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Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis and Dissertation Collection 1987 Evaluation of device of merit in microwave switching circuit design. Pibultip, Pitak. http://hdl.handle.net/10945/22782 NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS EVALUATION OF DEVICE FIGURE OF MERIT IN MICROWAVE SWITCHING CIRCUII DESIGN ' 1 by Pitak Pibultip June 1987 Thasio Advise ^ V» " ^ Atvatar Approved for public release; distribution is unlimited. T 233613 n.. L'nciassified REPORT DOCUMENTATION PAGE «£PO«T SECURITY I CC-ASSif ICATION «6STHICTIV£ lb. MA«<iNGS Unclassified I SECURITY Classification authority > OECLASSiFlCATiON/OOWNGRAOiNG SCHEDULE OlSTRiauriON/AVAILAaiLITY OF REPORT J Approved is PERFORMING ORGANIZATION REPORT \UMa£R(Sl NAME OF PERFORMING ORGANIZATION Naval Postgraduate School A00RE3S CA Naval Postgraduate School 62 AOORESSkOry. Un». imiilPCoa*) 'b 93943-5000 Monterey, NAME OF FUNDING /SPONSORING ORGANIZATION ADDRESS NAME OF MONITORING ORGANIZATION 7j iGry. Sut*. j/x* ^ipCoo*) Monterey, unlimited MONITORING ORGANIZATION REPORT NUfvaERCS) S 60 OFFICE SYMaOL (It 4pph<4bl*) 8b OFFICE (I* for public release; distribution SYMBOL CA 93943-5000 PROCUREMENT INSTRUMENT lOEN TiPiCATlON NUMBER 9 jpphatH*) (Cry, Sutr. irxt ZIP Coat) SOURCE OF FUNDING NUM9ERS 10 PROGRAM PROJECT rAS< WORK ELEMENT NO NO NO ACCESSION NO UNIT TITLE (/nc/oO» S»ciw»fy CUiufi<jtion) Evaluation of Device Figure of Merit in Microwave Switching Circuit Design PERSONAL AUTW0«(S) Pibultip, Pitak rvog OF REPORT 1 3a Time covered FROM Master's Thesis 14 DATE OF REPORT (Yttr. Month. Diy) 15 PAGE COUNT 93 1987 June TO SUPPLEMENTARY NOTATION COSATi COOES GROUP ^•ElO 18 SU9JECT TERMS (Continue on rf¥«rt* and iSS TRACT (Continu* on rrytnr if it nrteu^rf tnd Kjfntity Oy Oiock nutnotr) Semiconductor Device Figure of Merit, SU9-GR0UP n^^eu^ry Isolation, j/xJ ia*ntity Switch Insertion Loss Diode Power dissipation and Juntion Temperature Oy biO(k numOtr) microwave switching circuit design, a switching- semiconductor of merit can be defined and used as the measure of device switching effectiveness. In this thesis research switching3emiconduc~or figures of merit were applied to general switching :ircuit3. Compuzer-aided circuit analysis program Touchsrone and a ror-ran program were used for "che compuua-ion of switching circui" In figure ( ) , 3erf ormance. t S'RiauTlON/ AVAILABILITY OF ABSTRACT w'NClaSSiFiEQ/UNlimiTED Q 21 same as RPT O NAME OF RESPONSIBLE ^NOiViOUAi. Professor Hany A. Acwater ORM 1473. 84 MAR 9J ABSTRACT SECURITY CLASSIFICATION OTIC USERS 2Zb TELEPHONE f'nc/u<3e Are* Cooe) 62An (408) 646-3001 APR eOitfOn '^*y All t3« ^i*d otn«r eoitiom n* until e«n«u»te<J Unclassified 22c OFFICE SYMBOL (:g(;ijfl)TV CLASSlFlCAriQN Qf ooioiet* Unciassified rui<, l>a.Ct Approved for public release; distribution is unlimited. Evaluation of Device Figure of Merit in Microwave Sv^dtching Circuit Design by Pitak Pibultip Lieutenant Royal Thai Nav>' , B.S.E.E., Royal Thai Naval Academy, 1978 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL June 1987 A ,,*! ABSTRACT In microwave switching circuit design, a switching-semiconductor figure of merit can be defined and used as the measure of device switching effectiveness. In this thesis research switching-semiconductor figures of merit were applied to general switching circuits. Computer-aided program were used for the circuit analysis program (Touchstone), and computation of switching circuit performance. a Fortran TABLE OF CONTENTS I. II. INTRODUCTION 8 A. BACKGROUND B. SCOPE OF THE THESIS RESEARCH 8 CIRCUIT ANALYSIS A. B. 12 CLASSIFICATION OF MICROWAVE SWITCHES 1. Single Pole Single 2. Single Pole N Throw Throw Switches (SPST) Switches (SPNT) SCATTERING MATRIX REPRESENTATION OF MICROWAVE SWITCHES SWITCHING CIRCUIT MORPHOLOGIES . C. D. E. F. 1. Number 2. Switch "BOX" Topologies M 1. Figure of Merit, 2. Quality Factor, 3. Comparison of Figure of Merit 3. ABCD ABCD Q B. 12 12 13 13 13 14 15 17 Matrix Representation of a Two-port Network 18 19 21 21 Matrix Representation of the Switching Circuit Model 21 Calculation of Power in a Cascade Circuit 23 MICROWAVE SWITCHING DIODE A. 12 17 TRANSMISSION LINE SECTION REPRESENTATION OF SWITCHING CIRCUIT MODEL APPROACHES TO COMPUTATION OF CIRCUIT POWER-DISSIPATION 2. IIL. of Semiconductor Devices SWITCHING SEMICONDUCTOR DEVICE CHARACTERIZATION 1. 11 THE P-I-N DIODE STRUCTURE THE ELECTRICAL EQUIVALENT CIRCUIT MODEL 1. Forward Bias Equivalent 2. Reverse Bias Equivalent Circuit Circuit 26 26 .27 27 27 3. P-I-N Diode Cutoff Frequency 29 POWER HANDLING C. 1. Maximum 29 Voltage across the P-I-N Diode Maximum Junction Temperature TABLE OF TYPICALLY AVAILABLE 30 30 2. D. IV. P-I-N DIODES EVALUATION OF SEMICONDUCTOR MICROWAVE SWITCH CHARACTERISTICS A. INSERTION LOSS AND LOAD ISOLATION CALCULATION USING COMPUTER-AIDED CIRCUIT ANALYSIS PROGRAM (TOUCHSTONE) D. V. 35 Insertion Loss in the Switch On-state 38 2. Load 39 3. Example of Insertion Loss and Load Isolation in the Switch OfT-state Isolation 40 THE SEMICONDUCTOR DEVICE FIGURE OF MERIT WHICH BEST CHARACTERIZES THE SWITCHING PERFORMANCE NODAL VOLTAGE CALCULATION USING TOUCHSTONE PROGRAM EVALUATION OF POWER DISSIPATION AND HEATING USING FORTRAN PROGRAM C. 35 1. Evaluation B. 33 52 57 59 1. Nodal Voltage and Current Calculation 60 2. Power Dissipation 63 3. Junction Temperature in the Individual P-I-N Diode 4. An Example in the Individual P-I-N Diode and Results of Power Dissipation and Diode Junction Temperature Evaluation CONCLUSIONS AND REMARKS 63 64 68 APPENDIX A: TOUCHSTONE CIRCUIT FILE FOR APPENDIX B: TOUCHSTONE CIRCUIT FILE FOR SPDT SWITCH 75 APPENDIX C: TOUCHSTONE CIRCUIT FILE FOR NODAL VOLTAGE EVALUATION 78 FORTR.AN PROGR.\M FOR DIODE POWER AND HEATING CALCULATIONS 81 APPENDIX LIST D: OF REFERENCES INITIAL DISTRIBUTION LIST SPST SWITCH 72 91 92 LIST L 2. 3. 4. 5. 6. 7. 8. 9. OF TABLES TYPICAL PARAMETERS OF P-I-N DIODES TOUCHSTONE OUTPUT SPSTD.CKT TOUCHSTONE OUTPUT SPSTQ.CKT TOUCHSTONE OUTPUT SPDTD.CKT TOUCHSTONE OUTPUT SPDTQ.CKT COMPARISON BETWEEN FIGURES OF MERIT M, AND DIODE Q COMPARISON OF FIGURES OF MERIT M, FROM DIFFERENT APPROACHES NODAL VOLTAGE FROM TOUCHSTONE SPDTV.CKT DIODE POWER DISSIPATION AND JUNCTION TEMPERATURE OF THE 100- WATT CW POWER SWITCH 34 44 45 51 52 55 56 58 65 LIST N OF FIGURES Throw Switches 2.1 Single Pole 2.2 Scattering Parameters 2.3 Example of Switching 2.4 Transmission Line Model of Switch Networks 20 2.5 ABCD 22 14 14 Circuits 16 Matrix Model 2.7 N Two-Port in Cascade with Equivalent Matrix ABCD Matrix Representation of Devices 3.1 Profiles for the 3.2 P-I-N Diode Chip Equivalent Circuit 28 3.3 P-I-N Diode C: vs I-Region Diameter and Thickness 31 3.4 Junction Voltage at High 4.1 Resistance vs Capacitance as a Function of Diode 4.2 Flow Chart of a 4.3 Single Pole Single 4.4 SPST Switch Insertion Loss and Isolation vs Frequency 43 4.5 SPST Switch Insertion Loss vs Q^^Q^g 46 4.6 SPST Switch Load 4.7 Single Pole 4.8 4.10 SPDT SPDT SPDT 4.11 Nodal Voltage Measurement Equivalent 4.12 ABCD 4.13 Flow Diasram for Calculation of Power Dissipation and Diode Junction Temperature 62 4.14 Power Dissipation 67 5.1 Switch Insertion Loss vs Diode 5.2 Switch Isolation vs Diode 2.6 4.9 22 24 two P-I-N Diodes Types RF 28 and Reverse Bias 31 Q 40 Circuit File Throw Switch Equivalent Isolation vs Circuit ^'^ Circuit and Isolation vs Frequency Switch Insertion Loss vs Q(jiQ^e Switch Load Isolation vs Matrix Representation of SPDT Q 50 ^^ Circuit Switch Circuit Model an Individual Diode Q 49 53 Q^^ode in 42 Q^jio^e Double Throw Switch Equivalent Svvitch Insertion Loss 37 for Multi-diodes Switch for Multi-diodes Switch 58 61 70 71 I. INTRODUCTION BACKGROUND A. The switching function applications essential for the is practical cases, switching as performed in microwave performance of the circuitry utilized in radar circuit objective. In the majority must be done by semiconductor devices, since mechanical switches are ruled out by requirements of speed and allowable system weight and Therefore the semiconductor switch is component a vital of in most microwave size. circuit applications. Despite its practical importance, relatively little to fundamental aspects of the switching problem, in problem of microwave amplifier or filter research attention has been given comparison with, for example, the design. Therefore it is the purpose of this examine some of the basic features of the switching problem. thesis to requirement in the design of a switching circuit is A general the conversion of the set of given switch performance specifications into a set of device requirements for the necessary semiconductors to be used in the switch. It is be defined which provides a unifying factor in in the definition and use of switch known this that a device figure of merit can conversion process. Some progress been made by earlier workers, figures of merit has but few practical procedures have been developed, and further work area. It is is needed in this the purpose of this thesis to investigate the characterization of several aspects of switch performance as a function of device figure of merit, as well as to investigate the important aspect of the selection and use of devices so as to maximize the power-handling capacity of the switch. The fundamental specifications governing microwave switch selection and/or design are: 1. Low 2. High 3. Broad bandwidth insertion loss in on-state isolation in off-state 4. SulTicient power capability These characteristics are interactive, a change in one affecting the others. The microwave switches considered here are those which employ semiconductor devices (p-i-n diodes and FET's) operated in two alternate bias states. characterized by a pair of two-terminal impedance values Zj and X^ The device is in the respective bias states. The necessitates some form of impedance compensation parasitic capacitance associated with semiconductor switching devices lossless been oriented toward the study of two-state impedances embedded impedance transformers have introduced under states, order to achieve acceptable Consequently the theoretical analysis of switching insertion losses for the switch. circuitry has in lossless Kurokawa and These researches on switching theory [Refs. 1.2,3]. specific invariant parameters related to the device impedance in Schlosser [Ref. r = q2 its two impedance transformation. 1], showed that diodes incorporated in a one-port can be characterized by a quality factor parameter, Q"^ reflective switch in : 21 11) ( R1R2 where Ri R2 is is component of Zp and the resistive component of Z2. the resistive The numerical value of Q unchanged when the impedances are subjected is to a lossless impedance transformation. Atwater and Sudbury [Ref merit, serving as 2] showed of Kurokawa and and not both states. had the character of a Equation q2 1.1 = for semiconductors figure of embedded restricted to the original reflection-type They followed the research of Kurokawa and Schlosser. Schlosser and assumed that Zi and in Q an indicator of switching performance in variety of circuit configurations, circuit that this Z2 had been transformed to real (resistive) values becomes: ^' ^ ^^ (eqn 1.2) R1R2 From equation we have the relationships: Ri is a function of Q R-> is a function ot Q and Knowing is fully 1.2, the value of specified. Q and R-). and R, and given that Ri, R2 are kno'wn, the switching performance Kawakami found a [Ref. 3] form of switching invariant parameter. He different M: defined this parameter as a semiconductor figure of merit, M The. parameter impedance IZ1-Z9I = ^ M in coefficients in the Kawakami and on and off states, and 1, showed also two-port symmetrical a 1.3) 1 assumes values between transformation. incorporated (eqn -V. IZ^-Z, junction S2][(l) is that as a and S2i(2), by also unaltered when switch, a its lossless was device transmission respectively, are related by equation: Equation 1.4 parameter M fully |S-,,(1)1(1-M) ^^ = |Soi{2)l 21^ characterizes as a figure of merit. It M is performance of the the switching may inverted to yield the form: 1.4) — — uith device, |S2i(2)l-|S2i(l)l = |S2i(2)| This expression (eqn l-M[|l-2S2i(l)|] , (eqn + |S2i(l)|[l-21S2i(2)|] based on the assumption that the switching device in its two ,. , 1.5) states has the properties: Equation satisfy 1.5 Fj = ^2 = (matched; ^max = Z = Zq ^^ presents a useful tool for the selection of a semiconductor device to low power switching applications.^ A fundamental zheorem was denved by Hines [Ref can be switched by a singie-diode switch when circuit ) it is 4], to predict the connected in a power that iumped-eiement such as to resonate the parasitic reactance of the switch at a single frequency. Hines showed that the power which can be switched by the diode, ^In the absorption switch assumed in equation energy in the switch ofT-state. 10 1.4, P^.^, is given by: the diode absorbs the incident Psw sw where V^^^^ ^max is ^^ = a diode ^ 0.5[V^,,I^,J "•^'max'max breakdown maximum voltage, (eqnl.6) and forward current rating. Hines conjectured that P^^^ represents a theoretical limit for power switching by a given device in an impedance-matched circuit. many In diodes in applications, microwave switching circuits typically require multiple cascade connection to achieve adequate levels of off-state isolation. For example, radar and phased-array modules need a double-throw switch of high isolation to protect the receiver front end. B. SCOPE OF THE THESIS RESEARCH For the application to microwave switching, the proposed semiconductor of merit are tested for different types of switching to use in a switch selection and/or design problem circuitry, to find the best in order to figures parameter minimize insertion loss in the on-state, and maximize isolation in the off-state. Additional objectives are to determine, for the designed switch, what are the power dissipation and heat removal problem in the individual semiconductor components. 