The method of synthesis of analog frequency-dividing devices on the basis of wave filters has been offered. Various variants of configurations of such filters are considered. It is shown that frequency-dividing filters synthesized according to the offered method, have the minimal order

Dovgun, V. P.

Novikov, V. V.

Electronic archive of Tomsk Polytechnic University

may be written down following the Fig. 5, whence the value(4)is determined, where ZВХ.Σ=ZС||X11.1 (Fig. 5).Fig. 5. The part of the circuit of amplifier loaded by the secondcascode stepThe value ZВЫХ.1 may be judge by (4). At high frequencies when ZВХ.Σ decreases greatly, ZВЫХ.1 is comparatively high, about |X12.1|. At low frequencies, it equals approximately (1/S1)(X12.1/ZВХ.Σ).In the circuit in Fig. 3 the resistance of the elementsconnected in parallel denoted by ZВЫХ.1 and C11.2 havingrather high resistances is indicated by the variable Z||.Bridging the output resistance by the capacitance C11.2makes no difference. Value Z|| remains of the same orderthat ZВЫХ.1. Product S2Z||, met in formulas (2) and (3), ismuch more than a unit while S2X12.1>>1, i.e. while frequency f << S2/2πC12.1. So, applying the fieldeffect transistors of the type KP341 this product can not be less thanthe ratio C11/C12, which equals approximately five.Summary. The relative influence of active elementson noises of video amplifier cascode circuit at resistiveload and application of active element of as the cascadedynamic load was considered. It was shown that in bothcases the second transistor of the cascode circuit contributes insignificantly into the amplifier noises in comparison with the first one (<10 %). Contribution of noisesof the dynamic load active element exceeds considerably the contribution of the traditional cascade resistiveload and doubles practically in power the noises conditioned by the first active element at uniformity of allthree active elements.U1 S1U1i?Z?C11.1C12.1I12 1 ÂÕ.ÂÛÕ.1 ÂÛÕ.1 01 ÂÕ.1.X ZZ U I ,S ZΣΣ+= = +Bulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 486REFERENCES1. Dobretsov A.I. Wideband amplifier with a high gain / A.I. Dobretsov, V.A. Karzhavin, Yu.A. Tuflin // Devices and experimental technique. – 1978. – № 1. – P. 88–90.2. Shustov M.A. Practical circuit technology. In 5 books. B. 1. 450 usefulcircuits for radio amateurs: collection. – Moscow: AlteksA, 2003. –352 p. – P. 44–53. – Bibliog.: p. 336351. – ISBN 5942710023.3. Van der Zil A. Noise. Sources, description, measurement / Translated from English by V.N. Kuleshov and D.P. Tsarapkin; ed. byA.K. Naryshkin. – Moscow: Sovetskoe Radio, 1973. – 228 p.Received on 07.12.2006Processing and transmitting signals the necessity ofusing the frequency dividing devices intended for dividing signal spectrum into nonoverlapping parts oftenoccurs. Such devices are called directional filters ormultiplexers [1, 2]. The questions of directional filterapplication in radio systems and devices are examinedin detail in monograph [1].A particular case of multiplexer is twochannelfrequencydividing devices – diplexer. Diplexer implements two transfer functions meeting the conditionDiplexers are the basic elements at construction offrequencydividing devices with any amount of channels.A significant number of works where various aspectsof theory and design of the directional filters are discussed indicates the importance of the problems of theirsynthesis [1, 3–8]. The work [7], where the generaltechnique of calculating the transfer functions of the directional filters with maximum flat gainfrequency characteristics (GFC) and controlled attenuation at frequency of GFC junction is considered, should be especially noted. The question of branching filter implementation on the basis of parallel or series connection of passive LC filters realizing separate transfer functions areexamined in [4–6]. Such approach is not optimal aseach transfer function is implemented by a certain filterand realizing circuit has a high order. The technique ofsynthesizing diplexer in the form of reactive sixpole is2 21 2( ) ( ) 1.H j H jω ω+ ≤UDC 621.372.57ACTIVE FREQUENCYDIVIDING FILTERSV.P. Dovgun, V.V. NovikovSiberian federal university, KrasnoyarskEmail: vdovgun@emf.krgtu.ruThe method of synthesis of analog frequencydividing devices