Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1991 Design and performance of a broadband microwave active inductor circuit with an application to amplifier design Charles Forrest Campbell Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Electrical and Electronics Commons, and the Electromagnetics and Photonics Commons Recommended Citation Campbell, Charles Forrest, "Design and performance of a broadband microwave active inductor circuit with an application to amplifier design" (1991). Retrospective Theses and Dissertations. 16684. https://lib.dr.iastate.edu/rtd/16684 This Thesis is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Design and performance of a broadband microwave active inductor circuit with an application to amplifier design by Charles Forrest Campbell A Thesis Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE Depar tmen t : Electrical Engineering and Computer Engineering Major: Electrical Engineering Signatures have been redacted for privacy Iowa State University Ames, Iowa 1991 ii TABLE OF CONTENTS Page ABSTRACT iv CHAPTER 1. INTRODUCTION 1 Statement of Problem 1 Review of Past York 1 CHAPTER 2. ACTIVE INDUCTOR SYNTHESIS 3 Inductance Simulation with Gyrators 3 Gyrator Approximation using BJTs 5 Synthesis of the Feedback Network 9 CHAPTER 3. ACTIVE INDUCTOR ANALYSIS 15 S-parameter Analysis 15 Simplified Hybrid-n Model Analysis 24 CHAPTER 4. ACTIVE INDUCTOR MICROSTRIP CIRCUIT DESIGN 33 Device Characterization 33 S-parameter and Hybrid-n Simulations 38 Effect of Distributed Elements 42 Transistor Biasing Networks 43 CAD Layout and Analysis 47 CHAPTER 5. ACTIVE INDUCTOR PERFORMANCE 51 Experimental Data 51 Tunability 60 Comparison with Spiral Inductors 65 Power Handling Capability 71 iii Page CHAPTER 6. APPLICATION TO NARROYBAND AMPLIFIER DESIGN 74 Amplifier Circuit Design 74 CAD Layout and Analysis 80 Experimental Data 80 CHAPTER 7. SUMMARY AND RECOMMENDATIONS 87 BIBLIOGRAPHY 89 ACKNOYLEDGEMENTS 91 APPENDIX A: MOTOROLA MRF901 DATA 92 MRF901 Data Sheet 92 Packaging Information 93 Data Sheet S-parameters 94 APPENDIX B: LIBRA SIMULATION FILES 96 Microstrip Active Inductor Simulation 96 Rectangular Spiral Inductor Simulation 97 Microstrip Narrowband Amplifier Simulation 97 iv ABSTRACT The synthesis, analysis and fabrication of a broadband microwave active inductor circuit utilizing BJTs has been presented and applied in a narrowband amplifier design. The circuit realizes inductance by impedance gyration using a CC-CE pair with the parasitic capacitance between the base and emitter of the CE transistor as the load. A feedback network consisting of two parallel RC networks in series is used to produce a flat inductance versus frequency response by compensating for the n-model elements of the transistors. Hybrid-n and S-parameter simulations of the circuit predict a maximum bandwidth of about f~/2. Microstrip circuits were fabricated employing Motorola MRF901 BJTs which have a f~ of about 4.5GHz. The fabricated circuits produced flat inductance responses for inductance values and resonant frequencies of 7nH to 29nH and 670MHz to 1050MHz respectively. The maximum measured quality factors for the flat inductance responses ranged from 1.1 to 2.0, however, the circuit was tuned for a quality factor as high as 8.5. A 500MHz narrowband amplifier was designed employing the active inductor circuits in the impedance matching networks. The microstrip realization of the amplifier produced a measured transducer gain of 18.8dB and a 1dB fractional bandwidth of 21.6%. 1 CHAPTER 1. INTRODUCTION Statement of Problem In the design of microwave amplifiers, lumped element networks are often required to obtain an impedance match between the source and the load or to improve the bandwidth of the circuit. The realization of lumped element networks on monolithic microwave integrated circuits (MMICs) is often accomplished with capacitors and spiral inductors. Unfortunately, spiral inductors require large amounts of substrate area and air bridges; they have limited bandwidth, high series resistance, and crosstalk problems. Spiral inductors have also proven to be quite difficult to model accurately. One possible solution to this problem is to realize inductance with an active circuit and avoid the use of spiral inductors altogether. The objective of this thesis is to investigate the design and performance of microwave frequency active inductor circuits utilizing bipolar junction transistors (BJTs) and to demonstrate an application to narrowband amplifier design. Review of Past Vork Inductance has been synthesized extensively with active devices in the audio frequency range with the use of generalized immittance converters (GICs), which can be readily realized with operational amplifiers or operational transconductance amplifiers [1,2]. However, at microwave frequencies these circuits normally can no longer be used, and other methods of inductance realization must be employed. The use of 2 active shunt peaking to increase the bandwidth of VHF amplifiers has been accomplished by Choma and others by exploiting the inductive output impedance of a common collector transistor [3,4,5]. The most recent published advance in the realization of microwave frequency active inductor circuits is by Hara et al. [6,7]. These circuits employ GaAs field effect transistors (FETs), and they have been demonstrated to have performance superior to that of spiral inductors. The first of these circuits uses a common source-common gate cascode and a feedback resistor to produce inductance in the microwave frequency range. The inductance value is set by the feedback resistor and the series resistance of the realized inductor is approximately equal to I/gm. The other circuit designs realize near loss less (Rs~20Q) inductors by employing a FET in a negative resistance configuration as the feedback element. The inductance realized by these circuits is not as independent of frequency as the other design and the possibility of the circuit becoming unstable is much greater. In all cases, for the circuits to be broadband, the FETs must be identical and under the same bias. 3 CHAPTER 2. ACTIVE INDUCTOR SYNTHESIS Inductance Simulation with Gyrators In the design of active filters, the simulation of grounded inductors is often accomplished with a gyrator loaded with a capacitor. A gyrator is a two port device with a z-parameter matrix (2.1) where r is the gyration resistance [1]. Many circuit realizations of gyrators are available in the literature and one such circuit is shown in Fig. 2-1 [8J. This circuit can be shown to have gyrator action by relating the terminal currents to the terminal voltages. (2.2a) (2.2b) Writing these in the form of Eq. (2.1) 0 -l/g 1[ 11 1 [ (2.3) l/g 0 12 the gyration resistance is seen to be equal to 1/g. When this ideal gyrator circuit is loaded with a capacitor, as in Fig. 2-2, the impedance looking into port 1 is given by Eq. (2.4), and the circuit simulates a grounded inductor of value L=C/g2 • The gyrator approach will be the technique used to realize an active inductor in this investigation. 4 Figure 2-1. Ideal gyrator realization + + c Figure 2-2. Ideal active inductor circuit 5 Z12 Z21 ------- = sC/g2 sL (2.4) Gyrator Approximation using BJTs In order to approximate gyrator action with transistors, a circuit model which approximates the frequency response of a transistor needs to be employed. The gyrator realization of Fig. 2-2 consists of two voltage controlled current sources, one oriented so that the current leaves the common node, the other so that it enters the common node. Therefore, the simplified hybrid n-model [91 illustrated in Fig. 2-3 would be convenient to use because it also contains voltage controlled current sources. B c + ~ E Figure 2-3. Simplified hybrid-n model of BJT The circuit and model for the connection of a common collector transistor driving a common emitter transistor are shown in Fig. 2-4. A comparison of this circuit with the ideal active inductor circuit in 6 (a) Common collector BJT driving common emitter BJT (b) Equivalent circuit model Figure 2-4. Gyrator approximation using BJTs 7 Fig. 2-2 reveals that the desired current source orientation and load capacitor required for inductance simulation are realized. In order to examine the effect of a resistor in parallel with the load capacitor for the ideal active inductor circuit, apply Eq. (2.4). (2.5) Therefore, as a consequence of Rn2' the realized active inductor will have series resistance no matter how nearly the actual gyrator is approximated. Unfortunately, the remaining circuit elements for the model are not included in the active inductor circuit of Fig. 2-2. The voltage driving the current source associated with the common collector transistor is not across pprt 1 and is effectively disconnected. Therefore, a feedback network must be designed that would complete the connection from port 1 to the input of the common collector transistor and compensate somewhat for the additional circuit elements in the model. The circuit in Fig. 2-4 is repeated in Fig. 2-5 with the proposed feedback network connecting port 1 to the input of the common collector transistor. Nodal equations for the network are (2.6a) (2.6b) (2.6c) 8 (a) Gyrator approximation with feedback 1---7 (b) Equivalent circuit model Figure 2-5. Proposed active inductor circuit 9 where the impedances Zl and Z2 are defined as follows: R~ (2.7a) R~ Z2 (2.7b) Solving Eq. (2.6) for the voltages Vnl and Vn2 , (2.8a) VZ2(l + Zlgl) Vn2 = -------------------- (2.8b) Zf + Z2 + Zl(l + Z2gl) and substituting Eq.