11 II. In the present chapter CIRCUIT ANALYSIS we generalize the circuit representation of Following switches of our interest. this, the particular type of switch required. a The representation selected for that of an is N- determined by the is and the type of switch (single-throw or multiple- devices For the semiconductor devices, there are three possible ways of connection to throw). our simplest model may be The number of ports port, with scattering matrix description. number of semiconductor suitable circuit microwave circuit model, in shunt or in sinking considerations we combination of both. series or a select the Because of heat- shunt connection and use a one-port network to represent the two-terminal semiconductor device. A. CLASSIFICATION OF MICROWAVE SWITCHES 1. Throw Switches (SPST) Single Pole Single The single pole* single throw switch is a switch which has one input port and topology we consider our switch as a 'box' and one output port. In this box network shown in Figure 2.1(a). the load at the output port in its For an on-state, ideal switch, all the power it is is a two-port transferred to and no power transferred to the load in its off-state. 2. Single Pole N Throw Switches (SPNT) For these types of switches, there is an input port and N output ports. Their switching circuit models are a three-port box network for single pole double throw switches, shown in Figure 2.1(b), throw switches, shown interested chapter. arm is in and a (N+l)-port box network Figure 2.1(c). for single pole In microwave switch apphcation, we Nare in single pole double throw switches as mentioned in the introductoiy For SPDT switches, in the off-state, and two SPST switches with states to the when one arm of the vice versa. In general, dieir Input semiconductor devices ^Single pole is m arms we may tied together the diiTerent a line-over-ground circuit. 12 switch is in the on-state, the other consider a SPDT and apply two arms of the switch. switch as aiilerent bias SCATTERING SWITCHES We can use the B. Figure 2.2, MATRIX REPRESENTATION OF properties of the S-matrix [Refs. 5,6: pp. and assume that our switches are We input and output ports. ideal switches MICROWAVE 112, 50], defined in mth matched load at both can represent the scattering matrices for both on and off states of our switches as follows. I. Single Pole Single Throw Switch 1 ON STATE: = [S] 1 1 OFF STATE: = [S] 1 2. Double Throw Switch Single Pole 1 ARM (2) ON: = [S] 1 1 ARM (3) ON: = [S] 1 C. SWITCHING CIRCUIT MORPHOLOGIES 1. Number of Semiconductor Devices SPST In an switch or one arm of SPDT s^v^itch there at is semiconductor device. For improvement of load isolation, the switch semiconductor additional devices. In general, a SPNT switch least may may one require use semiconductor devices. M where M = pN :eqn2.I) is the number of semiconductor N is the number of throws, and p is a positive integer. 13 devices, M 2 PORT EOX a. SPST b. SPDT *2 N+1 POR:! *z BOX 4-4 4-'^nl C. Figure 2.1 ^ SPNT Single Pole N Throw ^IL Switches. b2 ? N PORT portl ^a2 .^ V2 NETWORK port2 port n Cb] = [s] [a] That is b n = Sii^i + 512^2 + = S^^a.^ + S^2^2 + Fisure 2.2 - ~ Scattering Parameters. 14 + 2ln% + 2nn^ 2. Switch ''BOX" Topologies We input port, can define the switching N The coupled. M output ports, and total SPST SPST given by: • (eqn 2.2) 1 semiconductor device. Figure 2.3(a) of ports = (1 = 3 + + 1 1) ports switch with 2 semiconductor devices. Figure 2.3(b) Number SPDT (N+l + M) is circuits. switch with Number 3. ports to which the semiconductor devices are = of ports Example of switching 2. embedding network with one number of ports of the embedding network Number 1. circuit as a lossless of ports = (1 + 1 + 2) = 4 ports switch with 2 semiconductor devices. Figure 2.3(c) Number (2+1 + = of ports = 2) ports 5 SWITCHING SEMICONDUCTOR DEVICE CHARACTERIZATION D. The semiconductor network, as stated can be represented by a one-port device in shunt connection The device above.'^ itself the in switching circuit may characterized by: 1. Two-states of impedance [Ref 2. Two-states of reflection coefficient [Ref The relations i = 1]. 1,2 ) F- ( or i = 1,2 ). + are: T; (eqn 2.3) l-Ti = ri device ( Zq ^i The Z^ between impedance and reflection coefficient 1 3 2]. Z.;- Z,1 (eqn 2.4) Zi-Zo is in shunt to ground in the single pole circuit. 15 be • 2 a. SPST 1 DEVICE 2 b. SPST 2 DEVICES c. SPOT Figure 2.3 2 DEVICES ExamDie of Switching 16 Circuits. Figure of merit of the semiconductor device is defined based on the device characterization chosen. M Figure of Merit, 1. From equation 1.3 M* IZ1-Z2I = |Zi-Z2"1 Kawakami two specific states of F- impedance . He assumed = r^ A postulated that the fundamental characterization was in terms of ( Z the following conditions: Z = Zq matched; is lossless matching network to the matched condition is assumed However, 2. in terms this type ~ l^max' of switch is *> ^^^^ ^^ to be used to transform the device in this state. In the second bias state of the by the transformed device impedance device, the reflection coefficient presented ''"2' ) equal to the figure of merit, M, of the is then: devices ) a reflection switch.'^ Quality Factor, Q Kurokawa and Schlosser postulated that the fundamental characterization was of two states of impedance and their real parts Q quality factor , shown (resistive). They defined a in equation 1.1, as the figure of merit of the semiconductor devices. From the parameters defined above we can characterize the p-i-n diode and specify a diode quality factor or the figure of merit for the device used in switching circuits. Diode quality to the switching quality factor, as From equation factor, may Q,^iode' ^'^^ microwave ^ typical switching diode is equal be shown: 1.1 Q^ R^R2 '^The F: = state, absorbs energy and circuits. 17 is not suitable for high power switching For a impedance p-i-n simple a diode, model circuit is assumed in which the two states are: If we Z| = Rj forward bias Z2 = R2 + iX2 reverse bias assume that R| = R2 = R for ( both bias states ) R^ 1 ( RCco Thus Kurokawa-Schlosser's Q^ 3. Q reduces to the conventional diode Q: (^q^ 2.6) Q^diode Comparison of Figure of Merit We factor, = )^ can find the relationships between the figure of merit, M, and the quality Q, as follows: Kurokawa-Schlosser, quality factor, from equation Q Kawakami, ^ 2 IZi- 1.1 Z2 i2 RjR2 figure of merit, 7 |M|2 = from equation iZi-Z^P 2L^ U + r Zt iz^ -) |Mr "MmP = 1.3 (Ri - R.r ^ -^-^ } (Rj + R2)^ , IZj IZi - (X, (eqn 2.8) + (Xj Z2i^ + Z2 18 -x^r |2 - X2)2 IZi = = + z^V IZj 4- Z{\^ |Z| + Z2V • |Zi - Z2P 4R^R2 q2 = 4|M|2 » 4^ = q2 IMp Q2 = q2 > > 1 |M| E. (eqn2.10) + q2 4 If (eqn 2.9) = •? (eqn 2.11) TRANSMISSION LINE SECTION REPRESENTATION OF SWITCHING CIRCUIT MODEL From an N-port box representation, the semiconductor devices are in shunt to ground and have two alternate impedance values. circuit (MIC) applications, it is For practical microwave integrated convenient to use transmission line sections in the embedding network of the switches Figure 2.4, shows the semiconductor device insertion loss unchanged at in and high circuit each arm. isolation, model of SPST and To optimize the SPDT switches with one the switch characteristics for low impedance values of the devices are kept rhs particular frequency in each state. impedance of the transmission ime section are vaned characteristics in a particular frequency interval. 19 The length and to achieve the characteristic optimum switching 1 Zo Zo SEMICONDUCTOR T SPST 1 DET/ICE DE77ICE *2 Zo SEMICONDUCTOR DF/ICE t Zo a. Zo SEMICONDUCTOR DEVICE SPOT 2 DEVICES Zo = Transmission Line Electrical Lengt±i = Transmission Line Characteristic Impedance Fi<'ure 2.4 Transmission Line Model of Switch Networks. 20 F. APPROACHES TO COMPUTATION DISSIPATION OF POWER- CIRCUIT Using the Touchstone program, we can design a switch to have optimum switching characteristics. But the semiconductor devices in the optimized circuit may not be able to handle the amount of power dissipated due to heating of the devices. For switching effective design, it is advisable calculate to the maximum power dissipation in each device before construction of the switch. ABCD 1. From Matrix Representation of a Two-port Network. Figure 2.5 the Vi Ij ABCD matrix is defmed in equations 2.12 and 2.13 = AV2 + BI2 (eqn2.12) = CV2 + DI2 (eqn2.13) Equations 2.12 and 2.13 have the matrix form. A B C D "A B" vf .C D. hi 'D -C" vf _-B A. Uii ^2 (eqn2.14) -1 The utility (eqn2.15) of the general circuit parameter matrix lies in the fact that cascaded two-ports can be represented by the chained product of element matrices [Ref 5: p 110]. = "Ai An b,' 52 Thus ports is (eqn 2.16) -In+lJ the general circuit parameter matrix representation of cascaded two- the matrix product of general circuit parameter matnces of the individual two- ports, as 2. D2_ B„' shown ABCD m Figure 2.6. Matrix Representation of the Switching Circuit Model In the circuit model we have transmission line sections and semiconductor devices combined. Lumped-circuits can be characterized by [Ref 7: p. 188], as follows: 21 ABCD two-port matrices 12 II Zg -AAW^ Fa 3 1 C D J Vg 1 AZl + B _vi m II CZj^ + D V2. I2 ABCD Figure 2.5 Zg Ii Matrix Model. 1 2. A Vg (CV In+1 1 3. -vvwv-*c A C B D TT- A C B D 7,1 Figure 2.6 N Two-Port in Cascade with Equivalent Matrix. 22 vi d^L 2.1 Series impedance, as shown in Figure 2.7 A B C D Z 1 (eqn2.17) 1 Shunt admittance, as shown 2.2 A B 1 C D Y in Figure 2.7 (b) (eqn2.18) 1 2.3 Lossless transmission line section, as shown A B CosG jZQSinG C D jYQSinG Cose is an electrical leneth of a transmission line section, as A B CoshCY C D YQSinh(Y = 1 Figure 2.7 in (c) (eqn2.19) Lossy transmission 2.4 (a) shown line section in Figure 2.7 (d) ZoSinh(7 1) 1 (eqn 2.20) I) Cosh(Y I) Physical length of a transmission line section. = a + jp a = transmission line P = wavenumber. Y Calculation of 3. From Power in a attenuation constant. Cascade Circuit Figures 2.5, and 2.6 [Ref AZl + Z: m 8: p. 393]. B (eqn 2.21) CZl + D v. Zg- (eqn 2.22) Zin Zin Z ^2 Ij+1 ^ a = = 4- (Ajlj) V -^ Z- ^m - (eqn 2.23) g (CjVp (eqn 2.24 for a lossless transmission line section. 23 ) SERIES IMPEDANCE a. i b. SHUNT .\DMITT.\NCE • a 1 . 1 = ELECTRICAL • LENGTH C.LOSSLES TRANSMISSION LINE SECTION I. d. Figure 2.7 yi ^ LOSSY TRANSMISSION LINE SECTION ABCD Matrix Representation of Devices. 24 Vj+1 i Power = (DjVp = (eqn2.25) (Bjip ,n dissipated in each two-port network. = 0.5^e[(Vi^Ii^*)-(V]^+lIk+l*)] ?^ k Power Pl 1,2,3, - = 1,2,3, (eqn2.26) ,n at load = O.S^elY^^yl^^^*] (eqn2.27) = Pin-f Pk k=l ^^^^2.28) 25 III. MICROWAVE SWITCHING DIODE The use of the semiconductor diode is as a switching element in microwave circuits based on the difference between the diode impedance under reverse and forward The diode appears as a very small impedance under reverse its on state most of the power impedance (reverse bias reflected bias. impedance under forward bias and a very large For a shunt-connected diode as a microwave switch, is state). delivered to the load, On and the diode looks the other hand, in back to the source, or dissipated in the diodes, off state, its introduce some characteristics of the p-i-n diode, reverse bias states, the equivalent circuit, THE P-I-N its in like a large power the and the diodes look small impedance (forward bias state) in shunt to ground. A. bias. In this chapter is like a we will behavior under forward and and power handling capability. DIODE STRUCTURE In a p-i-n diode, the semiconductor wafer has a heavily doped P-region and a heavily doped N-region separated by a layer of high resistivity material that intrinsic. The thickness of the high microns [Ref 9: p. 5]. The resistivity layer lies in the electrical contacts are made range between is nearly 1.5 to 150 two heavily doped to the regions. In practice, there are no materials without any impurities. A practical p-i-n diode consists of extremely high resistivity P or N-type material between low resistivity (highly doped) for P material, P and N-regions. The and v-type for either V or TC-type material. region is of sufficiently high the depletion zone will N doped, high lightly material. The resistivity layer is called 7t-type I-region of a p-i-n diode can consist of Figure 3.1(a) shows a P-v-N diode structure. resistivity, If the I- with few impurity atoms that will be ionized extend throughout the I-region and include a small penetration into both the P and N-regions. Because of heavy doping in the P and Nregions [he depieiion depletion zone will be zone wiU not extend ven.^ far :nto essentially equal to the I-layer width, \V. the structure of P-Ti-N diode, the depletion zone width width of the intrinsic ihem, ana che vvidth region. Most p-i-n I-laver. 