on the basis of wave filters has been offered. Various variants of configurations of such filters are considered. It is shown that frequencydividing filters synthesized according to the offered method, havethe minimal order.proposed in the article [8]. However, the examples givenin [8] show that a number of reactive elements insynthesized network exceeds considerably the order ofthe implemented transfer functions.In this paper the method of implementing diplexersbased on the use of the analog wave filters (WF) is considered. The proposed approach allows obtaining thefrequencydividing filters of minimal order. It is suitable for designing both active (ARC) and passive (LC)frequencydividing devices.Wave filter represents an unbalanced network realizing simultaneously four transfer functions (Fig. 1). Theconnection between stresses on external terminals ofwave filter is determined by the equations in transfer(1)or chain parameters:The elements of matrix of the transfer parameters[T] are the transfer functions between separate inputsand outputs.Fig. 1. The wave filterMatrix of wave filter coefficients in eq. (1) is a bounded transfer matrix of spreading parameters meeting theparaunitarity condition [2, 3]:(2)Matrix [T]• comes out of transposition [T] andchange of jω by –jω. The Feldtkeller equalities [2](3)are the consequence of the (2).It follows from the (3) that the elements t11(jω) andt21(jω) are complementary, i.e. the pass band t11(jω) corresponds to the stop band t21(jω). Thus, the wave filterimplements automatically the branching filter. It wasfirstly noticed in the review [2].A general theory of realizing the analog wave filtersis examined in works [9, 10]. The synthesized structurerepresents the cascade connection of firstsecond ordersections implementing zeros of the transfer functionH1(jω) (Fig. 2). Section principle circuit depends on atype of realizable zeros.Fig. 2. The structure of synthesized circuitFor the filters of Butterworth and Chebyshev, zeros,the transfer of which are in infinity, the first order section are enough to be used. The matrix of section chainparameters realizing zero in infinity is of the formParameters ci and di depend on the type of the realized transfer function t11(jω). The parameters of sectionsof Butterworth filters are given in the Table.Table. The parameters of sections of Butterworth filters.Order n=2–9Structure chart of the section implementing transferzeros placed on imaginary axis is shown in Fig. 3.T(s)=1/(1+sci) corresponds to transfer zeros in infinity.One of the variants of this structure chart realization inthe base OURC is shown in Fig. 4.The filter formed by the cascade connection of sections showed in Fig. 4 contains minimal quantity of reactive elements equal the order of the realized transferfunctions. However, the number of active elements(operational amplifiers – OA) turns out to be high. Forexample, 12 OA are required for realization of the filterof the third order.Fig. 3. The structure chart of the section implementing zero onthe imaginary axisFig. 4. Principle circuit of the section implementing zero on theimaginary axisThe parameters of the recovered fourterminal networks ci2 3 4 5 6 7 8 90,7071 0,5000 0,3827 0,3090 0,2588 0,2225 0,1951 0,17360,7071 1,0000 0,9239 0,8090 0,7071 0,6235 0,5556 0,50000,5000 0,9239 1,0000 0,9659 0,9010 0,8315 0,76600,3827 0,8090 0,9659 1,0000 0,9808 0,93970,3090 0,7071 0,9010 0,9808 1,00000,2588 0,6235 0,8315 0,93970,2225 0,5556 0,76600,1951 0,50000,1736( ) 1[ ] .1i iii ic s d sbd s c s−⎡ ⎤= ⎢ ⎥− −⎣ ⎦2 211 212 222 12( ) ( ) 1,( ) ( ) 1.t j t jt j t jω ωω ω+ =+ =[ ] [ ] [1].T T• =1 111 122 221 22.âûõ âõâõ âûõU Ub bU Ub b⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦ ⎣ ⎦1 111 122 221 22,âûõ âõâûõ âõU Ut tU Ut t⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦ ⎣ ⎦Power engineering87In order to obtain more saving implementation themethod of equivalence conversions of chain parametermatrix is used [9]. Let us examine the conversion of similarity of the chain parameter matrix(4)Here [Q] is the nonsingular transformation matrix.The variables on external terminals of fourterminalnetwork are transformed to a new coordinate base:(5)Structure chart shown in Fig. 5 corresponds to transformation (4). It is formed by the cascade connectionof fourterminal network having a matrix of chain parameters [B~(0)] and two sections of zero order having chainmatrices [Q]–1 and [Q] respectively.Fig. 5. Structure chart corresponding to transformation (5)It is not difficult to show that transformation of thechain or transfer parameters of the whole circuit according to (4) is equivalent to transformation of parametersof each constituent fourterminal network separately.Let us use the transfer matrix of the formHere K(s) is the fractional rational function offrequency in general case. Transforming the chain matrix [B(0)] according to (4), the structure chart shown inFig. 