COMMUTATION THEORY AND A NEW TECHNOLOGY OF DESIGN OF

MICROWAVE FILTERS

B.V. Sestroretzkiy, K.N. Klimov, V.Yu. Kustov, Yu.O. Shlepnev

JSC "Vega-Star", Moscow, RUSSIA

Abstract

A new theory of synthesis of microwave filters consisted of "null-pole" elements that are equivalent for resonant frequencies f1 and f2 to two resistances with ratio of values

theories of the synthesis, the emphasis here is on optimization of attenuation characteristics in active resistances circuit part (values of active losses on poles frequencies are rigidly limited) instead of optimization in reactive circuit part (infinite attenuation peaks are allowed). This new approach makes it possible to form rectangular attenuation characteristic over a stopband at minimum losses value over a passband. It is shown that "null-pole" elements may be arranged along a transmission line and separated by small segments of the line (λ / 12), that allows to design compact microwave filters. Design of filters that do not have simple circuit models is performed on the base of the topological synthesis using general purpose electromagnetic programs TAMIC. A filter with losses over the passband 10.9-11.7GHz less than 0.2dB and with attenuation over the stopband 14.0-14.5GHz no less than 82dB is designed and communicated as an example.

Theoretical backgrounds

Substantial improvements of the main parameters of microwave filters (active losses over the passband, selectivity, the overall dimensions) may be achieved throughout the extension of the "quality" concept of the lumped switching diodes [1,2] to the "null-pole" elements of the band passing filters.

To obtain an optimal attenuation value in switching devices of any one type at one frequency f0 , the circuit shown in Fig.1.a and comprising a diode impedance Z1,2 (Z1 = r1 + jx1 ;

Z2 = r2 + jx2 for two values of the operating voltage) and two reactive impedance jxA and jxB should have two resonant conditions (see Fig.1.c). As this takes place, the circuit in the Fig.1.a is transformed at the frequency f0 to the circuit shown in Fig.1.b with switching resistances R1 and R2 . The attenuation values for "on" Lz0 and "of" Lpo conditions are related by equations:

By analogy with circuits in the Fig.1.a, the circuit "null-pole" (NP) shown in Fig.2.a consists

of three impedances (ZL1 = jωL1 +r1 ; ZL2 = jωL2 +r2 ;ZC =(jωC + g)−1 ) and is transformed to the circuits shown in Fig.2.b at two resonant conditions at frequencies f1 and f2 (see

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Fig.2.c). The equations (1) are valid for the circuit in Fig.2.b. As this takes place, the value of NP element "quality" at given reactive elements own Q-factor Q0 = ωL / r =ωC / g is determined by:

If M have been chosen, then passband (ω = ω1 ±δz ) and stopband (ω = ω2 ±δp ) at the levels

The equations (3)-(5) determine the selectivity of one "null-pole" element of the first order with chosen Q0 and α. It does not matter how NP element will be realized and what circuit will be used for its description. Neighboring null and poles should absent in the vicinity of the frequencies f1 and f2 . Analyzing the characteristics of the real NP element shown in Fig.3 by means of equations (3-5), it is possible to estimate the values Q0 and M achieved in the design.

If selectivity of NP element of the first order with given Q0 and α is insufficient, the effective value of Q0 may be increased using circuits of n NP elements connected in the line as shown in Fig.4 or using compensating channel with a resistance R as show in Fig.5. The attenuation of the circuits in the Fig.5 at θ = 90° (element of NPn) is determined by:

That is obtain from (6) at n =∞. When L∑z0 is small (≤ 0.4dB) and n = 3 −8 (see Fig.6) the values of L∑p0 are 28 −40dB and close to the optimal value ( L∑p0 )opt = 45dB. The single NP element gives Lp0 =16dB. Substituting values L∑p0 = 40dB (n = 8) and L∑z0 = 0.4dB in (2) we determine increasing Keff by 20 times (2000 instead of 100) and increasing Q0eff by 4.5 times. For a (NP)n element the equation for Lp and δp is equivalent of (5):

For the circuit in the Fig.5 (NPR ) at θ = 90° the resistance R is adjusted so, that signal passing through the parallel channel with R compensates completely the signal

then one of a (NP)n element while the values L∑po are close. The NP R element at K ≥1200 is more profitable at ( Lz0 )opt ≤ 0.4dB, since it gives grater values L∑po (62dB instead of 40dB for

the (NP)n element at n = 8).