26 diodes is ot the Figure 3.l{b) shows approximately equal to the use v material [Ref 7: p. 41] for the THE ELECTRICAL EQUIVALENT CIRCUIT MODEL B. The p-i-n diode used in microwave application has under forward and reverse bias L Forward Under region, states as showTi in Figure 3.2. Bias Equivalent Circuit the forward bias state, both holes and electrons are injected into the and the mobile carriers form a conductive plasma whose the carrier density obtained from the injection process. may be expressed = R^ The forward depends on bias resistance, + R^^ = resistance due to the = resistance of Rj|- resistivity I- Kc as: Rf where R- a simplified equivalent circuit I (eqn3.1) region, and P and N-regions and their ohmic contacts. For an abrupt junction diode, the resistance due to the I-region can be expressed as follow: R: = (eqn 3.2) 2ifH,,iL where W = I-region thickness, i|> = DC ]i^y = the average carrier mobility, and Tj^ = the carrier lifetime in the intrinsic region. forward bias current, In the shunt configuration R-, is of a application the forward bias resistance, the major factor of power dissipation in the diode. Since R- DC diodes, to switching bias current, i^ an i|- of 10 make R^ equal 2. to , we can mA, and increase i^ to minimize R- . for high voltage p-i-n diodes 150 to R^^fRef is an inverse function For low voltage p-i-n 200 mA is sufficient 9: p. 8]. Reverse Bias Equivalent Circuit Under die reverse biased state, the I-region is depleted of carriers and "he p-i-a diode appears as a constant capacitance to a microwave signal. The dissipation losses occur in the ohmic contacts and the resistances of the P and N-regions. represent these losses in the equivalent circuit model. at microwave frequency, the circuit Due used to to the capacitive reactance impedance of the p-i-n diode 27 R^. is in its reverse bias a. ?-V-H IMPURITY PROFILE I(1T) - b. Figure 3.1 «1- ^+ P-t-H IMPURITY PROFILE Profiles for the two P-I-N Diodes Types. R. 3 T i REVERSE BIAS FORWARD BIAS Figure 3.2 P-I-N Diode Chip Equivalent 28 Circuit. state much is larger than the of the p-i-n diode impedance in the determined by the diode is forward bias size state. The capacitance, C: shown in and I-region thickness as equation 3.3 -^^ = C: (eqn3.3) where £q = free space permittivity, Ej. = the relative dielectric constant of the material, D = W the junction diameter, and = region thickness. I- This equation minimum voltage is valid for all reverse bias voltage complete for I-layer magnitudes greater than the Figure depletion. 3.3 shows equation 3.3 graphically for typical available p-i-n diode I-regions. P-I-N Diode Cutoff Frequency 3. Hines [Ref 4], defmed a figure of merit for p-i-n diodes to relate the switching effectiveness in terms of switching cutoff frequency, f^^. The Hines figure of merit is given by 1 = ^cs The figure design, and and we can Rj. for R^- ._^ of merit, = (eqn3.4) ^ /^ 27rC:VRfRj. f^^ is R^., f^^g/f is one of the parameters used in microwave switching equal to the conventional diode Q. Knowing C:, Rp estimate the operating frequency range of the selected p-i-n diode from equation 3.4 C. POWER HANDLING In the off-state of the microwave switch, the to ihe scarce or dissipated of the junction lo withstand. rise. The other m incident which limits the is a maximum is reflected the p-i-n diode specification sheets these important estimate the power handling switches. 29 temperature that amount of power handling voltage that appears across the junction, which can cause designer to power back the p-i-n diode. This dissipation causes the temperature For each diode there factor RF capability damage is it can the peak to the junction. In parameters are available for the of the diode in the designed 1. Maximum Voltage across the P-l-N Diode The instantaneous voltage across RF the voltage and breakdown as a DC is is If the junction voltage bias voltage. voltage, the p-i-n diode a p-i-n diode junction in the sum of exceeds the device's avalanche region, and the p-i-n diode acts low resistance causing high negative current flow and rapid temperamre Figure 3.4 shows the condition for a high RF maximum when voltage across the junction occurs The maximum instantaneous voltage appUed = Vmax where Vj^^^^g is the DC White [Ref is Maximum to the junction is defined as: (^^^ 3.5) on the diode. breakdown voltage. A circuit an acceptable margin of safety designer maximum CW. a p-i-n diode is determined by the ambient The power dissipated In either case, junction temperature must be kept below the allowable value. This maximum temperature is dependent on the diode material (semiconductor), and the materials used in mounting and connecting to semiconductor. The recommended 200 °C [Ref a. a for the designed switch. temperature of the circuit and the power dissipated in the diode. pulsed or may choose Junction Temperature The junction temperature of be maximum (eqn3.6) 0-5 Vfe the p-i-n diode different safety factor within 2. in the reverse bias state. as: = Vax where V^^ is suggested the conservative limit of the safe 7: p. 155], The voltage drive with reverse bias. + ^bias ^RFp,,i, rise. the diode reverse bias impressed voltage across the junction may the algebraic maximum the junction temperature for safe operation is 10: p.290]. CW Power Dissipation In the case of a continuous or a long-duration pulse, ^he temperature !imit is determined by the initial temperature of the diode matenals, the temperature of the heat sink, and thermal resistance between the wafer and the heat sink [Ref 6:„ is the total thermal resistance unit in °C /watt. 10: p. 290]. The junction temperature, J*- T:, for a J given power dissipated, Tj P^ and = the ambient temperature, T. + PdGj, T^ is given by the equation: (eqn3.7) 30 I Figure 3.3 P-I-N Diode ACCION OlAMgTER. C vs. 0. iKf* I-Region Diameter and Thickness. CUROT Figure 3.4 Junction Voltage at High 31 RF and Reverse Bias. The value of 0:^ is determined by the physical volume of the junction, The maximum value of material and geometry of the package. packages can be as much A as 600°C/watt. 0- of 5°C/watt or thermal time constant T^^ 0: x^-^ mounted 9: p. 10]. = 0. = (eqn3.8) this value from the diode physical is available in the size. —W (eqn3.9) W = the "width of the I-region, K^j^ = the thermal conductivity of the material, A = HC = determined by the is e-HC the junction region thermal resistance, is limit o^ the active region. specification sheet or can be calculated where [Ref less glass Pulse Power Dissipation For a short duration pulse, the temperature where most large-area, high capacitance chip on copper heat sink can have extremely low b. 9:^ for the junction area, and the thermal capacity of the active region, available also the in specification sheet or can be calculated from: HC where C_ p = C pWA (eqn3.10) = the specific heat of the material, = the density of the material. For a pulse width of 0.25 t^j^ or and less, the pulse width with the thermal time constant. All the thermal energy area, not spreading units of C is to the surrounding. is is small compared absorbed in the active region The temperature nse of the junction. AT, exoressed bv: AT = Ph -S At (eqn3.ll) HC 32 m where At is from the above assumption rise The junction temperature^ the pulse duration. is the T: for a short pulse width sum of the ambient temperature and the temperature of the junction. T- = T^ + For pulse widths of AT (eqn3.12) 0.50t^j^ to 3t^j^ the diode junction temperature follows an exponential curve given by the equation T| Note = T^ + Pd that equation 3.13 contain total thermal resistance. ej [1 0-, - exp(-t/T^i^) For cooling between TABLE OF TYPICALLY AVAILABLE To lists a pulses, the junction temperature follows t^-^ P-I-N illustrate typical p-i-n diodes available for number of approximate typical diode electrical parameters. (eqn 3.13) the junction thermal resistance and not 0:„ the an exponential decay with the same time constant D. ] chips [Ref. 9: p. 10]. DIODES microwave switch design, Table from Microwave Associates, The symbols used this chapter. ^Neglecting the heat fiow from the junction. 33 Inc. and 1 their in this table are already defined in TABLE 1 TYPICAL PARAMETERS OF MODEL NUMBER P-I-N DIODES MA- MA- MA- MA- MA- MA- MA- 4P102 4P103 4P202 4P203 4P303 4P404 4P504 Minimum Vb(VoIt) 50 30 100 100 200 300 500 0.5 .15 .05 .15 .15 .20 .20 2.5 1.5 2.0 1.5 1.5 0.6 0.6 .100 .010 .100 .100 .200 1.00 2.00 60 40 60 30 30 20 20 2.5 3.75 2.5 5.0 5.0 7.5 7.5 Maximum Cj @ Vr(lO) (pF)(Volt) Maximum Rs @ IfllO) (ohm){ma) Typical Carrier Liretime(jLiS) Maximum Thermal Resistance ("C/watt) Power (max) Dissipation at25°C (watt) 34 IV. EVALUATION OF SEMICONDUCTOR MICROWAVE SWITCH CHARACTERISTICS M In this chapter, semiconductor device figures of merit, Kawakami's and diode Q, are tested for the shunted switch configuration, to find the best parameter for use in From equation a s"witch selection and/or design problem. M, of merit switching the provided. By using characteristics, CAD a the switch on-state, insertion and maximize the load its isolation, isolation in its off-state. should be insertion loss in From the value of of merit that of this type of microwave switch. The power terminal voltage. We semiconductor device terminal voltage, and 1. and load select the figure and heat removal requirements be estimated from and load loss we can compare and characterizes the performance dissipation that the figure In order to solve the equation mentioned program (Touchstone) we can minimize the these two switching characteristics, best we know a function of insertion loss, S2|(l), in the switch on-state, is isolation, S2j{2), in the switch off-state. above, 1.5, in the individual will its semiconductor device can introduce two methods to evaluate the power dissipation: Using a Touchstone application program to evaluate the terminal voltage of interest. 2, Using a Fortran program written from the in A. Chapter model and method introduced circuit II. INSERTION LOSS AND LOAD ISOLATION CALCULATION USING COMPUTER-AIDED CIRCUIT ANALYSIS PROGRAM (TOUCHSTONE) The Touchstone program aided engineering [Ref It 11]. is advanced software for RF/microwave computer- can provide an output of the S-parameters of a multi- port network, and can perform an interactive optimization, and has can be used in the measurement of selected terminal voltages. circuit, we can optimization create mode a circuit to get the file and evaluate circuit method uses semiconductor characteristics. The resistance (R:) and diode junction capacitance the circuit file. For a given electrical performance or use the optimized circuit-component values. There are two alternative methods of approach first applications which to analyze these device parameters, diode junction (C;), as the direct input The second method employs semiconductor Q, as an input parameter of the circuit 35 file. two switching parameters of device figure of merit, diode In this approach the diode junction capacitance and/ or resistance are calculated in the circuit procedure as the Two first types file, and then follow the same category. of microwave switches, single pole single throw, and single pole double throw switches, with one or multiple-semiconductor devices are investigated. By using the electrical equivalent circuit model introduced in Chapter circuit file we can create the following one of the above categories for the Touchstone system. assumptions for the circuit model All diodes in the switch are identical. 2. The transmission line configurations in the 3. The transmission line sections are lossless. 4. The transmission line 5. The transmission line electrical length is impedance If the input of the circuit The are: 1. resistance II, is switch are symmetrical. between 30 to 90 Ohms. between 30 to 120 degrees. the figure of merit, or diode Q, then the junction file is and junction capacitance are calculated from equations 4.2 and 4.3: 1000 J (eqn4.3) 2^Po<^iQdiode ^^ ^^^ figure of merit. ohm. R: is the diode junction resistance in C; is the diode junction capacitance in pF. Fq is the center frequency in relation of R-, C- 4.2, 4.3 1000 = 'J The {eqn4.2) 2^FoCiQdiode C; where Q^i^ode 1000 = R- is shown m and diode Figure 4.1. Q GHz. at the center In our circuit frequency of 15 GHz. from equation file for convenience we fix the value of capacitance and calculate the value of junction resistance (equation 4.2) and var\' the value of diode Q. ^For two-diode switches, TLINl is identical to 36 TLIN3 (see Figures 4.3 and 4.7). tS3 o >- 2 O iz; H— o CO p> o iz; CO CO (kho) aoNYxsisaH Figure 4.1 Resistance vs Capacitance as a Function of Diode Q. 37 In the procedure of creating a circuit for low insertion loss and high to optimize the switch characteristics file one more assumption isolation, is made; the impedance The values of the diode are kept unchanged at the particular frequency in each state. length and the characteristic impedance of the transmission line sections are varied to achieve the optimum the optimization switching characteristics in the operating frequency interval. mode of the maximize load isolation computation time to produce a It is only the insertion we can minimize file, same the at approach the wanted value. optimize circuit This time. found that a more approach may require a long efficient The computation time loss. normally produces satisfactory insertion chart of steps in creating a circuit the switch insertion loss and and the switch insertion result, file loss for the and load In loss still may method of approach typically is shorter, Figure 4.2 isolation. is not to is and the flow Touchstone system. Insertion Loss in the Snitch On-state 1. In the switch on-state, the ratio of the available power to the power reaching the load diode is is defined as the insertion loss of the switch. In this switching state, the p-i-n equivalent to a very high impedance in shunt with the circuit. of energy will be dissipated in the diode, but most of the energy is A small amount delivered to the load. Therefore the insertion loss of a well designed switch should be as low as possible. In order to achieve the low insertion loss, the optimization system is mode in the Touchstone used to perform the minimization of insertion loss to obtain the circuit design values. In practice the insertion loss has units of dB, [p. Insertion loss in dB = lOlog^Q -^^^^ and can be calculated from: ] (eqn 4.4) t^load From Chapter input and II, under the assumption of an ideal switch with matched load output ports, we can use the scattering transmission behavior for both types of switches. state matrices to Recall from Chapter at both represent II, for the on- reDresentadon of S-matrices: 1 SPST ON STATE: (eqn 4.5) [S] 1 38 the 1 ARM SPDT From equations 4.5 and (2) ON: Load circuit file (eqn 4.6) 1 of the switch 4.6, the insertion loss and can be evaluated from the 2. = [S] is defined as energy is power power reaching to the reflected also defined units of dB and has is For an transfer to the load. is ideal switch in is transferred to the load. as in equation 4.4. achieve the best performance of the designed swiT:ch, the Touchstone mode is and its off-state, the better switch performance. same formula the Most of the dissipated in the diode meaning that no energy In the real switch, the higher load isolation by the the load. In this switching state, the back to the source, some of the energy the load isolation should be infinite, isolation has is equivalent to a very low impedance in shunt with the circuit. amount of energy can a small dB^ Isolation in the S>vitch Off-state ratio of the available is in of Touchstone system. In the switch off-state, the load isolation of the switch p-i-n diode !S-.