6 is obtained.Fig. 6. The structure of the transformed wave filterThe transformed matrix of the transfer parameters isof the form:Function f(s) depends on the type of the recoveredzeros. At s=0 f(s)=s. Function f(s)=1/s corresponds tozero in infinity.Structure chart of a signal fourterminal network realizing the transfer matrix [i~(i)] is introduced in Fig. 7.K(s) = 1 for the active RCfilters.Fig. 7. Structure chart of the first order sectionOne of the variants of this structure chart realizationis shown in Fig. 8.Fig. 8. Principle circuit of the section implementing zero in infinityA more saving realization may be obtained connecting in turn the sections shown in Fig. 9, 10.Fig. 9. An odd section of frequencydividing filterFig. 10. An even section of frequencydividing filterThe resistor voltages in circuits in Fig. 9, 10 are calculated by the formulas:here i=1,2,3,... – are the serial numbers of filter sections.Integrating load sections with the first and the lastlinks the configurations showed in Fig. 11, 12, respectively, are obtained.So, for minimal realization of active frequencydividing filter the section of four types:• initial, Fig. 11;• final, Fig. 12;• intermediate even and odd, Fig. 9, 10 should be used.0,iicR f Cπ= ⋅ ⋅?( )( )( )1 ( )[ ] .( ) ( ) ( )ii if sf s K st c dK s f s f s⎡ ⎤⎢ ⎥= + ⎢ ⎥−⎣ ⎦11 ( )[ ] .11 ( )K sQK s⎡ ⎤⎢ ⎥= ⎢ ⎥−⎢ ⎥⎣ ⎦1 11 11 12 22 2[ ] , [ ] .âûõ âõâûõ âõâõ âûõâõ âûõU UU UQ QU UU U− −⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤= =⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦  (0) 1 (0)[ ] [ ] [ ][ ].B Q B Q−=Bulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 488Fig. 11. The initial section of frequencydividing filterFig. 12. The final section of frequencydividing filterFilters of various orders differ only in number of intermediate sections.The original data at designing filter are the order andthe form of the transfer function as well as the cutofffrequency f0. The procedure of calculation consists inchoice of suitable condenser capacities and resistor design by the ratio (10).The diagram of diplexer of the third order designedaccording to the proposed approach is shown in Fig. 13.The cutoff frequency f0=159 Hz. It is enough to realizethe only input for the diplexer proper operation. Thegainfrequency characteristics of diplexer are shown inFig. 14.Fig. 13. The frequencydividing filter of the third order.R1=0,5 kOhm; R2–R12=1 kO; С1–С3=1 mkFFinally, let us note that the proposed approach allows designing the frequencydividing filters of minimalorder realizing the functions of various types (of Butterworth, Chebyshev etc.). It may be used as well forsynthesis of passive diplexers.Power engineering89Fig. 14. The gainfrequency characteristics of the synthesized filterREFERENCES1. Alekseev O.V., Groshev G.A., Chavka G.G. Multichannel frequencydividing devices and their application. – Moscow: Radio andcommunication, 1981. – 136 p.2. Fettweis A. Wave digital filters // TIIER. – 1986. – № 2. – P. 35–99.3. Neirynck J., Carlin C.H. Synthesis of the lossless reciprocal threeportbased on a canonic form of its scattering matrix // IEEE Transactionson Circuits and Systems. – 1981. – V. CAS28. – № 7. – P. 736–744.4. Youla D. Several key representations of circuit theory being a principle of filters calculation by the classical method of attenuation characteristic // TIIER. – 1971. – № 5. – P. 45–87.5. Belevitch V. On filter pairs with Butterworth characteristics // International Journal of circuit Theory and Applications. – 1987. – V. 15.