cross-coupling in coaxial cavity filter -a tutorial overview.pdf

1368IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 4, APRIL 2003 Cross-Coupling in Coaxial Cavity FiltersA Tutorial Overview J. Brian Thomas, Member, IEEE AbstractThis paper presents a tutorial overview of the use of coupling between nonadjacent resonators to produce transmission zeros at real frequencies in microwave filters. Multipath coupling diagrams are constructed and the relative phase shifts of multiple pathsareobservedtoproducetheknownresponsesofthecascaded triplet and quadruplet sections. The same technique is also used to explore less common nested cross-coupling structures and to pre- dict their behavior. A discussion of the effects of nonzero electrical length coupling elements is presented. Finally, a brief categoriza- tion of the various synthesis and implementation techniques avail- able for these types of filters is given. Index TermsCoaxial cavity filter, cross-coupling, nested cross- coupling, tutorial. I. INTRODUCTION L IFE IS really simple, but we insist on making it compli- cated”Confucius. This paper will attempt to provide a simplified, qualitative, and intuitive understanding of an impor- tant and complex topic in the field of microwave filters: cross- coupling, especially cross-coupling in coaxial cavity filters. The everincreasing need for capacity in cellular and personal communications systems (PCSs) has led to more stringent re- quirements for basestation filters and duplexers. The transmit and receive bandpass filters composing basestation duplexers may have required rejection levels greater than 100 dB on one side of the passband and, at the same time, have very mild re- jection requirements on the opposite side 1. The technique of cross-coupling to produce asymmetric frequency responses has become popular for these applications because it concentrates the filters ability to provide rejection only over the band where it is needed. This “concentration of rejection” means the filters response is trimmed of unnecessary rejection anywhere it is not absolutely required, increasing the overall efficiency of the de- sign. The tradeoff in slope between the bandpass filters upper andlowerskirtisoptimizedfortheparticularrequirement.Fig.1 shows a filter response with and without two transmission zeros on theupperskirt.Using the technique ofcross-coupling to pro- duce transmission zeros, the rejection above the passband is in- creased, while rejection below the passband it is relaxed. This can reduce the number of resonating elements required to meet a specification and this, in turn, reduces the insertion loss, size, and manufacturing cost of the design, though at the expense of topological complexity and, perhaps, development and tuning time. Manuscript received January 31, 2002. Theauthor iswiththeEngineeringDepartment,BaylorUniversity,Waco,TX 76703 USA. Digital Object Identifier 10.1109/TMTT.2003.809180 Fig. 1.Two possible filter responses, with (dashed line) and without (solid line) finite transmission zeros produced by cross-coupling. Note the increase in rejection above the passband and the relaxation in rejection below. This asymmetrical response concentrates a filters ability to provide rejection only where it is required. Not only has the industry seen electrical requirements be- come more stringent, but mechanical packaging requirements havebecomelessflexibleduetobasestationminiaturizationand multiple-sourcing considerations. The choices of overall size andshapeandconstraintsinconnectorlocationsplayavitalrole in determining a filters layout, topology, and internal structure. The differences can be substantial between a filter with con- nectors on the same surface versus opposite surfaces, all other parameters being equal. Cross-coupling provides an additional degree of flexibility in these design scenarios. When all things are considered, the use of cross-coupling produces a superior design for many requirements. It is not surprising then that these circuits have been the subject of the fields best and brightest for some time 2. However, despite the prodigious numbers of expert-level publications available, the nonspecialist RF engineer may be left with the impression that cross-coupling is unapproachably complex: likely a mix- ture of Maxwells equations and Voodoo magic. The intent of this paper is to provide a general understanding of some fundamental cross-coupling techniques by using mul- tipath coupling diagrams to illustrate the relative phase shifts of multiple signal paths. This technique can also be used to under- stand, and aid in the design of, less common topologies using nested cross-couplings. Section II reviews the simplified phase relationships of fundamental components in the equivalent circuit of coaxial cavity filters. Although the technique of cross-coupling can be 0018-9480/03$17.00 © 2003 IEEE THOMAS: CROSS-COUPLING IN COAXIAL CAVITY FILTERS1369 Fig. 2.Prototype equivalent