|I The load In order to optimization used, if desired, to optimize the load isolation as well as insertion loss. The S- matrix representation of the switch in the off-state with the same assumptions as for the insertion loss is defmed as follows: 1 SPST OFF STATE: = [S] (eqn 4.7) 1 1 ARM SPDT (3) ON: [S] = (eqn 4.S) 1 From of the [Refs. 5.61, SPST and equations switches, and 4.7 jS^^i m and dB 4.8 IS^^il in is switches. ^dB value = 20 log^Q S21 39 dB is denned as the load isolation defined as the load isolation oi the SPDT (start j 1. 2. 3. INPUT PARAMETERS: TRANSMISSION LINE Initial Characteristic Impedance Initial Zlecrrical Length DIODE PARAMETERS Junction Capacitance, Resistance OPERATING FREQUENCY V/L OUTPUTS: SWITCH CHARACTERISTICS Inser1?ion LOss Load Isolation 1. 2. -^TOPj MINIMIZE INSERTION LOSS TRANSMISSION LINE Characteristic Impedance Electrical Length SWITCH CHARACTERISTICS Insertion Loss Load Isolation io Figure 4.2 Flow Chart of a 40 Circuit File. Example 3. We of Insertion Loss and 2. Single pole double The 4.3 (b) and are applied to both cases. file Two- Diode Switch electrical circuit representation The switch on- and in Figure 4.3(a). (c) respectively. numbers are assigned The example of To circuit files off-state equivalent circuits are create a circuit switching for SPST two-diode SPSTD.CKT, SPST two-diode of the file listed in switch shown from the equivalent component, then the steps to every isolation, evaluation of a is shown in Figures circuit, node in Figure 4.2 are followed. characteristics, insertion and load loss switch are listed in Appendix A. Appendix Al, is an example of the created for the single pole single throw switch in the resistance cases: throw switch with four diodes.^ categories of creating the circuit SPST two throw switch with two diodes. Single pole single a. Isolation Evaluation divide the evaluation of switciiing characteristics into 1. Two Load first circuit file category, in which diode and capacitance values are chosen and used as input data for the circuit file. Input parameters are diode junction resistance and diode junction capacitance from typical p-i-n diode parameters available in Table MA-4P203 with pF 0.15 We junction capacitance and 1.5 the input parameters for the circuit GHz, we have 1. the output file file. select the number diode model ohms junction After optimizing the circuit resistance to be file from 10 to 20 of the switch insertion loss and load isolation as shown in Table 2. From LINDOFF are the Touchstone switch insertion loss The file listing in Table 2, switch insertion loss and load isolation respectively. switch operating frequency range dB. output is around is LINDON Our and load isolation -0.1 to -0.2 is required between 10 and 20 GHz, the wanted value of dB and the load isolation greater than -45 characteristics of Table 2 satisfy our switch design requirement. insertion loss and shown The plot of in Figure 4.4. After optimization, the circuit-component values, characteristic impedances and electrical circuit file. lengths of the transmission line sections, The optimized transmission line section line section A line-section parameters of the has are given in example Z^ of 39.40 ohms and E^ of B has Z^ of 38.25 ohms and E^ of 62.7 degrees. m the optimized Appendix Ai are: 106.3 degrees, transmission In switch construction, to obtain the design value of the insertion loss and load isolation, the transmission line ^There are two diodes in each branch of the switch. 41 TLIN A ZS VvW I TLIN TLIN A B H 1 1^ Vc D2 ^ 4.3(a) SPST 2-DIODE EQUIVALENT CIRCUIT - TLIN B TLIN A 2 hj- \ 4.3(b) 1 Cj CD Rj Rj ^ 2 TLIN B I 1 Rj 4.3(C) Figure 4.3 -dZZH SPST ON-STATE EQUIVALENT CIRCUIT TLIN A 1 TLIN A 3 h 1 TLIN A 3 ^ 1 I 4 Rj SPST OFF-STATE EQUIVALENT CIRCUI' Single Pole Single Throw 42 Switch. Equivalent Circuit. (aa) o o NoriYiosi avoi o o C3 O en m 1 1 1 1 1 1 OJ en , C3 a o ^ t— y 1 / + OJ 1 / e5 1 ) UJ cz en / 1 r a: cz o r 1 Tj a 'i\ 1 J a 1 f a . cu en c: 2: . 1 \ C3 s n r \ 1 "»-' 1 1 o o n o o C3 C3 O o in 1 (sa) Figure 4.4 ssGi :ioiiHZSm SPST Switch Insenion Loss and 43 Isolation vs Frequency. TABLE 2 TOUCHSTONE OUTPUT SPSTD.CKT Frequency GHz - dB dB [S21] LINDON [S21] LINDOFF 10.0000 -0.150 -46.276 12.0000 -0.053 -47.025 14.0000 -0.085 -48.011 16.0000 -0.110 -49.261 18.0000 -0.141 -50.590 20.0000 -0.195 -51.750 sections in the switch should have their characteristic impedances and electrical lengths close to the calculated values. SPSTQ.CKT, value of diode file. Q Appendix A2, throw switch are between 10 After optimizing the circuit diode Q values. 3 is and 500 are used as input parameters of file from 10 the collection of of This table diode isolation vs frequency of a SPST diode SPST have the output file of the 3. outputs evaluated for different has the character of a figure of and high switch with two diodes with diode 4.1 for a Q is, the isolation. cne plot of insertion loss vs frequency can use these two figures together with Figure switch from a given specification. Q this circuit performance. The higher diode better the suitcii characteristics: low insertion loss show Table in SPSTQ.CKT verifies that the Figures 4.5 and 4.6 GHz we to 20 shown merit, serving as an indicator of switching We circuit file created in switch insertion loss and load isolation as Table an example of a is which input parameters are Q^j^ode ^^^ diode The selected value of junction capacitance is 0.15 pF and the for the single pole single junction capacitance. listed in Q and load as a parameter. design problem of a SPST For example, a specification may require a two p-i-n switch to have at least -0.1 dB insertion loss and isolation better than 44 TABLE 3 TOUCHSTONE OUTPUT SPSTQ.CKT INSERTION LOSS IN dB Frequency Diode Diode Diode Diode GHz Q=10 Q=20 Q=50 Q=100 Q = 200 Diode Diode Q=500 * 10.0000 -.367 -.342 -.135 -.064 -.056 -.052 12.0000 -.194 -.111 -.049 -.031 -.019 -.011 14.0000 -.342 -.170 -.082 -.062 -.044 -.034 16.0000 -.499 -.231 -.101 -.052 -.037 -.013 18.0000 -.517 -.269 -.134 -.072 -.039 -.019 20.0000 -.724 -.393 -.186 -.096 -.048 -.019 Diode Diode LOAD ISOLATION Frequency Diode Diode Diode GHz Q=10 Q=20 Q = 50 10.0000 -20.21 -30.53 -47.38 12.0000 -20.51 -30.84 14.0000 -21.05 16.0000 IN dB Diode Q=200 Q = 500 -58.78 -70.62 -86.42 -48.06 -59.46 -71.30 -87.09 -31.37 -48.88 -60.53 -72.37 -88.17 -21.89 -32.27 -50.17 -61.90 -73.76 -89.57 18.0000 -22.93 -33.42 -51.39 -63.26 -75.14 -90.96 20.0000 -23.95 -34.57 -52.40 -64.28 -76.13 -92.01 Q=100 i -60.00 dB at the mid- frequency of 15 GHz. In Figure 4.5, with 50 or more the switch can have insertion loss the diode Q of 50 is less than -0.1 dB. the value of diode But from Figure 4.6 not great enough to obtain load isolation of -60.00 dB. 45 Q in in o o m > Q O 9'0- fO(aaj Figure 4.5 ssoi NoiraasNi SPST Switch 46 Insertion Loss vs Q^^jode* o IN CO —ffl - •:< _ •O- 3 i; Q O '^ ' o CO 3 > CO 1 O I _® •Ei CSJ in I I I ( ( o ( o 2: CO > •r •i> cr Q o Ej.. ..(tv "a- Q - I I I I o,'oicio OICS^C^.C J 92- 09(aa) Figure 4.6 9i- 01 01 D Oi<p + OOT- S3T- Moiiviosi avoi SPST Switch Load 47 _M Isolation vs Q^jjode" 091- we Therefore From diode select a Q= Figure 4.1 with the that has the switch for the value of we can choose one of 100 curve has the value of junction capacitance and resistance close to we If model number MA-4P504 with diode junction capacitance of 0.2 dB and 88.42, switch insertion loss of -.102 circuit shown from the equivalent file Appendix SPDTD.CKT, listed in Appendix Bl, in the off-state. model number as in the circuit GHz, we have the output ohms and file We the SPST switch circuit switch insertion is an example of the With the used circuit file same p-i-n diode after optimizing this circuit file from section line characteristic impedances and 93.58 degrees for transmission line section A, listing in GHz, the designed insertion loss 0.15 However is SPDTQ.CKT, shown of the The SPDT for the required operating four-diode switch using p-i-n junction capacitance and -1.0 dB and load SPDT the insertion loss requirement of a switch design problem. vs operating frequency pF around realize that the insertion loss switch case. shows that Table 4 number MA-4P203 with junction resistance, has dB SPDT SPST of the insertion loss and load isolation shown in ohms and frequency between 10 to 20 diode model SPST as in 32.82 degrees for transmission line section B. The output -50 file The optimized transmission electrical lengths are: 46.56 to the create a B. SPSTD.CKT, file To (b) respectively. throw switch with four diodes. for the single pole double 4. and circuit files for evaluating listed in 89.06 is same procedure can be followed circuit, the and load isolation are Table dB from the modified in the on-state, the other is in Figure 4.7(a) Appendix A. The example of 10 to 20 o'C considered as two SPST.switches with is Or we can make some necessary modifications switch case. loss value four-diode switch has the electrical circuit representation and the switch on off-state equivalent circuit files in isolation of -60 switch when one arm input arms tied together, A SPDT Q obtain the diode file. SPOT Four-Diode Switch A single pole double throw b. circuit GHz we junction resistance of 0.6 ohm, at 15 SPST.CKT diodes that the p-i-n our estimated value. select p-i-n diode pF and of 100. Q<;iiQ(je ohms isolation greater than switch case and load 1.5 is not so low as for isolation satisty the general plot of insertion loss and load isolation in Figure 4.8. listed in Appendix B2, is an example of the circuit created for the single pole double throw switch for which input parameters are and diode junction capacitance. In this 48 example, the value of 0.15 pF file Q(jiode junction TLIN A TLIN B 2" 2di 2s 3 TLIN A 4- XZ D2 Zl 1 ^^w vs TLIN A 5 TLIN B — S' TLIN A 7 IH xz D4 D3 4.7(a) SPOT 4-DIODE SWITCH EQUIVALENT CIRCUIT ZS AAVV Vc TLIN A 2 TLIN A -5 TLIN A TLIN B — ^ TLIN B Rj TLIN A 6 Rj 4.7(b) SPOT ON,OFF-STATYE EQUIVALENT CIRCUIT Figure 4.7 Single Pole Double Throw 49 Svvitch Equivalent Circuii. Rr (aa) Moiiviosi ovoi o o o o o o CJ C3 1 1 1 u. — —< u_ 1 [ , c\i en , a \ czi OJ 2: C3 t-H _i a T 4- 1 \ •" 1 C3 LU a Li- / Q. CO I / 03 c a j^ 1 tn "o / o a iri 1 * en 1 LU UJ V OJ CO \ \ o . —1 2: , en 1 1—. C2 _J n o o o / "-< 1 1 o o o o o I (aGj Figure 4.S SPDT ssoT .voirjiSi^i Switch Insertion Loss and Isolation vs Frequency, 50 TABLE 4 TOUCHSTONE OUTPUT SPDTD.CKT Frequency - GHz dB dB [S21] LINDON Table LINDOFF 10.0000 -0.756 -56.199 12.0000 -0.327 -57.856 14.0000 -0.226 -59.898 16.0000 -0.385 -61.603 18.0000 -0.417 -61.471 20.0000 -0.665 -59.573 capacitance, and values of diode parameters of the [S21] circuit Q from 10 to 500 are selected The optimized output file. and used as input SPDTQ.CKT file is shown in 5. For general use of diode Q as the figure of merit to characterize the switching performance of this type of switch, the choice of junction capacitance value selected as input parameter to the Touchstone dependence of switch performance shown SPDTQ.CKT listed in merit, serving as diode Q Table 5 The a function of diode mentioned plot of insertion loss Q from the The procedures in the Q The result of output file has the character of a figure of parameter that characterizes the switching transmission These two plots can be used specification. diode 5. an indicator of the switch performance. In a switch design problem, can be used as a characteristics. does not strongly affect the Q- Table in verifies that the file SPST results m and load isolation vs operating frequencv m a design for the Table 51 are of a m Figures 4.9 and 4.10. SPDT switch iroin a given shown problem of design switch case. 5 a as SPDT switch are the same as TABLE 5 TOUCHSTONE OUTPUT SPDTQ.CKT INSERTION LOSS INdB Frequency Diode Diode Diode Diode GHz Q=10 Q = 20 Q = 50 Q=100 Q = 200 10.0000 -1.96 -1.38 -1.04 -.926 -.824 -.796 12.0000 -1.36 -.725 -.345 -.217 -.148 -.117 14.0000 -1.13 -.577 -.265 -.179 -.129 -.095 16.0000 -1.32 -.756 -.394 -.294 -.232 -.190 18.0000 -1.69 -.935 -.395 -.214 -.118 -.059 20.0000 -2.37 -1.49 -.835 -.564 -.515 -.425 Diode Diode LOAD ISOLATION B. Diode Diode Q = 500 IN dB Frequency Diode Diode Diode Diode GHz Q=10 Q = 20 Q=50 Q=100 10.0000 -33.55 -44.74 -59.50 12.0000 -34.35 -45.92 14.0000 -35.82 16.0000 Q = 200 Q = 500 -71.18 -83.59 -99.46 -60.83 -72.58 -85.09 -100.95 -47.90 -63.08 -74.99 -87.56 -103.43 -37.56 -49.71 -64.75 -76.66 -89.13 -105.00 18.0000 -38.27 -49.68 -64.27 -75.97 -88.18 -105.04 20.0000 -37.54 -48.24 -62.75 -74.37 -86.21 -102.20 THE SEMICONDUCTOR DEVICE FIGURE OF MERIT WHICH BEST CHARACTERIZES THE SWITCHING PERFORMANCE Two well performance known figures of merit were used as parameters to predict the switching of semiconductor microwave 52 switches. In this thesis research, the m o in o w > Q O 3o"0- 09*0- S*L"0- (aa) Figure 4.9 SPDT T- SS"T- QQ'T- o-j- 3- 32'o-0g*2- SSOT N0IXH3SNI S\^'itch 53 Insertion Loss vs Q^io^e- o o in Q < O > Q o 09- S^.