As the number of wireless communications devices continues to increase logarithmically, a natural by-product is a crowded spectrum. One method of addressing this crowded spectrum integrates tunable filters in systems.

Tunable filters can provide surprising benefits, especially for multimode portable terminals and tunable transceivers. However, tuneability causes undesirable changes in other important characteristics such as deviation of insertion loss, bandwidth and matching conditions. Implementing tuning elements (varactors for instance) may lead to a drastic degradation of the circuit's Q, for example.

This article presents the theory and application of stepped-impedance planar resonators and filters with L and T - coupling sections. It will also introduce an active device for loss compensation.

Tuned resonators and filters can be realized through a number of methods 1, 6. The topology used below is based on step impedance sections and varactor diodes in series or parallel (see Figure 1). It consists of the two lines with different impedances, Z1 and Z2 and electrical lengths q1 and q2, respectively. A varactor diode used as a tuning element is placed in the center of the resonator. Reactive coupling elements Xc are used at the input/output of the resonator.

The analysis of resonance conditions for the configurations shown in Figure 1 can be carried out on a transmission matrix approach, similar to one described in ². More detailed analysis demonstrates that frequency tuning range and mode separation depend on parameter ζ = θ₁/(θ₁ + θ₂), as well as a type of coupling element capacitive or inductive.

The best results are observed for the parameter θ = 0.75 - 0.8. These are illustrated in Table 1. The following parameters of the resonator are assumed: Z₁ = 20Ω Z₂ = 80Ω; limits of a varactor capacitance C_v = 0.5 - 2.5 pF; operating frequency - 1.8 GHz, system impedance - 50 Ω.

Comparing the results of this table, it can be concluded that the resonators with a series varactor demonstrate higher separation between principal and nearest higher modes, while its counterpart, with a parallel varactor, has better tuneability.

The major drawback of tuned resonators is a change of bandwidth in the tuning process. This issue is caused by the frequency behavior of reactances of coupling elements. For illustration purposes, Figure 2 shows this effect for a step-impedance resonator with a varactor in series. An approximated a 50% widening in bandwidth has taken place from 20 MHz to 32 MHz.

The following resonator parameters are assumed: Z₁ = 20Ω; Z₂ = 80Ω; limits of a varactor capacitance C_v = 0.5 - 2.5 pF; operating frequency - 1.5 GHz; system impedance - 50Ω; coupling capacitor - 0.5 pF. The resonator is designed on the basis of microstrip line with substrate ε_r = 2.6, h = 2 mm, and loss tangent tgδ = 0.001.

The first step in stabilizing bandwidth uses proper reactive coupling elements to compensate for bandwidth change. One such element is the L-section³. Among eight available configurations, the capacitor-based L-section is preferable when taking into account fabricating facilities. Table 2 and Figure 3 present the effects of bandwidth stabilization when L-type coupling elements are used instead of a single capacitor. Bandwidth stabilizing factor is about 50.

To verify the bandwidth stabilization effect, the experimental version of the step-impedance resonator was fabricated with specifications shown in Table 3. The comparison of the calculated and measured transmission coefficients, S₂₁, are presented in Figure 4. Taking into account the biasing circuit, an agreement between calculated and measured data is observed.

Bandwidth stabilization with L-type capacitor coupling elements at input/output of the step impedance resonator.

The same approach can be applied to the design of passively coupled tuned resonators with constant bandwidth. In this case, choose both the external and internal coupling elements to compensate for a change of coupling coefficients in the process of tuning. Figure 5 demonstrates the transformation of a single resonator to its coupled counterpart based on capacitive L-type sections. As a result, the coupling element between resonators can be formed using a T-type capacitive section. The configuration of a tuned step-impedance filter of the second order is shown in Figure 6.

Optimization, based on the simplex search technique, finds a specification of the T-section providing constant bandwidth of the second-order tuned filter. Table 4 demonstrates characteristics of such a filter before and after internal coupling elements are optimized. The frequency response of the tuned second-order filter is shown in Figure 7. The bandwidth stabilization factor is 12, but the insertion loss has increased to 10 dB. Thus, a measurement must be undertaken for loss compensation.

An experiment was carried out with the microstrip second-order tuned filter. Its specifications are given in Table 5. A comparison of calculated and measured filter performance is depicted in Figure 8, which takes biasing circuits into account.

Having chosen the topology of uncoupled and coupled tuned resonators with near-constant bandwidth, a proper filter of higher order can be built up. However, insertion losses are increased drastically. As a result, special measures for their compensation must be suggested in a practice.

