Practical Microstrip Design and Applications

Appendix G: Circuit Theory

A circuit is an interconnection of n-port components that interact only at the ports. Each n-port is described by n 2 complex parameters. The circuit behavior can be predicted solely from knowledge of these parameters. Circuit analysis can be based on the voltage-current description, or make use of the S matrix concept.

G.1 Circuit Parameters Interrelating Voltage and Current

The electrical properties of an n-port can be described by various circuit parameters interrelating voltage V and current I at the ports of an n-port, such as H, Y, and Z. For a two-port (Figure G.1), the following relations are valid:


Figure G.1: Two-port representation and definition of voltage and current.
H Parameter

The H parameters, also termed hybrid coefficients, relate the input voltage and output current, respectively, to the input current and output voltage:

(G.1)

The H matrix is often used for the characterization of transistor devices [1]. In particular

(G.2)

denotes the current gain. H 21 is measured with short-circuited termination at port 2.

Y Parameter

The Y parameter relates the port currents to the port voltages,

(G.3)

In matrix form, (G.3) reads

(G.4)

or

(G.5)
Z Parameter

The Z parameter relates the port voltages to the port currents,

(G.6)

In matrix form, (G.6) reads,

(G.7)

or

(G.8)

The Z and Y matrices are the inverses of each other:

(G.9)

Note that both the Z and Y matrices relate...

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