On the base of the elements of chosen types the demanded band passing filter is formed. For instance, the characteristics of a filter with one passband 2∆fz and one stop band 2∆f p and

characteristics of its elements are shown in Fig.7.

Let us carry out the design of a filter consisted of NP elements of the first order connected in the line as shown in Fig.4. All NP elements will be considered to have equal

where: θ - electric length of the line segment between the NP elements, Lpz - attenuation

value of one NP element at the intersection point. Two neighboring elements give an additional "null" at θ = 0° ( L∑p =1) and form an "anti resonant" condition at θ = 90°

( L∑p = 4 L2pn ). More optimal variant may be realized at a particular condition (δpz ′ ≈ δpz ″ = δpz ), when θ = 30° and:

decrease losses in the stopband, the Lp0 level of the elements NP should be reduced to the level Lp :

Using equations (15-18) and taking into account (3-5) it is possible to estimate characteristics of the filter that could be realized using the geometrical synthesis procedure [3-6].

Numerical example

To cite one example of how to design a filter with the next parameters:

f1 =11.35±0.35GHz, f2 =14.25±0.25GHz, L∑z ≤ 0.3dB, L∑p ≥80dB. The filter is expected to

be formed from rectangular waveguide segments with cross section dimensions of 19õ9.5 mm2. The own Q-factor of a waveguide resonator are Q0 = 2000 that follows from the

known formula. For Q0 = 2000 and α = f2 /f1 =1.25 we determine K =1.6 105 . The filter will

section of the filter. Using (5) for Q0 = 2000 and Lz0 =1.004 we obtain ∆fz / f1 = 0.016 that

is less than demanded bandwidth ∆fz /f1 = 0.035. The bandwidth of the filter is assumed to be expanded by adjusting the dimension between the sections and inserting reactive matching elements into the sections of the filter.

Geometry of a variant of the filter in the E-plane designed by the geometrical synthesis method on the base of the data cited above is shown in Fig.8. All dimensions are in millimeters. The overall sizes of the filter are 60õ40õ40 mm3. The filter consists of two identical sections. Every section has the attenuation more than 50 dB. Fig.9 shows the calculated magnitude of the transmission coefficient of the filter. Program TAMIC-E was used to calculate frequency characteristics of the filter. Calculation of S-parameters for ten frequency points on computer IBM PC/486 (Norton SysInfo CPU Speed Index was about 130) has required about 3 min. Experimental attenuation characteristics of the filter over the passband and over the stopband are shown respectively in Fig.10 and Fig.11. Measured data were obtained by using the HP8510B analyzer. The agreement between the theoretical and measured results is good enough.

Conclusion

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A new efficient approach has been developed for the synthesis of the filters with improved parameters. The approach is based on the geometrical synthesis and on the numerical electromagnetic programs TAMIC that make it possible to remove turning stage from the filter design cycle.

References

1.Sestroretzkiy B.V. Microwave semiconductor commutators (in Russian), - in "Current problems of antenna and waveguide techniques", Edited by Pistolkors A.A., Moscow, "Nauka", 1966, p. 126-144.

2.Microwave devices with semiconductor diodes (in Russian), Edited by Malskiy I.V. and Sestroretzkiy B.V., Moscow, "Sov. Radio", 1969.

4.Sestroretzkiy B.V., Kustov V.Yu. Procedures and invariants of electromagnetic synthesis of small coaxial filters (in Russian), - "Voprosi radioelectroniki", ser. OVR, N3, 1987, p.3-

5.Klimov K.N., Kustov V.Yu., Sestroretzkiy B.V., Shlepnev Yu.O., - Efficiency of the impedance-network algorithms in analysis and synthesis of sophisticated microwave systems, - Proc. of 27th Conference on Antenna Theory and Technology (ATT'94), Moscow, Russia, 23-25 August, 1994, p. 26-30.

6.Kuharkin E.S., Sestroretzkiy B.V. - Dialogue optimization of devices' geometry in electromagnetic CAD systems (in Russian), textbook, MPEI, v. 1, 1987.