circuit for combline or coaxial cavity filter. Shunt inductor/capacitor pairs represent individual resonating elements and the series inductors represent the dominantly magnetic coupling between resonators. used with other types of filter realizations, (such as dielectric resonators, microstrip, or waveguide) special attention will be given to coaxial cavity filters because of their dominant role in wireless basestation filter applications. Section III illustrates the multipath coupling diagram ap- proach to describe the operation of well-known cascaded triplet (CT) and cascaded quadruplet (CQ) sections. The techniques of Section III require slight modification for realizations other than coaxial cavities; however, these are beyond the scope of this tutorial. In Section IV, less common nested structures are explored, similar to the design of 3, where a five-section dielectric resonator filter with three transmission zeros is described. Section V gives a very broad description of the various imple- mentation techniques in use today. Special focus will be given to methods accessible to most RF engineers. The conclusions are summarized in Section VI. II. PHASERELATIONSHIPS Combline and coaxial cavity filters may be represented by the prototype equivalent circuit of Fig. 2 4. Although simple lumped components are being used to represent three-dimen- sional structures with complex field patterns, nonetheless, they are useful and illustrative for purposes of this tutorial. The shunt inductor/capacitor pairs represent individual res- onating elements and the series inductors represent the domi- nantlymagneticcouplingbetweenresonators.Thetotalcoupling between adjacent resonators has both magnetic and electric components. However, these are out of phase with each other; the total coupling is the magnetic coupling less the electric coupling 5. This is the reason a tuning screw placed be- tween the open ends of two resonators increases the coupling between them (see Fig. 3). The screw decreases the electric coupling and, hence, increases the total coupling (less is sub- tracted from the total). By the same reasoning, a decoupling wall between the shorted ends of two resonators decreases the overall coupling by decreasing the magnetic coupling. For a more rigorous treatment of the coupling phenomenon, see 69. The off-resonance (away from the passband) behavior of the components of Fig. 2 is utilized to produce the destructive in- terference resulting in transmission zeros and, therefore, needs to be understood. Let the phase component of the-parameters andbe denotedand, respectively. Consider the series inductor of Fig. 4 as a two-port device. A signal en- tering port 1 will undergo a phase shift upon exiting port 2. This is, and it tends toward90 . The fact that the magnitude ofis quite small at this point is not problematic in that the Fig. 3.Coupling fields between adjacent resonators. Total coupling may be affected by decoupling walls and/or tuning screws. Fig. 4.Primary coupling between coaxial cavity resonators may be modeled as a series inductor. When considered as a two-port device, the phase of? ?approaches?90 . off-resonance behavior is what is of concern. It should be em- phasized that, although this phase shift only approaches90 and, in general, may be much less, for purposes of general un- derstanding, the approximation of90 is quite useful. Thus, (for series inductors).(1a) The shunt inductor/capacitor pairs of Fig. 2 (resonators) can also be thought of as two-port devices. However, the phase shift at off-resonance frequencies is dependent on whether the signal is above or below resonance (see Fig. 5). For signals below the resonant frequency (below the passband), the phase shift tends toward90 . However, for signals above resonance, the phase shift tends toward90 . This behavior is due to the simple fact that below resonance, the resonator is dominantly inductive and an inductorin shunt is thedualofa capacitor inseries. Similarly for frequencies above resonance; the resonator is dominantly 1370IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 4, APRIL 2003 Fig. 5.Coaxial cavity resonators may be modeled as shunt inductor/capacitor pairs. When considered a two-port device, phase?approaches?90away from resonance, and passes through 0 at the resonant frequency. capacitive and a shunt capacitor is the dual of a series inductor. Thus, (for resonators below resonance)(1b) (for resonators above resonance).(1c) Although there are no series capacitors in Fig. 2, the series capacitor is an important cross-coupling device. The phase shift is (for series capacitors).