- (aa) Figure 4.10 SPDT 001- 9oT- MoiiYiosi avoT Switch Load Isolation vs Q^Q^jg. 54 091- semiconductor device considered microwave p-i-n diode, tlie is The conventional diode switch. simplified equation of use the conventional Kurokawa and Q Q used in a sliunt-configuration was shown to coincide with Schlosser for quality factor Q, and therefore In Chapter as our semiconductor device figure of merit. the we II equations 2.10 and 2.11 showed the relationship between both figures of merit: the Q diode and Kawakami's M. equation 1.5. Q Table 6. and the switch transmission loss which has the diode characteristics defined in and load Q as isolation were evaluated an input parameter. For the values of insertion loss and load isolation evaluated with different s'W'itch case, diode circuit file two equations, we investigated the verify these Optimal values of switch insertion from the Touchstone SPDT M Kawakami's relationship of To values at 15 GHz. are substituted in equation 1.5, and the results are listed in TABLE 6 COMPARISON BETWEEN FIGURES OF MERIT M, AND DIODE Q Diode Q 10.0000 M S21 (1) S21 (2) 0.9421413 0.1590319 AM (eqn 1.5) — xi00(%) AQ 0.9770399 0.1667 0.9677804 20.0000 0.0865225 0.9937131 0.0161 0.9830945 50.0000 0.9985498 0.0404859 1.8e-3 0.9872322 100.000 0.0222759 0.9994510 2.9e-4 200.000 0.9897033 0.9997507 0.0118343 5.2e-5 500.000 Table 6 0.9915362 0.9999076 0.0053798 shows the comparison of the two from equation 1.5. Note that in this table 55 figures of merit, with S2i(l), S2j(2) M correspond calculated to switch insertion = form: $21 this type value of and loss load isolation 10^*^°'-^^'. of switch at M is 0.9999. respectively, The values of M where are less than "^^^^^ °^ ^^ Q^jjode °^ ^^ ^^^ For Q typical diode the percentage of deviation values, ^^ M reduced tremendously is value the as 1 mentioned 0.9762, and at departs very in the of S2J high in the earlier. Q^j^ode For °^500 the from unity, and region. Thus the little Q is parameter Q^jjode ^^ niore convenient to use due to its wider range compared with the parameter M. When tested for different types of switch, ^^ the results are nearly the shown same as each interval). in Table 6 for An conventional diode is that it is Q additional merit iVI, - the values of reason in M (almost unity and small deviation in support of our to select the Table 7 shows the comparison of the result well kno\^Ti and widely used. M calculated from equations 2.10 and 2.11, this table equation 2.10 can be used to convert the diode and vice decision as the best figure of merit to characterize switching performance from Table 6 and values of verifies that all Q value to the figure of versa. TABLE 7 COMPARISON OF FIGURES OF MERIT M, FROM DIFFERENT APPROACHES Diode M (eqn Q 1.5) M (eqn 2.10) M (eqn 2.11) 10.0000 0.9770399 0.9805806 0.9800000 20.0000 0.9937131 0.9950372 0.9950000 50.0000 0.9985498 0.9992001 0.9992000 100.0000 0.9994108 0.9998000 0.9998000 200.0000 0.9997507 0.9999499 0.9999500 500.0000 0.9999076 0.9999919 0.9999920 1 10 SPDT s\\itch with tuning stub, micro strip model. 56 NODAL VOLTAGE CALCULATION USING TOUCHSTONE PROGRAM C. The power across dissipation in a particular diode can be calculated by the voltage resistance or the current flow in the resistor of the p-i-n diode equivalent its circuit. In the Touchstone program there circuit file a technique for probing the nodes within a is An determine the voltages at those nodes. to voltage source (VCVS) terminals of the used as a non-loading voltmeter probe [Ref is VCVS voltage-controlled ideal are connected to the nodes between 12]. The input which the voltage is to be determined. The output terminals are connected to an output port so that the voltages may be read. The voltages read out from this the open circuit generator voltage [Ref Touchstone calculation The is SPDT shown circuit Touchstone are normalized to unity value of Appendix C shows examples of the 12]. of nodal voltages of circuit files written for the evaluation For switches. method SPST and SPDT switch case, the equivalent circuit model using in nodal voltage in Figure 4.11. file SPDTV.CKT, VCVS circuit file using listed Appendix C2, in modules acting voltages from the attached terminals. is an example of a as voltage probes reading the nodal The input parameters for this circuit file are the diode parameters and the optimal transmission line section values of the SPDT evaluated in Appendix B2. circuit file that we can more than define up to four ports in our circuit while the circuit file last three both on and P^ = SPDT a VCVS module switch with four diodes, there measured to the is meaning that we can measure no in the SPDTV.CKT circuit nodes are measured by making some modifications to new positions). The output this files of 8. voltage across the resistive part of the p-i-n diode equivalent off-state, the individual p-i-n diode file, three nodes are first are listed in Table Knowing terminal where The (by moving the SPDTV.CKT circuit To measure three nodes at a time. are six nodes of interest. file, The major disadvantage of the Touchstone switch next step is to calculate the power dissipation in the from the equation: -^ P^^ is the dissipated power (eqn4.9) at node n, y^ is the terminal voltage at node n, and Rj^ is the resistive component of the n^^ 57 p-i-n diode. TLIN A TLIN TLIN A B 10 vcvs Figure 4.11 Nodal Voltage Measurement Equivalent TABLE Circuit. 8 NODAL VOLTAGE FROM TOUCHSTONE SPDTV.CKT SWITCH ON-STATE Frequency ^load Vdi SWITCH OFF-STATE Vd2 ^load Vdi Vd2 10.0000 .458 .006 .006 7.7e-4 .017 7.3e-4 12.0000 .482 .008 .008 6.4e-4 .016 6.0e-4 14.0000 .485 .010 .009 5.1e-4 .015 4.7e-4 16.0000 .478 .012 .010 - 2e— .014 3.9e-^ 18.0000 .477 .015 .011 4.2e-4 .015 4.0e-4 20.0000 .463 .018 .012 5.3e-4 .021 5.0e-4 58 In practice the dissipated power in a particular diode delivered to the load in the switch on-state. Therefore each from equation 4.9 is normalized to switch the normalized to the power is power dissipation calculated For the output power. on-state normalized power value, equation 4.9 becomes: ^joad ^^n^ p^ = the load terminal voltage of the switch on-state. is The use of Touchstone circuit SPSTV.CKT and SPDTV.CKT, files, convenient for evaluating the diode terminal voltage, but solve for so one power power may dissipation dissipation in each diode calculate the heat production Touchstone output file has from equation from equations only three Chapter significant them in a use Touchstone to digits after However may the digit. to see that the decimal point, These outputs for a very small nodal voltage when we cause significant error equation such as equation 4.10. quadratic To do directly. However we III. numerical round off takes place in the third across the diode, these rounded off outputs very and use these dissipated powers 4.10, in is computer program calculating the a special ""vrite generally satisfy engineering requirements. substitute we cannot and the diode junction temperature problem use a hand calculator or meaning that * ^n f^loaJ where V^^^^ (eqn4.10) It a is serious disadvantage to use these outputs for high output power microwave switches. For example an output voltage of 0.010 from Touchstone to represent a value of 0.0103 volts can cause an error of 0.88 watts of diode power number may look temperature small, however it in a one kilowatt switch. can cause an error of 30-40 C This in diode junction This error can affect the decision of selection of a proper p-i-n diode rise. for the switch design. D. EVALUATION OF POWER DISSIPATION AND HEATING USING FORTRAN PROGRAM To avoid some disadvantages of evaluation for power computation, we a specific computer program have been written now there circuit is [Ref in may use FORTRAN IV for Touchstone nodal voltage CAD program or create Many microwave CAD programs both mainframe and minicomputers, but up to to solve for the The Fortran language of the search for another to solve this problem. no program written 7]. the power dissipation in a microwave requires specific formats of input and output 59 and has the compiled before running the program. to be microwave engineer are These two capability. program advantages lead outputs, for example in cascade. To write a accurate to to evaluate the terminal voltages of the diode appropriate two-port matrix forms. admittance and series m impedance simple ABCD matrix components For our switch the iumped-circuits. Fortran into ^ of the two-port networks for a transmission line section, representation the circuit we introduced an In chapter 2 the in microwave switch equivalent components of the switch are converted two-port electrical circuit, complex number notation, and double precision its more than ten complex matrices multiplication of Nonetheless, the advantages to a shunt circuit model, characterized as boxes in cascade connecting with the are applied voltage at one end and the load at the other end. To SPDT evaluate the power dissipation and junction temperature switch which has an equivalent circuit in Figure 4.12, with the optimal by use of Touchstone, the procedure follows the flow transmission line sections diagram shown shown in the diodes of a in Figure 4.13. Nodal Voltage and Current Calculation 1. We assume that the switch we series impedance. state branch the other transmission First line divide the equivalent circuit into the off-state and the section ABCD transformed into supplied by a one volt generator with 50 is equivalent circuit one parts, For both on- and branch. diode two the on- off-states, two-port matrix form (Figure 4.12(a)) by subroutine ohms each network MATRIX. is This subroutine using equations 2.18 and 2.19 for the transformation of a shunt diode and a lossless transmission line section into the and currents voltages the in individual two-port elements ABCD circuit, two-port matrices respectively. the To obtain impedances of the successive input must be determined. All two-port networks in the branch MATMUL and produce a new equivalent circuit as MATMUL provides a complex matrix product of a pair are cascaded by subroutine in Figure 4.12(a). Subroutine of matrices. From Figure 4.12(b), input impedance in each branch The impedance of calculated from equation 2.21. paralleling of input current (I'^^) impeaances of both branches and input voltage 2.22 and 2.23. state branches. The next step (v- is ) iZ- _-, . ) is ^^ determined by the Z-^^r). The switch input to find the currents is and voltages in the on- as follows: 60 and off- equal to the switch input voltage Current flow in the on- and off-state branches method ^inofT^ from the generator are calculated from equations The input voltage on each branch (paralleled ports). current divider the switch 'Z- {'Z.-^^q^, is determined by vvvwHi'' — A^AA fii N r^— N r^==^'' ll^ > Figure 4.12 ABCD Matrix Representation of 61 SPDT switch Circuit Model. INPUT PAKAiMETERS: DIODE: Rj, Cj, DIODE Q, NO. OF OIODE 2. TRANSMISSION LINE: Zo, EL 1. :. OPERATING rRECUENC: Jt. SUBROUTINE MATRIX ABCD REPRZSZNTATION SUBROUTINE MATRIX ABCD REPRESENTATION SUBROUTINE MATMUL N-TOO PORTS CXSC\DE SUBROUTINE MATMUL N-TWO PORTS CASCADE OFF^STATE SRANOi INPUT IMPEDANCE ON-STATE 3RANCT INPUT IMPEDANCE NO SWITCi: INPUT IMPEDANCE INPUT VOLTAGE INPUT CURRENT NO -i. OFF-STATE 3RANCT INPUT VOLTAGE INPUT CURRENT ON-STATE BRANCi INPUT VOLTAGE INPUT CURRENT INPUT PO'.'fEa POWEn IN LOAD INPUT POWER LOAD POlfES IN SUBROUTINE POWER TERMINAL VOLTAGE DIODE POWER DISSIPATION SUBROUTINE POWER TERMINAL VOLTAGE OIODE POWER DISSIPATION NO CI INPUT SIGNAL SUBROUTI^fE THERM I PULSE INPUT SIGNALI UoRCUTI^fE THE?-!- STOP Figure 4.13 Flow Diagram for Calculation of Power Dissipation and Diode Junction Temperature. 