1. Lecture - 10 Two port circuits

2. Outline Introduction. Model limitations. The terminal equations.
Two-Port Parameters.

3. Introduction
The two-port model is used to describe the performance of a circuit in terms of the voltage and current at its input and output ports.

4. Model limitations The model is limited to circuits in which:
no independent sources are inside the circuit between the ports;
no energy is stored inside the circuit between the ports;
the current into the port is equal to the current out of the port; and
no external connections exist between the input and output ports.

5. The terminal equations
Two of the four terminal variables (V1, I1, V2, I2) are independent.
Therefore, only two simultaneous equations involving the four variables are needed to describe the circuit.
The six possible sets of simultaneous equations involving the four terminal variables are called the z-, y-, a-, b-, h-, and g-parameter equations.
The parameter equations are written in the s domain. The dc values of the parameters are obtained by setting s=0, and the sinusoidal steady-state values are obtained by setting s=jw.

6. The terminal equations (2)
z – parameters
V1 = z11I1 + z12I2
V2 = z21I1 + z22I2
b- parameters
V2 = b11V1 - b12I1
I2 = b21V1 – b22I1
y- parameters
I1 = y11V1 + y12V2
I2 = y21V1 + y22V2
h-parameters
V1 = h11I1 + h12V2
I2 = h21I1 + h22V2
a- parameters
V1 =a11V2 – a12I2
I1 = a21V2 – a22I2
g-parameters
I1 = g11V1 + g12I2
V2 = g21V1 + g22I2

7. Two-Port Parameters
Any set of parameters may be calculated or measured by invoking appropriate short-circuit and open-circuit conditions at the input and output ports.
for example suppose that the problem is to find the z parameters for a circuit:
z11 is the impedance seen looking into port 1 when port 2 is open.
z12 is a transfer impedance. It is the ratio of the voltage at port 1 to the current at port 2 when port 1 is open.
z21 is a transfer impedance. It is the ratio of the voltage at port 2 to the current at port 1 when port 2 is open.
z22 is the impedance seen looking into port 2 when port 1 is open.

8. Two-Port Parameters (2)
The two-port parameters are also described in relation to the reciprocal sets of equations.
The z and y parameters are called impedance and admittance parameters. because they describe the ratio of a voltage to a current and vice versa.
The a and b parameters are called the transmission parameters because they describe the voltage and current at one end of the two-port network in terms of the voltage and current at the other end.
The h and g parameters relate cross-variables, that is, an input voltage and output current to an output voltage and input current. Therefore the h and g parameters are called hybrid parameters.

9. Example 1

10. Example 2
Find the y parameters for the circuit shown.

11. Example 3
Find the g and h parameters for the circuit shown.