One way to do this is to transform a passive tuned filter to its active counterpart by adding an active device. A variety of microwave active filter configurations are available for practice⁴. Recently, an idea based on actively coupled resonators was presented⁵. Such resonators are almost non-interactive because of the use of a transistor as a coupling element between resonators. Therefore, the circuit sensitivity to fabricating tolerances is reduced by applying them in a cascade arrangement.

Different combinations of resonators can then be applied to achieve the desired filter characteristic. The two passively coupled resonators are actively coupled in a cascade configuration shown in Figure 9 to form the equivalent active filter of the fourth order. The bandwidth is almost constant, but insertion loss is increased about 5 dB when the filter is tuned toward higher frequencies. Therefore, an active device must provide a gain of 9 dB at low, and 14 dB at high frequencies of the tuning range for a loss compensation and amplitude equalization. The above requirement has been realized using commercial, off-the-shelf (COTS) transistors. The matching elements of the amplifier have been designed to provide the required slope of the gain.

The active filter consists of two Al₂O₃ substrates 48 × 60 mm², having h = 1 mm, ε_r = 9.6. Each is used for arranging passively coupled resonators and matching circuits of the active device on its input and output. The active device is placed between them. Figure 10 demonstrates the final performance of the active tuned filter of the fourth order with the constant bandwidth.

By implementing an active device, the full compensation of the insertion loss is achieved. However, the change of return loss takes place when the filter is tuned. This drawback can be eliminated by more careful design of the matching elements of the active device.

When designing tunable resonators and filters with constant bandwidth, implement L-and T-types of coupling elements to achieve the stabilization of bandwidth in the tuning process. An active device with predicted slope of the gain can be used for a loss compensation. The final active filter layout and performance has been verified in experiments carried out with fourth-order filter in a cascade configuration.

This work has been supported by EC INTAS Project 96-0851, and the authors would like to thank the project coordinators Prof. B. Jarry (I.R.C.O.M., France) and Prof. M.Guflielmi (ESA ESTEC, The Netherlands) for their useful advice and discussions of some problems associated with the topics considered, as well as engineer V. Smirnoff (SibSUTI, Russia) for his help in experiments.

1. F.E. Van Vliet, “Modern Very Narrow Band MMIC Filters and Tuning Methods”, Paris EuMW'2000 - Workshop (WS8) - “New Techniques and New Technologies for RF and Microwave Filters”

2. B.Kapilevich, R.Lukyanets, “B. Kapilevich, R.Lukyanets, “Modeling Varactor Tunable Microstrip Resonators for Wireless Applications,” Applied Microwave & Wireless, Vol.10, no.7, September 1998, pp.32 - 44; Vol. 13, no. 5, May 2001, pp. 54-64.

3. P.H.Smith, “Electronic Applications of the Smith Chart in Waveguide, Circuits and Component Analysis”, McGraw Hill Book Co., 1969.

4. B. Kapilevich, “Microwave Active Filters for Wireless Applications”, Paris EuMW'2000 - Workshop (WS8) - “New Techniques and New Technologies for RF and Microwave Filters.”

5. F. Sabouri-S, C.Christensen, T.Larsen, “A Single-Chip GaAs MMIC Image-Rejection Front-End for Digital European Cordless Telecommunications”, IEEE Trans. on MTT, vol.48, no.8, August, 2000, pp.1318 - 1325.

6. K. Jeganathan, “Design of Simple Tunable/Switchable Bandpass Filter” Applied Microwave & Wireless, March 2000, pp.32 - 40.

Boris Kapilevich is a professor at Siberia State University of Telecommunication & Informatics, Novosibirsk, Russia. He received his M.S. degree from Tomsk State University in 1961, a Ph.D. in 1969 from Novosibirsk State Technical University and a Dr.Sc.(technol.) in 1986 from Moscow Power Energy University. He has more than 30 years of experience in analysis and design of various microwave/RF components and devices for the communications industry. His teaching and research interests are in areas of microwave and RF components for mobile and space communications. He can be reached at his office by tel.: +007-3832-660943, by fax: +007-3832-222581 or by e-mail: boris@neic.nsk.su.

Roman Lukjanets is a Ph.D. student at Siberia State University of Telecommunication & Informatics, Novosibirsk, Russia. He received his M.S. degree from Siberia State University of Telecommunication & Informatics in 1996. His research interests are focused in microwave and RF components for mobile communications, including microwave active filter. Contact the authors at: Siberia State University of Telecommunications and Informatics 86 Kirova str., Novosibirsk, Russia - 630102.

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