62 I ^in^^nofT = on ^inon "*" ^mon ~ in where I^^ " (eqn4.11) ^inoff ^inofr on is the current flow in switch on-state branch, is the current flow in the switch ofi'-state branch, \q^ ^inon ^^ ^^^ input impedance of the switch on-state branch and, ^inoff ^^ ^^^ input impedance of the switch off-state branch. The 4.12(a). final step of nodal voltage and current calculation returns to Figure In each branch, starting from the leftmost node, currents and voltages in adjacent nodes are calculated by equations 2.24 and 2.25. In this step we obtain the currents flowing in and out of each particular node, as well as the input and output power calculation voltages, leading us to the 2. Power Dissipation in the Individual as in the next section. P-I-N Diode For the calculation of diode power dissipation we named POWER. create the subroutine input voltage of each branch are the initial in each branch of the switch, In this subroutine, the input currents and input parameters. These currents together with input and output voltages of the diode's node are calculated from equations 2.24 and 2.25. Equation 2.26 used to calculate the diode power dissipation with is corresponding nodal voltage and current. rightmost nodal current and voltage equation 2. 28 (I^^, For the power V^^) at power dissipation in each diode we can all power dissipation in dissipation in the transmission line sections). and all use the as inputs to equation 2.27 or using with the branch input power minus the total of that branch (include load its the calculated powers are normalized The power to the power delivered to the load in the switch on-state. 3. Junction Temperature :n the Individual The junction temperature of a p-i-n P-I-N Diode diode is determined by the ambient temperature of the switch and the power dissipation in the diode temperature is assumed dissipation in the diode to be constant at is The ambient about the room temperature. The power a major factor that causes 63 itself damage to the semiconductor From devices in the switch. we can section, CW the calculation of the diode dissipation mentioned in previous separate the calculation of diode junction temperature into two cases, power dissipation and pulsed power THERM! subroutine power dissipation. In the Fortran program, the CW-power case, for considered by summing evaluates the junction temperature of the mounted on a heat sink. The junction temperature is the ambient temperature .and the increment of temperature of the diode caused by the CW-power input diode available is (equation from the rise. In this case we assume For the pulsed input-power used for evaluating the diode junction temperature is that the input pulse width thermal time constant, meaning that with no energy spreading out of a particular total thermal resistance, 6:^, p-i-n diode specification sheet. THERM2 case, the subroutine The 3.7). the thermal energy all surroundings. the to small compared with the is absorbed is The junction temperature obtained by summing the ambient temperature and the temperature (equation 3.12), where the temperature of the junction rise in the diode, is is of the junction rise determine by the thermal capacity of the diode active region (HC), the pulse width in microsecond and the power dissipation maximum recommended [Ref diode the in For the switch temperature for safe (equation junction 3.11). problem, design operation the 200 °C is 10: p.290]. 4. An Example and Results of Power Dissipation and Diode Junction Temperature Evaluation Appendix power switch, dissipation and D is the listing of two Fortran programs using for the evaluation of and junction temperature a single pole double PSPST and PSPDT, programs, each branch in each diode of a single pole single throw throw switch with one or more diodes. The number of diodes are written for general use. file, As an example of power and the From evaluation. capacitance, 1.5 of the dissipation and junction temperature specificanon sheet, ohms junction transmission resistance characteristic transmission line SPDTD.CKT Touchstone section are circuit the file. or junction interactively results of the evaluation are listed in with four .\iA-4P203 p-i-n diodes, we use value Q and junction capacitance. All input parameters can be entered or in an unformatted input file. in an input variable that determines the switch construction (number of is transmission line sections). Diode input parameters can be either diode resistance These two SPDT. switch PSPDT program m Appendix D2 MA-4P203 diode and 30°C/watt impedance optimal For a 64 in a an output has 0.15 for :he pF. junction total thermal resistance. and electrical component 100 watt values CW length for obtained power SPDT The each from switch operating at 10 to 20 listed in Table GHz frequency range, the results of using PSPDT program are 9. TABLE 9 DIODE POWER DISSIPATION AND JUNCTION TEMPERATURE OF THE 100- WATT CW POWER SWITCH POWER(watts) (GHz) ON-STATE POWER(watts) TEMP(°C) D2 D2 Dl Dl Dl D2 10.00 0.814 0.578 39.4 32.3 2.523 0.002 90.7 15.1 12.00 1.124 0.832 48.7 40.0 2.653 0.002 94.6 15.1 14.00 1.486 1.133 59.6 48.9 2.770 0.002 98.1 15.1 PRE OFF-STATE TEMP(°C) D2 Dl • 16.00 1.908 1.479 72.2 59.4 2.865 0.002 100.9 15.1 18.00 2.407 1.872 87.2 71.2 2.932 0.002 102.9 15.1 20.00 3.003 2.311 104.1 84.3 2.971 0.002 104.1 15.1 From the result in Table dissipated in the first we realize that most of the switch power is shared among the two diodes, with the the whole range of frequencies the first first one dissipating diode of the off-state branch dominates the power dissipation and undergoes the greatest junction temperature The switch can be damaged value (200 C ). is diode of each branch, particularly in the switch-off branch. In the switch on- state the power more power. For 9, if the junction temperature exceed In most diode specification sheets, the the given amoieni temperature given based on the is The CW-input power has more effect in the its maximum rise. allowable maximum power dissipation at CW-mput power to temperature rise in because of the heat accumulated continuously in the junction. For the diode. the diode junction this reason a diode switch with short-duration input power pulses can handle higher peak powers than for CW-input power. For example the MA-4P203 65 diode has the maximum power handling capability of 5 watts of designed switch has a CW-input power maximum power at 25 °C ambient temperature. In Table 9 the dissipation in the diode of about three watts and 105''C junction temperature (20*'C ambient temperature). shows that our switch design is The capable to handle a 100-watt input result of Table 9 CW power. Figure 4.14 shows the plot of normalized powers to one watt output power of an individual diode in both branches. 66 POWER DISSIPATION VS FREQUENCY 12 14 13 FREQUENCY (GHZ) SPDT 4-DIODE SWITCH Figure 4,14 Power Dissipation 67 in an Individual Diode. CONCLUSIONS AND REMARKS V. CAD In microwave switching design, the program (Touchstone) and Fortran programs, are used for evaluating different types of microwave diode switches in order to obtain switching estimated their The characteristics. Q diode selected as a switching-semiconductor figure of merit can be used as the measure of device switching effectiveness, as shown in chapter 4. For radar applications, a single pole switch with high isolation over a broad operating frequency range requirement for radar systems. all improve the switch An The Touchstone insertion loss and load and two circuit file evaluated for the different diode Q selected to characterize the behavior of this switch. power handling Figures 5.1 and 5.2 4.1, is its Q These two figures values. value. to be used for specified An value. dissipation. The value of diode The problem diode which can handle the power dissipation of the switch. lower diode resistance to avoid too trade-off in increased power the previous chapter; resistance of 1.5 and resistance. we can suggestion However dissipation. An Q GHz, and power diode branch (1.68 and 2.82 watts). In is very close to that of the some switch heat accumulated in the diode junction at cause shorter diode lifetime. If we all applications, first it is is to select value but greater junction resistance, for example 2.0 is dissipation in the diode in the off-state not desirable co have may which has the same diode ohms in the junction times (both switching state), which select a p-i-n diode more example of this number MA-4P203 has fu-st select this leads to a the p-i-n diode model of 47.15 at 15 One of to select that p-i-n is One dissipation in the on-state branch. ohms and diode on-state branch of the much power used to is resistor in the diode these two values can be set as an arbitrary parameter, meaning that Q value The a function of both junction capacitance than one diode having the same diode Q appropriate The Fortran program power more produced from the capability of the designed switch. equivalent circuit plays an important role in Q, from equation the switch can to figures are number of diodes switch insertion loss and isolation, based on the diode estimate the an essential isolation for switches with one or isolation in these are very useful to the designer selecting the is more diodes isolation, while increasing the insertion loss. are plots of the switch insertion loss diodes. addition of is double throw junction resistance, Q we obtain 3.478 watts power dissipated in the off-state branch and 1.313 watts in the onstate branch. The best way to select the diode for the switch 68 is by using the Fortran program to estimate the the diode Q power dissipation in the diode of each branch, by fixing first value and varying diode junction resistance and select the satisfactory outcome. Due to the approximate circuit equivalent circuit, measurements the for the diode power calculation cannot produce in the laboratory. Nonetheless On guide lines to the designer. initial model used it a microwave switch reliable substitute for can reduce the design cost by providing the other hand these assumptions reduce the complexities of the circuit analysis and are mainly employed in the test of different figures of merit. Improvements for more accurate 1. Using more accurate p-i-n diode equivalent 2. Introducing loss in the transmission line sections. From power the knowledge that the can be achieved as follows: result circuit model. diode in the off-state branch dominates the first dissipation, in a switch circuit design for more efficient switch diodes used in the circuit can be differed (not necessarily identical). the generator should have higher diode Q The one closest to value (lower junction resistance) in order to dissipate less power, allowing the remaining diodes to This method can reduce the performance, the maximum power share the power dissipation. dissipation that occurs in the first diode of the off-state branch, and improve the power handling capability of the switch. still can use the Touchstone some necessary modifications circuit file to evaluate the switch to processed by the optimization it. The switch optimal mode performance by making insertion loss and isolation are to obtain the optimal switch circuit values to be used in the power dissipation evaluation with Fortran program. 69 We component u H CO Q CO m o 1 D 1 ^: o .•b) a o GO iz: I— CO > Q O OT-O OVQ(aa; Figure 5.1 'SS^O- 06-0- Of I- ssoi isiouaasNi Switch Insertion Loss vs Diode 70 Q for Multi-diodes Switch. o o o > Q g Q CO'OOICOI HWiHia QQQOia 2:OlO!OiO| 1—I'l— —1 m J I 1 C=3'^ CNJICO'* 1 D + 1 0-9E- O'OS- (aa) Figure 5.2 O'OOT- O'g^- 0"9ST- O'OQT- Noiiviosi ovoi Switch Isolation vs Diode 71 Q for Mul'ti-diodes Switch. APPENDIX A TOUCHSTONE CIRCUIT FILE FOR SPST SWITCH This appendix provides the listing of two circuit PJes using in the Touchstone CAD program for the evaluation switch insertion loss and load isolation for single pole single throw two-diode switches. Al. SPSTD.CKT evaluate with diode parameters (C;, R;). A2. SPSTQ.CKT evaluate with diode figure of merit (diode Q). Al. SPSTD.CKT SINGLE POLE SINGLE THROW DIODE SWITCH INSERTION LOSS AND LOAD ISOLATION CALCULATION INPUT PARAMETERS 1. JUNCTION CAPACITANCE, CJ 2. JUNCTION RESISTANCE, RJ 3. CENTER FREQUENCY, FO OUTPUT OPTIMIZED TRANSMISSION LINE IMPEDANCE AND ELECTRICAL LENGTH MINIMIZED INSERTION LOSS LOAD ISOLATION : : VAR ! INPUT PARAMETERS: FO = 15 CJ = .15 RJ = 1.5 FREQUENCY IN GHz JUNCTION CAPACITANCE IN pF JUNCTION RESISTANCE IN Ohm OPTIMIZED TRANSMISSION LINE IMPEDANCE (Ohm) ZA#30 39.40 90 ZB#30 38.25 90 OPTIMIZED TRANSMISSION LINE ELECTRICAL LENGTH(Degree) EA#30 106.3 120 EB#30 62.70 120 ! ! ! ! ! CKT TLIN 1 2 Z'^ZA E^EA F^FO DEF2P 1 2 SEGl TLIN 1 2 Z'^ZB E^EB F'^FO DEF2P 1 2 SEG2 SRC 1 2 R'^RJ C^CJ DEF2P 1 2 DON RES 1 2 R'^RJ DEF2P 1 2 DOFF ON STATE CALCULATION SEGl 1 2 DON 2 SEG2 2 3 DON 3 SEGl 3 4 DEF2P 1 4 LINDON OFF STATE CALCULATION SEGl 1 2 DOFF 2 SEG2 2 3 DOFF 3 SEGl 3 4 DEF2P 1 4 LINDOFF OUT LINDON DB(S21) GRl ! ! ! INSERTION LOSS IN dB 72 LINDOFF DB(S21) GRIA FREQUENCY SWEEP a 22 2 GRID GRl -2 ! ! LOAD ISOLATION IN dB FREQUENCY SWEEP FROM 8 TO 22 GHz .25 GRIA -20 -80 OPT RANGE 10 20 LINDCN DB(321)=0 ! A2. MINIMIZE INSERTION LOSS SPSTQ.CKT SINGLE POLE SINGLE THROW DIODE SWITCH INSERTION LOSS AND LOAD ISOLATION CALCULATION INPUT PARAMETERS 1. JUNCTION CAPACITANCE, CJ 2. FIGURE OF MERIT (DIODE Q) ,q 3. CENTER FREQUENCY, FO OUTPUT OPTIMIZED TRANSMISSION LINE IMPEDANCE AND ELECTRICAL LENGTH MINIMIZED INSERTION LOSS LOAD ISOLATION : : VAR ! INPUT PARAMETERS: FO = 15 CJ = .15 = 100 Q FREQUENCY IN GHz JUNCTION CAPACITANCE IN pF FIGURE OF MERIT (DIODE Q) OPTIMIZED TRANSMISSION LINE IMPEDANCE (Ohm) ZA#30 36.66 90 ZB#30 37.30 90 OPTIMIZED TRANSMISSION LINE ELECTRICAL LENGTH (Degree) EA#30 108.3 120 EB#30 58.7 120 EQN RJ = 1000/(2'^PI*F0*CJ*Q) JUNCTION RESISTANCE CALCULATION ! ! ! ! ! ! CKT TLIN 1 2 Z'-^ZA E'^EA F^FO DEF2P 1 2 SEGl TLIN 1 2 Z'^ZB E'^EB F-^FO DEF2P 1 2 SEG2 SRC 1 2 R'^RJ C^CJ DEF2P 1 2 DON RES 1 2 R^RJ DEF2P 1 2 DOFF ON STATE CALCULATION SEGl 1 2 DON 2 SEG2 2 3 DON 3 SEGl 3 4 DEF2P 1 4 LINDON OF? STATE CALCULATION SEGl 1 2 DOFF 2 SEG2 2 3 DOFF 3 SEGl 3 4 DEF2P 1 4 LINDOFF OUT LINDON DB(S21) GRl LINDOFF DB(S21) GRIA FREQUENCY SWEEP 8 22 2 GRID -2 GRl .25 ! ! ! INSERTION LOSS IN dB LOAD ISOLATION IN dB ! FREQUENCY SWEEP FROM 8 TO 22 GHz ! 