Theory, Models, and ApplicationsUniversity of Southern California213–740–8677[USC Fax]Original: September 20021.0.INTRODUCTION2.0.FUNDAMENTAL TWO PORT CONCEPTS2.1.INPUT PORT MODEL2.2.OUTPUT PORT MODELS2.3.TWO PORT PARAMETERS OF IDEAL AMPLIFIERS2.3.1.Ideal Voltage Amplifier2.3.2.Ideal Transimpedance Amplifier2.3.3.Ideal Transadmittance Amplifier2.3.4.Ideal Current Amplifier2.4.GENERALIZED TWO PORT PARAMETERS2.4.1.Hybrid h–Parameters2.4.2.Hybrid g–Parameters2.4.3.Short Circuit y–Parameters2.4.4.Indefinite Admittance Parameters2.4.5.Open Circuit z–Parameters2.4.6.Chain Parameters2.4.6.1Input and Output Impedances2.4.6.2Voltage Transfer Function2.4.6.3Cascade Interconnection2.4.6.4Series and Shunt Elements3.0.TWO PORT METHODS OF CIRCUIT ANALYSIS3.1.CIRCUIT ANALYSIS IN TERMS OF h–PARAMETERS3.1.1.Open Loop and Loop Gain Concepts3.1.2.I/O Impedances3.2.CIRCUIT ANALYSIS IN TERMS OF g–PARAMETERS3.3.CIRCUIT ANALYSIS IN TERMS OF y–PARAMETERS3.4.CIRCUIT ANALYSIS IN TERMS OF z–PARAMETERS4.0.SYSTEMS OF INTERCONNECTED TWO PORTS4.1.SERIES-SHUNT FEEDBACK4.2.SHUNT-SERIES FEEDBACK4.3.SHUNT-SHUNT FEEDBACK4.4.SERIES-SERIES FEEDBACK5.0.REFERENCESEE 541, Fall 2006: Course Notes #1 Linear Two port Networks: Theory, Models, and Applications Dr. John Choma Professor of Electrical & Systems Architecture Engineering University of Southern California Department of Electrical Engineering-Electrophysics University Park: Mail Code: 0271 Los Angeles, California 90089–0271 213–740–4692 [USC Office] 213–740–8677 [USC Fax] [email protected] ABSTRACT: This report defines the commonly used two port parameters of generalized linear electrical networks and discusses the theory that underpins two port parameter models. It develops two port circuit analysis methods for evaluating the driving point input impedance, the driving point output impedance, the transfer function, the loop gain, and the stability characteristics of simple and relatively complex active and passive two port network architectures. Basic measurement strategies for the various two port parameters are also addressed. Original: September 2002Course Notes #1 University of Southern California John Choma 1.0. INTRODUCTION The majority of linear passive electrical and active electronic systems can be viewed as two port networks. A network port consists of two electrical terminals, thereby suggesting that a two port network has two readily accessible pairs of electrical terminals. One of these terminal pairs is the input port, to which a known signal voltage or current is applied. The network of interest processes this input voltage or current to produce a desired or designable response at the second of the two network pairs, which is called the output port. The theories and analytical techniques indigenous to basic circuit theory allow the output response of a two port network to be related to its applied input energy as a function of the volt-ampere characteristics of the individual branches embedded in the network. Although this direct formulation of the output response -to- input signal relationship is systematic, three engineering issues limit the utility of this straightforward analytical strategy. One of the foregoing engineering issues derives from the sheer topological complexity of practical circuits. A useful circuit, and particularly a useful electronic circuit, may contain hundreds or even thousands of branch elements. The immediate effect of this ubiquity of electri-cal elements is an explosion of the required number of equilibrium equations that must be solved simultaneously to forge the desired input -to- output (I/O) transfer relationship. Manual solution is therefore rendered daunting, if not impossible, thereby encouraging the use of the omnipresent computer. But neither cumbersome manual analyses nor computationally efficient computer-based numerical solutions are likely to inspire the engineering design insights whose assimilation is, in fact, the fundamental goal of circuit analysis. A second shortcoming of direct circuit analyses is that the electrical characteristics of many internal network branches may not be well defined or clearly understood. This issue is especially nontrivial when the network in question contains active elements, such as bipolar junction transistors (BJTs) and metal-oxide-semiconductor field effect transistors (MOSFETs), that are incorporated to process electrical signals at high speeds. In such an event, electrical responses are vulnerable to stray capacitances, parasitic lead inductances, device processing uncertainties, and undesirable electromagnetic coupling from proximately positioned circuits. To be sure, mathematical models of active elements and the aforementioned second order electri-cal phenomena can be constructed. But in the interest of analytical tractability, these macromod-els are invariably simplified to an extent that virtually ensures inaccuracies in, or even miscomprehension of, the fruits of analysis. A final point of contention is the superfluous technical information generated as an implicit byproduct of conventional mesh and nodal analyses. The application of the Kirchhoff voltage law (KVL) and the Kirchhoff current law (KCL) produces, in addition to the desired out-put response, all node and branch voltages and all mesh and loop currents intrinsic to the net-work undergoing examination. But in many applications, such as active filters that exploit commercially available operational amplifiers (op-amps) or application specific high perform-ance amplifiers, the only engineering concern is the electrical relationship established between the I/O ports of the filter. This relationship can be forged without an explicit awareness of the voltages and currents established within the utilized amplifiers. Indeed, the overall I/O filter transfer function and other performance metrics can be deduced as a function of only electrical properties gleaned from measurements executed at the I/O ports of these amplifiers. These electrical properties, or two port parameters, are admittedly nonphysical entities in that they generally cannot be cast in terms of the physically sound phenomenology that underlie the August 2006 2 Two Port NetworksCourse Notes #1 University of Southern California John Choma electrical nature of observable I/O characteristics. Nonetheless, they are useful because they do derive from reproducible port