(1d) These phase shifts should not be confused with coupling co- efficients commonly found in the literature, which may be of opposite sign as the phase shift of (1a)(1d). III. MULTIPATHCOUPLINGDIAGRAMS A. CT With Inductive Cross-Coupling Consider the three resonator structure of Fig. 6(a) and (b), whichrepresentsaCTsectionusinganinductivecross-coupling between resonators 1 and 3. The resonators of the equivalent circuit (Fig. 2) have been replaced by circles, but the inter- resonator inductors remain shown. Using the relationships of Section II, the phase shifts can be found for the two possible signal paths. Path 123 is the primary path, and path 13 is the secondary path that follows the cross-coupling. When summing the phase-shift contributions of the individual components, the contributions from resonators 1 and 3 are not required. Both paths share a common beginning and ending location; only the contribution of circuit elements internal to resonators 1 and 3 need to be considered. (Indeed, 1 and 3 need not even be resonators; the signals can be combined at the input or output of the filter itself (see 3).) Furthermore, resonator 2 must be considered both above and below resonance. Table I shows these results. (a) (b) Fig. 6.(a) Multipath coupling diagram for CT section with inductive cross-coupling and possible frequency response including transmission zero (solid line). (b) Physical representation of CT section of (a). Below resonance, the two paths are in phase, but above res- onance, the two paths are 180 apart. This is exactly the case at one frequency only (here, approximately 2030 MHz), but is approximately the case for frequencies in the region (approxi- mately 20202040 MHz). This destructive interference causes a transmission zero or null on the upper skirt. Stronger coupling between 1 and 3 causes the zero to move up the skirt toward the passband. Decreasing the coupling moves it farther down the skirt. This type of cross-coupling can be realized by a window between the cavities in the same way the primary coupling be- tween resonator 1 and 2 or between 2 and 3 is realized. This is THOMAS: CROSS-COUPLING IN COAXIAL CAVITY FILTERS1371 TABLE I TOTALPHASESHIFTS FORTWOPATHS IN ACT SECTIONWITHINDUCTIVE CROSS-COUPLINGSEEFIG. 6(a) Fig. 7.Multipath coupling diagram for CT section with capacitive cross-coupling and possible frequency response including transmission zero (solid line). Also shown is the standard Chebyshev response without cross-coupling (dashed line). advantageousinthatnoadditionalcomponentsarerequiredsee Fig. 6(b). B. CT With Capacitive Cross-Coupling In Fig. 7, the inductive cross-coupling between resonator 1 and3hasbeenreplacedwithacapacitiveprobe.Thephaseshifts for the two possible signal paths are given in Table II. Again, path123istheprimarypathandisnodifferentthaninTableI. Path 13 is the secondary path and now has a90 (positive) phase shift. Thus, for a capacitive cross-coupling, the destruc- tive interference occurs below the passband. C. CQ With Inductive Cross-Coupling In Fig. 8, the four-resonator scenario known as the CQ is shown with an inductive cross-coupling. The primary path in this case is 1234; the secondary path 14, therefore, by- passes two resonators. As Table III shows, transmission zeros are not produced at any real frequencies above or below the passband. However, zeros at imaginary frequencies can be pro- duced, which have the effect of flattening the group delay over the passband. These types of responses are useful in extremely linear systems using feed-forward amplifiers. The flattening of TABLE II TOTALPHASESHIFTS FORTWOPATHS IN ACT SECTIONWITHCAPACITIVE CROSS-COUPLING(SEEFIG. 7) Fig.8.MultipathcouplingdiagramforCQsectionwithinductive cross-coupling and possible frequency response. TABLE III TOTALPHASESHIFTS FORTWOPATHS IN ACQ SECTIONWITHINDUCTIVE CROSS-COUPLING(SEEFIG. 8) the group delay also has the effect of flattening the insertion loss. Midband losses increase slightly while band-edge rolloff effects are decreased.1These effects are not apparent from this analysis. See 10 and 11 for a more detailed analysis of filters with transmission zeros at imaginary frequencies. D. CQ With Capacitive Cross-Coupling Replacing the inductive element between resonators 1 and 4 with a capacitive probe, the other type of CQ is formed. This topology is particularly interesting, as Table IV shows, because transmission zeros are producedboth aboveand below thepass- band (see Fig. 9). 1R.Wenzel,“Designing microwavefilters, couplersand matchingnetworks,” a video tutorial published by Besser Associates, Los Altos, CA, 1986. 1372IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 4, APRIL 2003 TABLE IV TOTALPHASESHIFTS FORTWOPATHS IN ACQ SECTIONWITHCAPACITIVE CROSS-COUPLING(SEEFIG. 9) IV. NESTEDSTRUCTURES It has been shown that two signal paths can be combined to produce a transmission zero. In this section, nested structures having three or more signal paths will be explored. Consider first the circuit of Fig. 10. The outer path 123 combines with 13 to form one transmission zero. Simultaneously, the interior path 134 combines with the innermost path 14 to produce a second transmission zero. Both are on the upper skirt. See Table V. In the same way, the circuit of Fig.11 produces two transmis- sion zer