and hope that we achieve a minimum of 15 dB in practice. At the system level, we would like to have components with a minimum return loss around 15 dB to avoid mismatch ripple when components are cascaded. Once the prototype ripple level has been determined, the filter order N can be estimated based on the desired stopband rejection. The graphs and equations in Matthaei, Young, and Jones [10] are very useful for esti-