So the current remains same I s = I r.ĭividing the above equation from -V/B we get, it contains only passive components in the circuit like inductance, resistance, etc. The current flows through the receiving end is given by the equationĬonsider, the network is passive, i.e. Thus, the direction of the current in the network changes, which is shown in the diagram below Similarly, the voltage is applied at the receiving end, and the input voltage remains zero. Since, under short circuit the receiving end voltage is zero, the voltage and current equations become The voltage V is applied to the sending end, and the receiving end is kept short circuit, so the voltage becomes zero. Relation between ABCD parametersįor determining the relation between various types of network, like passive or bilateral network reciprocity theorem is applied. We get the value of D, which is the ratio of the sending current to the receiving current. Similarly, if we put V r= 0 in current equations, If we put V r = 0 in the equation, we get the value of B which is the ratio of sending end voltage to the receiving end currents. ABCD parameters for short circuitįor the short circuit, the voltage remains zero at the receiving end. We get the value of c parameter which is the ratio of the sending end voltage to the current. Similarly, if I r =0 is substituted in current equation, It is a dimensionless constant because their ratio has the same dimension. Since the circuit is open at the receiving end, the current I r remains zero.įrom above equations, we get the value of A parameter which is the ratio of sending end voltage to the receiving end voltage. V 1 are purely imaginary.In the open circuit, the output terminals are open, and the voltage measure across them is V r. They are usually expressed in matrix notation, and they establish relations between the variables These are all limited to linear networks since an underlying assumption of their derivation is that any given circuit condition is a linear superposition of various short-circuit and open circuit conditions. The common models that are used are referred to as z-parameters, y-parameters, h-parameters, g-parameters, and ABCD-parameters, each described individually below. In two-port mathematical models, the network is described by a 2 by 2 square matrix of complex numbers. The analysis of passive two-port networks is an outgrowth of reciprocity theorems first derived by Lorentz. An alternative tool in the frequency domain is the transfer function, which defines how a circuit network can act like an amplifier or filter. Any linear circuit with four terminals can be regarded as a two-port network provided that it does not contain an independent source and satisfies the port conditions.Įxamples of circuits analyzed as two-ports are filters, matching networks, transmission lines, transformers, and small-signal models for transistors (such as the hybrid-pi model). S-parameter measurements are commonly used to characterize high-speed and high-frequency circuits in the frequency domain. There is not uniqueness of the solution for the matrix inversion. The third line represents an unbalanced system where N i > N e. For example, transistors are often regarded as two-ports, characterized by their h-parameters (see below) which are listed by the manufacturer. The matrix inversion has to be done with the pseudo-inverse operator ( +). It also allows similar circuits or devices to be compared easily. This allows the response of the network to signals applied to the ports to be calculated easily, without solving for all the internal voltages and currents in the network. A two-port network is regarded as a " black box" with its properties specified by a matrix of numbers. The two-port network model is used in mathematical circuit analysis techniques to isolate portions of larger circuits. 9 Scattering transfer parameters (T-parameters).6 Inverse hybrid parameters (g-parameters).3.1 Example: bipolar current mirror with emitter degeneration.