– P. 51–60.6. Zhu Y.S, Chen W.K. On the design of a diplexer having Butterworth characteristics // IEEE Transactions on Circuits and Systems. – 1988. – V. CAS35. – № 11. – P. 1455–1457.7. Youla D. C., Pillai U., Winter F. Theory and design of maximally flatlowpass highpass reactanceladder diplexers // IEEE Transactionson Circuits and Systems. – 1992. – V. CAS39. – № 5. –P. 337–349.8. Neirynck J., Carlin C.H. Synthesis of the lossless reciprocal threeport based on a canonic form of its scattering matrix // IEEE Transactions on Circuits and Systems. – 1981. – V. CAS28. – № 7. –P. 736–744.9. Bondarenko A.V., Dovgun V.P. Synthesis of analog wave filters //Electricity. – 2005. – № 5. – P. 52–56.10. Dovgun V.P., Barybin P.A., Novikov V.V. The analog wave filters:main properties and procedure implementation // The Bulletin ofassociation of KSTU graduates. Krasnoyarsk. – 2005. – Issue 12. –P. 156–164.Received on14.05.2007Bulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 490The requirement of phase shift constancy at transferconstant adjustment is made to modules of active phaselattices, systems of automatic phasing in transmitters,precise wideband amplifiers, attenuators with smoothvariation of attenuation and other devices with adjustable characteristics of signal transmission. Change ofphase shift or group delay is conditioned by the influence of parasitic reactivity of elements with controlled resistance. There is a certain process limit in decreasingparasitic parameters. Therefore, one of the most important tasks is a balance of parasitic reactivities of the controlled elements by circuit solutions.1. The problem of phase shift invariance Electrically controlled attenuators (ECA) are intended for smooth change of signal level in a circuit. For anumber of practical tasks, for example, CDMA of communication systems, phased arrays, surface radars etc.,the excess requirement is made to attenuators; the requirement to phase shift stability of output signal relative tothe input one at adjustment of transfer constant [1]. Thisaim is complicated at system operation in a wide band,in general case from zero to several GHz. Phase variationis conditioned by the influence of parasitic reactivities ofthe controlled elements. They may be decreased technologically only to a certain limit, especially in superwideband. Therefore, the only method of supporting phaseshift invariance to attenuation is the balance of parasiticreactivities of controlled elements by a circuit way. Inparticular, the equalizers included specially into the basestructure find wide application in absorbing attenuators.The methods of phase correction are developed bestof all for ECA on pin diodes [1]. Schottkygate FETs(SFET) have a number of advantages although diodesgain in maximum power of controlled signal. In particular, the advantage is in switching time, decouplingbetween signal transmission circuit and control paths.Availability of using SFETs conditioned by low values ofparasitic reactivities simplifies considerably the problemof constructing wide band ECA in microwave range.The aim of the work is the investigation and simulationof circuit design characteristics for ECA on FETs, searchfor perspective circuit methods of phase shift correctionand comparison of the obtained results with known characteristics of base diode and transistor structures.UDC 621.372.852MODELING OF ATTENUATOR STRUCTURES ON FIELD EFFECT TRANSISTORS WITH MINIMAL PHASE SHIFT AT ATTENUATION REGULATIONO.V. StukachTomsk Polytechnic UniversityEmail: tomsk@ieee.orgControlled absorbing attenuators on Schottkygate FETs: Tcircuit, Tshaped bridge circuit and transistor attenuator in the mode withcontrolled slope of voltagecurrent characteristic have been considered. Attenuator phasefrequency characteristics were modeled. Themain difference of the circuits from the known ones consists in introduction of equalizers that conditions broadband feature and largeattenuation range where minimum of the phase shift is achieved at regulation. As a result, the optimal parameters of adjusting circuitsin attenuators are founded. It is shown that the least phase shift is provided in attenuators on transistor with controlled voltampere characteristic steepness. The comparative estimation of the considered base structures was given.

Active frequency-dividing filters

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