73 GRIA -20 -80 OPT RANGE 10 20 LINDON DB(S21) = ! MINIMIZE INSERTION LOSS 74 APPENDIX B TOUCHSTONE CIRCUIT FILE FOR SPDT SWITCH This appendix provides the CAD program for the evaluation listing of two circuit files using in the Touchstone switch insertion loss and load isolation for single pole double throw four-diode switches. Bl. B2. SPDTD.CKT SPDTQ.CKT evaluate \^ith the diode parameters (C:. R:). evaluate with diode figure of merit (diode Q). Bl. SPDTD.CKT ! ! ! ! ! SINGLE POLE DOUBLE THROW DIODE SWITCH INSERTION LOSS AND LOAD ISOLATION CALCULATION INPUT PARAMETERS 1. JUNCTION CAPACITANCE, CJ 2. JUNCTION RESISTANCE, RJ 3. CENTER FREQUENCY, FO 4 TERMINAL LOAD OUTPUT OPTIMIZED TRANSMISSION LINE IMPEDANCE AND ELECTRICAL LENGTH MINIMIZED INSERTION LOSS LOAD ISOLATION ! : !! !! !! . ! : ! ! ! ! ! VAR ! INPUT PARAMETERS FO = 15 CJ = .15 RJ = 1.5 RR = 50 FREQUENCY IN GHz JUNCTION CAPACITANCE IN pF JUNCTION RESISTANCE IN Ohm TERMINAL LOAD IN Ohm OPTIMIZED TRANSMISSION LINE IMPEDANCE (Ohm) ZA#30 46.56 90 ZB#30 39.06 90 OPTIMIZED TRANSMISSION LINE ELECTRICAL LENGTH (Degree) EA#30 93.58 120 EB#30 32.82 120 CKT TLIN 1 2 Z^ZA E^EA F'^FO DEF2P 1 2 SEGl TLIN 1 2 Z'^ZB E'^EB F'^FO DEF2P 1 2 SEG2 SRC 1 2 R'^RJ C^CJ DEF2P 1 2 DON ! ! RES 1 2 R'^RJ DEF2P 1 2 DOFF ON STATE BRANCH ! SEGl 1 2 DON 2 SEG2 2 3 DON 3 SEGl 3 4 OFF STATE BRANCH SEGl 1 5 ! DOFF 5 SEG2 5 6 DOFF 6 SEGl 6 7 DEFINE 3 PORTS SWITCH DEF3P 14 7 SWITCH ! 75 12 SWITCH RES 3 DEF2P 1 3 R^RR 2 SWON SWITCH 12 3 RES 2 R-^RR DEF2P 1 3 SWOFF OUT SWON DB(S21) GRl SWOFF DB(321) GRIA FREQUENCY SWEEP 8 22 2 GRID GRl -2 ! INSERTION LOSS SWITCH ON STATE ! LOAD ISOLATION SWITCH OFF STATE ! ! INSERTION LOSS IN dB LOAD ISOLATION IN dB ! FREQUENCY SWEEP FROM ! MINIMIZE INSERTION LOSS 8 TO 22 GHz .25 GRIA -20 -80 OPT RANGE 10 20 LINDON DB(S21)=0 ' B2. SPDTQ.CKT SINGLE POLE DOUBLE THROW DIODE SWITCH INSERTION LOSS AND LOAD ISOLATION CALCULATION INPUT PARAMETERS 1. JUNCTION CAPACITANCE, CJ 2. FIGURE OF MERIT (DIODE Q) ,Q 3. CENTER FREOUENCY, FO 4. TERMINAL LOAD, RR OUTPUT OPTIMIZED TRANSMISSION LINE IMPEDANCE AND ELECTRICAL LENGTH MINIMIZED INSERTION LOSS LOAD ISOLATION : : VAR INPUT PARAMETERS FO = 15 CJ = .20 = 100 Q RR = 50 FREQUENCY IN GHz JUNCTION CAPACITANCE IN pF FIGURE OF MERIT (DIODE Q) TERMINAL LOAD IN Ohm OPTIMIZED TRANSMISSION LINE IMPEDANCE (Ohm) ZA#30 36.66 90 ZB#30 37.30 90 OPTIMIZED TRANSMISSION LINE ELECTRICAL LENGTH (Degree) EA#30 108.3 120 EB#30 53.7 120 EQN RJ = 1000/(2*PI*F0'^CJ*Q) JUNCTION RESISTANCE CALCULATION ! ! ! CKT TLIN 1 2 Z'^ZA E^EA F'^FO DEF2P 1 2 SEGl TLIN 1 2 Z^ZB E'^EB F'^FO DEF2P 2 SEG2 SRC 1 R^RJ C^CJ DHF2P 1 2 DON RES 1 2 R'^P.J DEF2? 1 2 DOFF ON STATE BRANCH SEGl 1 2 DON 2 SEG2 2 3 DON 3 SEGl 3 4 OFF STATE BRANCH SEGl 1 5 DOFF 5 SEG2 5 6 ! ! 76 DOFF 6 SEGl 6 7 DEFINE 3 PORTS SWITCH DEF3P 14 7 SWITCH SWITCH 12 3 R-^RR RES 2 DEF2P 1 2 SWON SWITCH 12 3 RARR RES 3 DEF2P 1 3 SWOFF OUT SWON DB(S21) GRl SWOFF DB(S21) GRIA FREQUENCY SWEEP 8 22 2 GRID ! GRl -2 ! ! INSERTION LOSS SWITCH ON STATE LOAD ISOLATION SWITCH OFF STATE I INSERTION LOSS IN dB LOAD ISOLATION IN dB ! FREQUENCY SWEEP FROM 8 TO 22 GHz ! MINIMIZE INSERTION LOSS ! .25 GRIA -20 -80 OPT RANGE 10 20 LINDON DB(S21) = 77 APPENDIX C TOUCHSTONE CIRCUIT FILE FOR NODAL VOLTAGE EVALUATION CAD of two circuit using in the Touchstone This appendix provides the listing program of nodal voltages by using voltage-controlled voltage for the evaluation files source circuit model for single pole single throw two-diode switches and single pole double throw four-diode switches. CI. SPSTV.CKT C2. SPDTV.CKT single pole single single pole double throw nodal voltage evaluation CI. SPSTD.CKT SINGLE POLE SINGLE THROW DIODE SWITCH NODAL VOLTAGE CALCULATION USING VOLTAGE -CONTROLED VOLTAGE SOURCE INPUT PARAI^IETERS 1. JUNCTION CAPACITANCE, CJ 2. JUNCTION RESISTANCE, RJ FO 3. CENTER FREOUENCY 4. TERMINAL LOAD IMPEDANCE, RR 5. TRANSMISSION LINE IMPEDANCE, ZA, ZB 6. TRANSMISSION LINE ELECTRICAL LENGTH, EA, EB OUTPUT: NORMALIZED NODAL VOLTAGE OF THE INTERESTED NODE ! ! : ! ! ! ! , ! ! ! ! ! throw nodal voltage evaluation ! VAR ! INPUT PARAMETERS: = 15 = .15 = 1.5 FREQUENCY IN GHz JUNCTION CAPACITANCE IN pF JUNCTION RESISTANCE IN Ohm = 50 TERMINAL LOAD IMPEDANCE IN Ohm TRANSMISSION LINE IMPEDANCE (Ohm) ZA = 36.66 ZB = 37.30 TRANSMISSION LINE ELECTRICAL LENGTH(Degree) EA = 108.3 FO CJ RJ RR ! ! ! ! ! ! EB = 58.7 CKT TLIN 1 2 Z'^ZA E^EA F^FO DEF2P 1 2 SEGl TLIN 1 2 Z^ZB E^EB F^FO DEF2P 1 2 SEG2 CAP 1 2 C^CJ DEF2P DCJ RES 1 2 R'^RJ DEF2P 1 2 DRJ ON STATE CALCULATION SEGl 1 2 DCJ 2 5 DRJ 5 SEG2 2 3 DCJ 3 6 DRJ 6 SEG 3 4 RES 4 R-^RR VCVS 4 7 M=-.5 A=0 R1=1E8 R2=0 F=0 T=0 VCVS 5 8 M=-.5 A=0 R1=1E8 R2=0 F=0 T=0 VCVS 6 9 M=-.5 A=0 R1=1E8 R2=0 F=0 T=0 DEF4P 17 8 9 OUTVl ! 78 OFF STATE CALCULATION SEGl 11 12 DRJ 12 SEG2 12 13 DRJ 13 SEGl 13 14 R'^RR RES 14 VCVS 14 17 M=-.5 A=0 R1=1E8 R2=0 F=0 T=0 VCVS 12 13 M=-.5 A=0 R1=1E8 R2=0 F=0 T=0 M=-.5 A=0 Rl=iE8 R2=0 F=0 T=0 VCVS 13 19 DEF4P 11 17 18 19 0UTV2 OUT ! NORMALIZED NODAL VOLTAGE OUTVl MAG(S21) GRl OUTVl MAG(S31) GRl a OUTVl MAG(S41) GRl 0UTV2 MAG(S2l) GR2 0UTV2 MAG(S3l) GRIA 0UTV2 MAG(S41) GR2 FREQUENCY SWEEP 8 22 2 GRID RANGE 8 22 2 GRl .5 1 GRIA .15 .3 .0001 .001 GR2 ! ! C2. FREQUENCY SWEEP FROM 8 TO 22 GHz SPDTV.CKT SINGLE POLE DOUBLE THROW DIODE SWITCH NODAL VOLTAGE CALCULATION USING VOLTAGE-CONTROLED VOLTAGE SOURCE INPUT PARAMETERS 1. JUNCTION CAPACITANCE, CJ 2. JUNCTION RESISTANCE, RJ 3. CENTER FREQUENCY, FO 4. TERMINAL LOAD IMPEDANCE, RR 5. TRANSMISSION LINE IMPEDANCE, ZA, ZB 6. TRANSMISSION LINE ELECTRICAL LENGTH, EA, EB OUTPUT NORMALIZED NODAL VOLTAGE OF THE INTERESTED NODE VAR INPUT PARAMETERS: FO = 15 FREQUENCY IN GHz CJ = .20 JUNCTION CAPACITANCE IN pF RJ = 1.5 JUNCTION RESISTANCE IN Ohm RR = 50 TERMINAL LOAD IMPEDANCE IN Ohm TRANSMISSION LINE IMPEDANCE (Ohm) ZA = 35.90 ZB = 47.36 TRANSMISSION LINE ELECTRICAL LENGTH ( Degree ! ! ! ! ! ! : : ! ! ! ! ! ! ! ! ! HA Z3 = 101.20 =34.^ TLIN 1 2 Z^ZA E'^EA F'^FO DEF2P 1 2 SEGl TLIN 1 2 Z^ZB E^EB F'^FO DEF2P 1 2 SEG2 CAP 1 2 C^CJ DEF2P DCJ RES 1 2 R-^RJ DEF2P 1 2 DRJ ON STATE CALCULATION SEGl 1 2 ! 79 DCJ 2 8 DRJ 8 SEG2 2 3 DCJ 3 9 DRJ 9 SEG 3 4 R-^RR RES 4 OFF STATE CALCULATION SEGl 1 5 DRJ 5 SEG2 5 6 DRJ 6 SEGl 6 7 RES 7 R^RR VCVS 4 10 M=-. 5 A=0 R1=1E8 VCVS 8 11 M=-.5 A=0 R1=1E8 VCVS 5 12 M=-.5 A=0 R1=1E3 DEF4P 1 10 11 12 OUTVl OUT NORMALIZED NODAL VOLTAGE OUTVl MAG(S21) GRl OUTVl MAG(S31) GRl OUTVl MAG(S41) GRl FREQUENCY SWEEP 8 22 2 GRID RANGE 8 22 2 .5 GRl 1 .5 GRIA .1 ! R2=0 F=0 T=0 R2=0 F=0 T=0 R2=0 F=0 1=0 ! ! FREQUENCY SWEEP FROM 8 TO 22 GHz 80 APPENDIX D FORTRAN PROGRAM FOR DIODE POWER AND HEATING CALCULATIONS This appendix provides of two Fortran programs written for the listing tiie evaluation of power dissipation and junction temperature in the individual diode of the single pole single throw and single pole double diode switches. Dl. PSPST diode power dissipation and junction temperature of a single pole single throw diode switch. D2. PSPDT diode power dissipation and junction temperature of a single pole double throw diode switch. Dl. PSPST ANSWER CHARACTER*13 FILE CHARACTER'*^3 SELECT CHARACTER'*=1 TYPE INTEGER I,NPORT REAL TA,TR,HC,TJON(10) ,TJOFF(10) ,DT REALMS FRE Q C J EL ( 10 ) RR PI PIN PON POFF PLON PLOFF REALMS PDON(IO) ,PDOFF(10) AMP VDONM,PEX C0MPLEX*16 VIN ZOUT Z ( 10 ) ZINON ZINOFF ZIN UN, ION lOFF ILON, VLON C0MPLEX*16 ILOFF,VLOFF,VON,VOFF,VS,ZS C0MPLEX*16 GPI(2,2,20),GP(2,2,20),GNI(2,2,20),GN(2,2,20) C0MPLEX*16 IDON ( 10 ) IDOFF ( 10 ) VDON ( 10 COMPLEX^ie VDOFF(IO) OPEN (UNIT=2,FILE=' OUTPUT' PI = 3.1415926536 WRITE (6,*) 'POWER DISSIPATION AND JUNCTION TEMPERATURE EVALUATION' WRITE(6,*) 'OF SPST DIODE SWITCH WRITE(6,*) '"PRESS ANY KEY AND RETURN" TO CONTINUE, "Q AND RETURN"TO CfiARACTER'*^! , , , , , , , , , , , , , , , , , 5 , , , , , ' * QUIT' 10 READ (5, 10) ANSWER FORMAT (Al) IF ( ANSWER. EQ. 'Q' )STOP WRITE(6,*) 'ENTER^'0"TO READ INPUT FROM FILE, "1 "TO ENTER INPUTS INTE *RACTIVELY' READ(5,*)NUM IF(NUM.NE.O.AND.NUM.NE.l) GOTO 5 IF(NUM.EQ.O)THEN MN = 1 ELSE MN = 5 SriDIF 15 20 IF(NUM.£Q.O)THEN WRITE (6,*) 'ENTER THE NAME OF INPUT FILE' READ(5,15)FILE 0PEN(UNIT=1,FILE=FILE) FORMAT (Al 3) END IF IF(NUM.EQ.1)THEN WRITE (6,*) 'WHAT TYPE OF INPUT SIGNAL "PULSE" OR "CW" ? WRITE (6,*) 'FOR "PULSE" INPUT ENTER "P" WRITE (6,*) 'FOR "CW" INPUT ENTER "C" WRITE (6,*) 'DO NOT EVALUATE JUNCTION TEMPERATURE ENTER "N" ' ' ' 81 ' 25 ENDIF READ(MN,11)TYPE FORMAT(Al) IF(TYPE.NE. 'P' .AND. TYPE. NE. 'C .AND. TYPE .NE 'N')GOTO 20 IF(TYPE.EQ. 'N' )GOTO 30 IF(TYPE.EQ. 'C )THEN IF(NUM.EQ.1)WRITE(6,*) 'ENTER AMBIENT TEMPERATURE (DEGREE C) READ(MN,*)TA IF(MUM.S0.1)WRITE(6,*) 'TOTAL THERMAL RESISTAI^ICS (DEGREE C/WATT) READ(MN,^)TR ELSE IF(NUM.EQ.1)WRITE(6,*) 'ENTER AMBIENT TEMPERATURE (DEGREE C) . ' READ(MN,'^)TA IF(NUM.EQ.1)WRITE(6,*) 'ENTER THERMAL CAPACITY OF OF I-REGION (MICR *0-JOULE/DEGREE C) READ(MN,''')HC IF (NUM. EQ.l) WRITE (6,^) 'ENTER THE PULSE DURATION (MICRO-SECOND)' 30 35 READ(MN,^)DT ENDIF IF(NUM.EQ.1)THEN EVALUATION USE THE FIGURE OF MERIT, DIODE ^;rite(6,*) 'IS th: .^?II?(§')!?S_™IS. WRITE (6,*) 'ANSWER "YES" OR "NO"' ENDIF READ (MN, 35) SELECT FORMAT (A3) IF (SELECT. NE. 'YES' AND SELECT .NE 'NO' )GOTO 30 IF(SELECT.EQ. 'YES' )THEN IF(NUM.EQ.iyWRITE(6,''f) 'ENTER THE VALUE OF DIODE Q' . . . ' READ(MN,'')Q IF (NUM. EQ.l) WRITE (6,'^) 'ENTER THE VALUE OF JUNCTION CAPACITANCE (PF) READ(MN,'*=)CJ IF(NUM.E0.1)WRITE(6,*)'ENTER THE EVALUATE FREQUENCY (GHZ)' READ(MN,^)FRE RR = 1000/(2'^PI*FRE*Q*CJ) ELSE IF(NUM.EQ.1)WRITE(6,*) 'ENTER THE VALUE OF JUNCTION CAPACITANCE (PF) READ(MN,''^)CJ IF(NUM.EQ.1)WRITE(6,*) 'ENTER THE EVALUATE FREQUENCY (GHZ)' READ(MN,^)FRE IF(NUM.EQ.1)WRITE(6,*) 'ENTER THE VALUE OF JUNCTION RESISTANCE (OHM *)' READ(MN,*)RR Q = 1000/(2*PI*FRE*RR'^CJ) ENDIF VS = (1,0) ZS = (50,0) IF (NUM. EO.l) WRITE (6,*) 'ENTER NUMBER OF DIODES IN EACH BRANCH' READ(MN,^)ND IF(NUM.EQ.1)WRITE(6,*) 'ENTER THE EXPECT POWER AT LOAD (WATT)' READ(MN,'^)PEX IF(NUM.E0.1)WRITE(6,*) 'ENTER THE OUTPUT IMPEDANCE (COMPLEX)' READ(MN,'^)ZOUT NSEG = ND+1 DO 40 I =1,NSEG IFfNUM.E0.1)WRITS(6,*) 'TRANSMISSION SEGMENT NUMBER ', IF(NUM.Zd.l;WRITE;6,^) 'ENTER IMPEDANCE OF TRAI^ISMISSIOM LINE (COMPL ' ^SX) READ(MN,-^)Z(I) ' ' IF(NUM.EQ.1)WRITE(6,*) 'ENTER ELECTRICAL LENGTH (DEGREE)' READ(MN,'^)EL(I) EL(I) = EL(I)*PI/180 40 CONTINUE NPORT = ND+NSEG C ON STATE CALCULATION CALL MATRIX(RR,CJ,Z,EL, NSEG, ND,FRE,GP( 1,1,1)) DO 45 K =1, NPORT 82 45 IF(K.EQ.1)THEN GPI(1,1,1) = GP(1,1,1 GPI( 1,2,1} = GP( 1,2,1 GPI(2,l,l) = GP(2,1,1 GPI(2,2,1) = GP(2,2,1 ELSE CALL MATMUL(GPI(1,1,K-1),GP(1,1,K),2,2,2,GPI(1,1,K)) END IF CONTINUE ZINON = (GPI (1 1 ,NPORT)'^ZOUT+GPI (1 2 ,NPORT) )/ (GPI (2 1 ,NPORT)'^ZOUT #+GPI(2,2,NPORT)) , 50 , OFF STATE CALCULATION CALL MATRIX(RR,0.D0,Z,EL,NSEG,ND,FRE,GN(1,1,1)) DO 50 N =1, NPORT IF{N.EQ.1)THEN GNI( 1,1,1) = GN( 1,1,1' GNI(l,2,l) = GN(1,2,1' GNI(2,1,1) = GN(2,1,1' GNI(2,2,1) = GN(2,2,1 ELSE CALL MATMUL(GNI(1,1,N-1),GN(1,1,N),2,2,2,GNI(1,1,N)) ENDIF CONTINUE ZINOFF = (GNI ( 1 1 NPORT ) *ZOUT+GNI (1,2, NPORT ) ) / ( GNI ( 2 1 NPORT ) ^ZOUT #+GNI(2,2,NP0RT)) 100 , , , 55 60 65 70 75 35 90 95 , , ON-OFF STATE VON = ZINON'^VS/(ZINON+VS) ION = VON/ZINON VOFF = ZINOFF*VS/(ZINOFF+VS) lOFF = VOFF/ZINOFF PON = 0.5*REAL(VON'^DCONJG(ION)) POFF = 0.5*REAL(VOFF*DCONJG(IOFF)) ILON = GPI (1,1, NPORT )'^ION-GPI( 2,1, NPORT )*VON VLON = GPI(2,2,NPORT)'^VON-GPI(1,2,NPORT)*ION PLON = PON-0.5*REAL(VON'^DCONJG( ION) -VLON*DCONJG( ILON)) AMP = PEX/PLON WRITE (2, 55) FRE WRITE(2,60) Q WRITE (2, 65) ND WRITE(2,70) CJ WRITE (2, 75) RR WRITE (2, 85) PON*AMP WRITE (2, 90) POFF^AMP WRITE (2, 95) PLON* AMP ILOFF = GNI (1,1, NPORT )*IOFF-GNI( 2,1, NPORT )*VOFF VLOFF = GNI(2,2,NPORT)*VOFF-GNI(l,2,NPORT)'^IOFF PLOFF = POFF-0.5'^REAL(VOFF'^DCONJG(IOFF)-VLOFF*DCONJG(ILOFF)) WRITE (2, 100) PLOFF^AMP FORMAT 'OPERATING FREQUENCY' ,3X,F5. 2, 2X, 'GHZ' FORMAT 'FIGURE OF MERIT (DIODE Q)',3X,F8.3) FORMAT 'TOTAL NUMBER OF DIODE IN EACH BRANCH' 2X, 12' FORMAT DIODE JUNCTION CAPACITANCE 3X F5 3 2X PF FORMAT DIODE JUNCTION RESISTANCE 3X ?5 3 2X OHM FORMAT 'POWER IN ON STATE 2X FIO 2 3X, WATTS FORMAT 'POWER IN OF? STATE' IX. ?10. 2, 3X, 'WATTS' FORI-IAT { 'POWER DELIVER TO THE LOAD IN ON STATE ', FIO 2 3X, WATTS , , ' ' , . , , ' , , , ' ' , , ' ' ' ' , , . , ' , . FORMAT 'POWER DELIVER TO THE LOAD IN OFF STATE *S') POWER DISSIPATED IN ON STATE BRANCH CALL POWER ( GP ( 1 1 1 ) ION VON NPORT PDON IDON VDON WRITE (2,*) 'POWER DISSIPATION IN DIODE ON STATE' DO 105 I = 2,2*ND,2 WRITE(2,115)I/2,PD0N(I)*AMP , , , , , 83 , , , ', , ' FIO .6 3X, WATT , ' 105 CONTINUE C POWER DISSIPATED IN OFF STATE BRANCH CALL POWER (GN( 1 ,1,1), lOFF VOFF NPORT PDOFF IDOFF VDOFF) WRITE (2,*) 'POWER DISSIPATION IN DIODE OFF STATE' DO 110 J = 2,2*ND,2 WRITE (2, 115) J/2, PDOFF (J)*AMP CONTINUE FORMATC ', 'POWER DISSIPATED IN DIODE NO MX, 12 2X, FIO , 110 115 , , , , . , . 5 . 2 , 2X, WATT , 2X, DEGR ' '*'S' ) C C JUNCTION TEMPERATURE CALCULATION JUNCTION TEMPERATURE IN ON STATE BRANCH IF(TYPEoEQ. 'N' )STOP IF(TYPE.EQ. 'C )THEN CALL THERMl (ND T JON PDON AMP TA TR ELSE CALL THERM2(ND,TJ0N,PD0N,AMP,TA,DT,HC) END IF WRITE(2,*)' JUNCTION TEMPERATURE ON STATE BRANCH' DO 120 I = 1,ND WRITE(2,82)I,TJ0N(I) CONTINUE JUNCTION TEMPERATURE IN OFF STATE BRANCH WRITE (2,*) 'JUNCTION TEMPERATURE OFF STATE BRANCH' IF(TYPE.EO. 'C )THEN CALL THERMl (ND,TJOFF, PDOFF, AMP, TA,TR) ELSE CALL THERM2(ND,TJ0FF, PDOFF, AMP, TA,DT,HC) ENDIF DO 125 J = 1,ND WRITE(2,130)J,TJOFF(J) CONTINUE FORMAT (' ',' JUNCTION TEMPERATURE DIODE NO. 2X, 12 2X, F6 , 120 C 125 130 C , , 20 30 , ' *EE C) STOP END , , SUBROUTINE MATRIX SUBROUTINE MATRIX (RR C J Z EL NSEG ND FRE GP REALMS RR,CJ,EL(10),FRE,PI C0MPLEX*16 Z{10),Z1 COMPLEX^ie G(2,2,20),G1(2,2,20),GP(2,2,20) PI = 3.1415926536 DO 10 K = 1,NSEG G(1,1,K) = DCMPLX(COS(EL(K)),0.D0) G(1,2,K) = DCMPLX(0.D0,1.D0)*Z(K)*DCMPLX(SIN(EL(K)),0.D0 G(2,1,K) = DCMPLX(0.D0,1.D0)/Z(K)*DCMPLX(SIN(EL(K)),0.D0 G(2,2,K) = G(1,1,K) CONTINUE DO 20 L=1,ND IF(CJ.EQ.0.D0)THEN Zl = DCMPLX{RR,O.DO) ELSE Zl = DCMPLX(RR,-1000/(2*PI*FRE*CJ)) , 10 , , , , END IF G1(1,1,L) = DC:-IPLX(1.D0,0.D0) G1(1,2,L) = DCMPLX( 0.00,0. DO) Gl(2,i,L)= 1/Zl G1(2,2,L) = G1(1,1,L) CONTINUE DO 30 M =1,NSEG N = 2*M-1 GP(i,i,N) = g(i,i,m; GP(1,2,N) = G(1,2,M GP(2,1,N) = G(2,1,M GP(2,2,N) = G(2,2,m; CONTINUE DO 40 I =1,ND 84 , , , ' I k J = 2*1 40 C 30 20 10 C GP(1,1,J) GP(1,2,J) GP(2,1,J) GP(2,2,J) CONTINUE RETURN END = = = = G1(1,1,I' Gl 1,2,1 G1(2,1,I G1(2,2,I' SUBROUTINE MATMUL SUBROUTINE MATMUL ( AA, BB ,NN, MM, RR, CC) INTEGER NN,MM,RR 'COMPLEX^ie AA(2,2,1),BB(2,2,1),CC(2,2,1) DO 10 I = 1,NN DO 20 J = 1,RR CC(I,J,1) = DO 30 K =1,MM CC(I,J,1) = CC(I,J,1) + AA(I,K,1)*BB(K,J,1) CONTINUE CONTINUE CONTINUE RETURN END SUBROUTINE POWER SUBROUTINE POWER(G, I V,N,PD IID, VID) REALMS PD(IO) C0MPLEX*16 G(2,2,20),V,I,IID(20),VID(20),IOD(20),VOD(20) DO 10 J=2,N,2 IID(J) = G(1,1,J-1)*I - G(2,1,J-1)*V VID(J) = G(2,2,J-1)*V - G(1,2,J-1)*I lOD(J) = G(1,1,J)*IID(J) - G(2,1,J)*VID(J) VOD(J) = G(2,2,J)*VID(J) - G(1,2,J)*IID(J) = 0.5*REAL(VID(J)*DCONJG(IID(J))-VOD(J)*DCONJG(IOD(J))) PD(J) , 10 , I = lOD'"^ V = VOD \i] CONTINUE RETURN END SUBROUTINE THERMl SUBROUTINE THERMl (ND,TJ ,PD AMP ,TA,TR) INTEGER ND REAL TJ(10),AMP,TA,TR REALMS PD(IO) DO 5 1=1, ND TJ(I) = TA + (PD(I*2)*AMP)*TR CONTINUE RETURN END , SUBROUTINE THERM2 SUBROUTINE THERM2 (ND T J ?D AMP TA DT ,HC) INTEGER ND REAL TJ(10),AMP,TA,DT,HC REALMS PD(IO) DO 5 J =1,ND TJ(J) = TA + (PD(J*2)'^AMP)'*^DT/HC CONTINUE RETURN END , , , , 85 , D2.PSPDT CHARACTER'^1 ANSWER CHARACTER*13 FILE CHARACTER'S SELECT CHARACTER'*^! TYPE INTEGER I,NPORT REAL TA,TR,HC,TJOM(10) ,TJOFF(10) ,DT REAL'S FRE,0,CJ,EL(10) ,RR,PI ,PIN ,PON ,POFF ,PLON,PLOFF REAL'S PDONUO) ,PDOFF(10) AMP VDONM, PEX COMPLEX'16 VIN ZOUT Z ( 10 ) ZINON ZINOFF ZIN UN ION lOFF ILON VLON COMPLSX'16 ILOFF,VLOFF,VON,VOFF,VS,ZS COMPLEX'16 GPI ( 2 2 20 ) GP ( 2 2 20 ) GNI ( 2 2 20 ) GN ( 2 2 20 COMPLEX'16 IDON ( 10 ) IDOFF ( 10 ) VDON ( 10 COMPLEX'16 VDOFF(IO) 0PEN(UNIT=2,FILE=' OUTPUT' PI = 3.1415926536 WRITE (6,') 'POWER DISSIPATION AND JUNCTION TEMPERATURE EVALUATION' WRITE(6,') 'OF SPDT DIODE SWITCH WRITE(6,') '"PRESS ANY KEY AND RETURN" TO CONTINUE, "Q AND RETURN"TO , , , , , , , , , , , 5 , , , , , , , , , , , , , , ' ' QUIT' READ (5, 10) ANSWER 10 15 20 FORMAT (Al) IF(ANSWER.EQ. 'Q' )STOP WRITE(6,') 'cNTER"0"TO READ INPUT FROM FILE,"1"T0 ENTER INPUTS INTE 'RACTIVELY' READ(5,')NUM IF(NUM.NE.O.AND.NUM.NE.l) GOTO 5 IF(NUM.EQ.O)THEN MN = 1 ELSE MN = 5 END IF IF(NUM.EQ.O)THEN WRITE (6,') 'ENTER THE NAME OF INPUT FILE' READ(5,15)FILE 0PEN(UNIT=1,FILE=FILE) F0RMAT(A13) END IF IF(NUM.EQ.1)THEN WRITE (6 ,')' WHAT TYPE OF INPUT SIGNAL "PULSE" OR "CW" ? WRITE (6,') 'FOR "PULSE" INPUT ENTER "P" WRITE (6,') 'FOR "CW" INPUT ENTER "C" WRITE (6,') 'DO NOT EVALUATE JUNCTION TEMPERATURE ENTER "N" END IF RE AD (MN, 11) TYPE FORMAT (Al) IF(TYPE.NE. 'P' .AND. TYPE. NE. 'C AND TYPE NE 'N' )GOTO 20 IF (TYPE. EO. 'N' )GOTO 30 iF(TYPE.EO. 'c When I? (NUM. HO Ti) WRITE (6,^) 'ENTER AMBIENT TEMPERATURE ^DEGREE C) ' ' ' ' 25 . . . . READ(!-m,^)TA IF(NUM.E0.i)WRITE(6,^) 'TOTAL READ(MN,')TR ELSE IF(NUM.EQ.1)WRITE(6,')'ENTER READ(MN,')TA IF(NUM.EQ.1)WRITE(6,') 'ENTER '0-JOULE/DEGREE C) READ(MN,')HC IF(NUM.EQ.1)WRITE(6,') 'ENTER READ(MN,'^)DT END IF 86 THERMAL RESISTANCE (DEGREE C/WATT) AMBIENT TEMPERATURE (DEGREE C) THERMAL CAPACITY OF OF I-REGION (MICR THE PULSE DURATION (MICRO-SECOND)' 30 IF(NUM.EQ.1)THEN USE THE FIGURE OF MERIT, DIODE Q 'IS THIS EVALUATION WRITE(6,*) ^. -_ WRITE (6,*) 'ANSWER "YES" OR "NO" END IF READ (MN, 35) SELECT FORMAT ( A3 IF ( SELECT. NE. 'YES' .AND. SELECT. NE. 'NO') GOTO 30 IF(SELECT.EO. 'YES' )THEN IF(NUM.S0.lTWRITE(6,'^) 'ENTER THE VALUE OF DIODE READ(MN,^)Q IF(NUM.EQ.1)WRITE(6,*) 'ENTER THE VALUE OF JUNCTION CAPACITAI^ICE (PF) ^y 35 ' READ(MN,'^)CJ IF(NUM.EQ.1)WRITE(6,*) 'ENTER THE EVALUATE FREQUENCY (GHZ)' READ(MN,*)FRE RR = 1000/(2^PI*FRE*0*CJ) ELSE IF(NUM.EQ.1)WRITE(6,*) 'ENTER THE VALUE OF JUNCTION CAPACITANCE (PF) READ(MN,*)CJ IF(NUM'.EQ.1)WRITE(6,*) 'ENTER THE EVALUATE FREQUENCY (GHZ)' READ(MN,'^)FRE IF(NUM.EQ.1)WRITE(6,=^) 'ENTER THE VALUE OF JUNCTION RESISTANCE (OHM *)' READ(MN,''^)RR Q = 1000/(2*PI*FRE'^RR*CJ) END IF VS = (1,0)^ ZS = (50,0) IF(NUM.EQ.1)WRITE(6,*) 'ENTER NUMBER OF DIODES IN EACH BRANCH' READ(MN,^)MD IF(NUM.EQ.1)WRITE(6,'^) 'ENTER THE EXPECT POWER AT LOAD (WATT)' READ(MN,^)PEX IF(NUM.EQ.1)WRITE(6,*) 'ENTER THE OUTPUT IMPEDANCE (COMPLEX)' READ(MN,'^)ZOUT NSEG = ND+1 DO 40 I =1,NSEG IF(NUM.EQ.1)WRITE(6,*) 'TRANSMISSION SEGMENT NUMBER', IF(NUM.EQ.1)WRITE(6,*) 'ENTER IMPEDANCE OF TRANSMISSION LINE (COMPL '^EX) 40 C ' READ(MN,*)Z(I) IF(NUM.EQ.1)WRITE(6,*) 'ENTER ELECTRICAL LENGTH (DEGREE)' READ(MN,^)EL(I) EL(I) = EL(I)*PI/180 CONTINUE NPORT = ND+NSEG ON STATE CALCULATION CALL MATRIX ( RR C J Z EL NSEG ND FRE GP ( 1 1 1 ) DO 45 K =1, NPORT IF(K.EQ.1)THEN GPI(1,1,1) = GP(1,1,1 GPI(1,2,1) = GP(1,2,1 GPI(2,1,1) = GP(2,1,1 GPI(2,2,1) = GP(2,2,1' ELSE CALL MATMUL(GPI(1,1,K-1) G?(l 1 ,K) 2 2 2 GPI( 1 1 ,K) ENDIF CONTINUE ZINON = (GPI (1,1, NPORT) '^ZOUT+GPI( 1,2, NPORT) )/(GPI( 2,1, NPORT) ''^ZOUT #+GPI(2,2,NP0RT)) , , , , , C , , , 45 , , , , , , OFF STATE CALCULATION CALL MATRIX ( RR DO Z EL NSEG ND FRE GN ( 1 DO 50 N =1, NPORT IF(N.EQ.1)THEN GNI(1,1,1 = GN(1,1,1) GNI(1,2,1) = GN(1,2,1) , . , , , , 87 , , , , , 1 , 1 ) 50 GNI(2,1,1) = GN(2,1,1) GNI(2,2,1) = GN(2,2,1) ELSE CALL MATMUL(GNI(1,1,N-1),GN(1,1,N),2,2,2,GNI(1,1,N)) END IF CONTINUE ZINOFF =(GNI(l,l,NPORT)*ZOUT+GNI(l,2,NPORT))/(GNI(2,l,NPORT)*ZOUT #+GNI(2,2,NPGRT)) ON-OFF STATE ZIN = ZINON*ZINOFF/ (ZINON+ZINOFF) VIN = ZIN'^VS/(ZIN+ZS) UN = VIN/ZIN PIN = REAL ( 5* ( VIN^DCONJG ( I IN) ) ION = IIM^ZINOFF/ ^ZINON+ZINOFF) lOFF = UN - ION PON = 5*REAL ( VIN^DCON JG ( ION ) POFF = 0. S'^REAL ( VIN'^DCON JG ( lOFF ) ILON = GPI ( 1 1 NPORT) *ION-GPI (2,1, NPORT) '^^VIN VLON = GPI (2,2, NPORT ) *VIN-GPI (1,2, NPORT ) *ION PLON = PON-0.5*REAL(VIN*DCONJG(ION)-VLON*DCONJG(ILON)) AMP = PEX/PLON WRITE 2,55) FRE WRITE 2,60^ Q WRITE 2,65 ND WRITE 2,70 CJ WRITE 2,75 RR WRITE 2,80 PIN^AMP WRITE 2,85 PON^AMP WRITE 2,90 ^OF^'^-.MP WRITE 2,95) PLON'^AMP ILOFF GNI(1,1,NP0RT)*I0FF-GNI(2,1,NP0RT)*VIN VLOFF GNI ( 2 2 NPORT ) *VIN -GNI ( 1 2 NPORT ) *IOFF PLOFF POFF-0 5*REAL (VIN'^DCONJG ( lOFF ) -VLOFF*DCONJG( ILOFF) ) WRITE 100) PLOFF^AMP FORMAT 'OPERATING FREQUENCY 3X F5 2 2X GHZ FORMAT 'FIGURE OF MERIT (DIODE Q)',3X,F8.3) FORMAT 'TOTAL NUMBER OF DIODE IN EACH BRANCH ', 2X, 12) FORMAT 'DIODE JUNCTION CAPACITANCE 3X F5 3 2X PF FORMAT 'DIODE JUNCTION RESISTANCE' ,3X.F5.3,2X, 'OHM' FORMAT 'INPUT POWER ,F10.2,3X, 'WATTS' ] 'POWER IN ON STATE BRANCH ',2X,F10.2,3X,' WATTS FORMAT FORMAT 'POWER IN OFF STATE BRANCH ', IX, FIO 2 3X, WATTS FORMAT POWER DELIVER TO THE LOAD IN ON STATE ', FIO 2 3X, WATTS . . , , " , , , , . 55 60 65 70 75 80 85 90 95 100 , ' , , . , ' ' , ' , . , , ' ' ' . , ' ' FORMAT (' ',' , . ' POWER DELIVER TO THE LOAD IN OFF STATE ', FIO . 6 . 5 ' , 3X, WATT , 2X, 'WATT ' *S') C POWER DISSIPATED IN ON STATE BRANCH VON = VIN CALL POWER ( GP ( 1 1 1 ) ION VON NPORT PDON IDON VDON) WRITE (2,'^) 'POWER DISSIPATION IN DIODE ON STATE' DO 105 I = 2,2*ND,2 , 105 C , , , , WRITE(2,115)I/2,?D0N(I)*AI'1P CONTINUE POWER DISSIPATED IN OFF STATE BRAI^ICH VOFF = VIN CALL POWER (GN (1,1,1), lOFF VOFF NPORT PDOFF IDOFF VDOFF) WRITE (2,'*^) 'POWER DISSIPATION IN DIODE OFF STATE' DO 110 J = 2,2^ND,2 WRITE (2, 115) J/2, PDOFF ( J) *AMP CONTINUE FORMAT(' ', 'POWER DISSIPATED IN DIODE NO. MX, 12, 2X, FIO , 110 115 *S' C C , , , , , ) JUNCTION TEMPERATURE CALCULATION JUNCTION TEMPERATURE IN ON STATE BRANCH 88 , , IF (TYPE. EQ. 'N' )STOP IF (TYPE. EQ. 'C )THEN CALL THERMl (ND T JON PDON AMP TA TR) , 120 C 125 130 , , , , ELSE CALL THERM2(ND,T JON, PDON, AMP, TA,DT,HC) END IF WRITE (2,*) 'JUNCTION TEMPERATURE ON STATE BRANCH' DO 120 I = 1,ND WRITEf2,32)I,TJON(l) CONTINUE JUNCTION TEMPERATURE IN OFF STATE BRANCH WRITE (2,*) 'JUNCTION TEMPERATURE OFF STATE BRANCH' IF (TYPE. EQ. 'C')THEN CALL THERMl (ND T JOFF PDOFF AMP TA TR) ELSE CALL THERM2 (ND T JOFF PDOFF AMP TA DT HC END IF DO 125 J = 1,ND WRITE(2,130)J,TJOFF(J) CONTINUE 2X, 12 2X,F6 FORMAT (' ',' JUNCTION TEMPERATURE DIODE NO , , , , , , , , , , , . '^EE C ' , , . 2 ) STOP END c SUBROUTINE MATRIX SUBROUTINE MATRIX ( RR C J Z EL NSEG ND FRE GP REAL =^8 RR,CJ,EL(10) ,FRE,PI COMPLEX^ie Z(10),Z1 C0MPLEX*16 G(2,2,20),G1(2,2,20),GP(2,2,20) PI = 3.1415926536 DO 10 K = 1,NSEG G(1,1,K) = DCMPLX(COS(EL(K)),0.D0) G(1,2,K) = DCMPLX(0.D0,1.DG)'''Z(K)^DCMPLX(SIN(EL(K)),0.D0) G(2,1,K) = DCMPLX(0.D0,1.D0)/Z(K)'^DCMPLX(SIN(EL(K)),0.D0) G(2,2,K) = G(1,1,K) CONTINUE DO 20 L=1,ND IF(CJ.EQ.O.DO)THEN Zl = DCMPLX(RR,O.DO) ELSE Zl = DCMPLX(RR,-1000/(2*PI'^FRE*CJ)) ENDIF G1(1,1,L) = DCMPLX(1.DG,0.D0) G1(1,2,L) = DCM?LX(O.DO,O.DO) G1(2,1,L)= 1/Zl G1(2,2,L) = G1(1,1,L) CONTINUE DO 30 M =1,NSEG , 10 20 30 40 , , , N = 2*M-1 GP(i,i,N) = g(i,i,m; GP(1,2,N) = G(1,2,M GP(2,1,N) = G(2,1,M GP(2,2,N) = G(2,2,M CONTINUE DO 40 I =1,ND J = 2^1 GP(1,1,J) = G1(1,1,I GP(1,2,J) = G1(1,2,I GP(2,1,J'^ = G1(2,1,I GP(2,2,J) = G1(2,2,I CONTINUE RETURN END 89 , , , , 2X, DEGR ' C 30 20 10 C SUBROUTINE MATMUL SUBROUTINE MATMUL (AA,BB,NN, MM, RR, CC) INTEGER NN,MM,RR C0MPLEX*16 AA(2,2,1),BB(2,2,1),CC(2,2,1) DO 10 I = 1,NN DO 20 J = 1,RR CC(I,J,1) = DO 30 K =1,MM CC(I.J,1) = CCa,J,l) + AA(I,K,l)'^BB(K,J,l) CONTINUE CONTINUE CONTINUE RETURN END . SUBROUTINE POWER SUBROUTINE POWER(G, I V,N,PD IID VID) REALMS PD(IO) C0MPLEX^16 G(2,2,20),V,I,IID(20),VID(20),IOD(20),VOD(20) DO 10 J=2,N,2 IID(J) = G(1,1,J-1)*I - G(2,1,J-1)*V VID(J) = G(2,2,J-1)'^V - G(l,2,J-lpI lOD(J) = G(1,1,J)*IID(J) - G(2,1,J)*VID(J) VOD(J) = G(2,2,J)*VID(J) - G(1,2,J)'^IID{J) PD(J) = 0.5^REAL(VID(J)*DCONJG(IID(J))-VOD(J)*DCONJG(IOD(J))) , 10 , , I = lOD(J) V = VOD(J) CONTINUE RETURN END SUBROUTINE THERMl SUBROUTINE THERI^l (ND T J PD AMP TA TR INTEGER ND REAL TJ(IO) ,AMP,TA,TR REAL*8 PD(IO) DO 5 1=1, ND TJ(I) = TA + (PD(I*2)*AMP)'^TR CONTINUE RETURN END , , , , , SUBROUTINE THERM2 SUBROUTINE THERM2 (ND T J PD AMP TA DT HC INTEGER ND REAL TJ(IO) ,AMP,TA,DT,HC REALMS PD(IO) DO 5 J =1,ND TJ(J) = TA + (PD(J*2)*AMP)*DT/HC CONTINUE RETURN END , , , , 90 , , LIST 1. Kurokawa, K. and Schiosser, Modulation," Proc. IEEE, 2. OF REFERENCES O., "Quality Factor of Switching 1970. Atwater, H. and Sudburv' R., "Use of Switching Q Microwave Switches," IEEE Sympos. Microwave Theory 3. Kawakami, S.. "Figure of Merit Associated with RF Switching for o 321, 1965. Diodes ibr Digital ' v. 38, p. 180, A and Modulation," IEEE Trans. , in The Design of Tech., p. 377, 1981. FET Variable Parameter One-port Circuit Theory, v. CT-13, p. A. Hines, M., "Fundamental Limitation in R.F. Switching and Phase Shifting Using Semiconductor Diodes," Proc. IEEE, v. 52, p. 697, 1954. 5. Brown, R. G., Sharpe, R. A., Hughes, \V. L., and Post. R. E., Lines, Waves, and Antennas The Transmission of Electric Energy, aj', John Wiley J & Sons, New York, , , 1973. 6. 7. ^ Matthews. P. A., and Stephenson, Hail Ltd, London, 1968. White, J. Company, 8. 10. 11. PIN , Microwave Components, and Chapman ^ ^ . Microwave Semiconductor Engineering, Van Nostand Reinhold York, 1982. Inc., Massachusetts, 1983. Diode Designers Guide, Microwave Associates Company, Maryland, 1982. Watson H. A^ Microwave Semiconductor McGraw-Hill Book Company, New York, Guild, EEosf, 12. M. Cheng, D. K., Field and Wave Electromagnetics, Addison-Wesley Publishing Company, 9. F., New I. J., Devices and Their Circuit Application, 1969. S., and Skogrand, L., Touchstone Reference Manual Version 3li94 La Baya Drive, Westlake Village, California, 91362, 1987. Rein. Inc., Holmes, C, and Morton, D., "Determination of Node within A Application Note 2, EEsof Inc., Westlake Village. California. 1985. 91 Circuit," 1.5, EEsof INITIAL DISTRIBUTION LIST No. Copies 1. Defense Technical Informaiion Center 2 Cameron Station Alexandria, VA 22304-6145 2. 3. 4. Librarv^ Code 0142 Naval Tostgraduate School Monterey, CA 93943-5002 Department Chairman, Code 62 Department Of Electrical and Computer Engineering Naval Postgraduate School Monterey, CA 93943-5000 Professor Harrv A.Atwater, Code 62An Department Of Electrical and Computer Engineering Naval Postgraduate School Monterey. 5. 2 CA 1 4 93943-5000 Professor Jeffrey B.Knorr, Code 62Ko Department OfElectrical and Computer Engineering 1 Naval Postgraduate School Monterey, 6. CA 93943-5000 Library 1 RovalThai Naval Academy Parknam, Samutprakarn, Thailand 7. Library 1 Naval Officer College Royal Thai Navy Bangkokyai, Bangkok, Thailand 8. LT. Pitak Pibultip 808 mu 3 Sukumvit 107 3 Sumrongnour, Samutprakarn, 10270,Thailand 9. MAJ. Edward M. Siomacco 1 4913 Ashton Rd. Fayetteville. 10. NC LCDR. Sane SMC 28304 Sik Lee 1 # 1795 Naval Postgraduate School Monterey, CA 93943 92 lb25^T DUDLEY KNOX LIBRARY HAVAl. POSn'oa,,rn.,TE SCHOOL MOHTEREY, OALIFORHIA oSS 3003 PibultiP device microwave ^^ /" ^^^'^t In of merxt cxrcuxt designswitching . Thsgis P48655 c.l ,. Pibuitip EvslUAtinn of devic? of merit in microwave switching circuit design, » .t f^ MJ4, .*• ^.,yr:. y^ .T..:V J, A. •':*•;.* »;»: i: