Group A Question 1 The two port circuit presented in Fig. 1 can be described in terms of b-parameters as:

Question: Group A Question 1 The two port circuit presented in Fig. 1 can be described in terms of b-parameters as:

Solution:

It can be proved by advanced circuit theory that voltages and currents in Fig. can be related

by the following sets of equations :

v1 = h11 i1 + h12 v2 …(i)

i2 = h21 i1 + h22 v2 …(ii)

In these equations, the hs are fixed constants for a given circuit and are called h parameters.

Once these parameters are known, we can use equations (i) and (ii) to find the voltages and currents

in the circuit. If we look at eq.(i), it is clear that **h11 has the dimension of ohm and h12 is dimension-

less. Similarly, from eq. (ii), h21 is dimensionless and h22 has the dimension of mho. The following

points may be noted about h parameters :

(i) Every linear circuit has four h parameters ; one having dimension of ohm, one having di-mension of mho and two dimensionless.

(ii) The h parameters of a given circuit are constant. If we change the circuit, h parameters would also change.

The major reason for the use of h parameters is the relative ease with which they can be measured. The

h parameters of a circuit shown in Fig. 24.1 can be found out as under :

(i) If we short-circuit the output terminals (See Fig. 24.2), we can say that output voltage v2 = 0.

Putting v2 = 0 in equations (i) and (ii), we get,

v1 = h11 i1 + h12 × 0

i2 = h21 i1 + h22 × 0

∴ h11 = v1/i1 for v2 = 0 i.e. output shorted

and

h21 = i2/ i1 , for v2 = 0 i.e. output shorted

Let us now turn to the physical meaning of h11 and h21 . Since h11 is a ratio of voltage and current

(i.e. v1/i1), it is an impedance and is called * “input impedance with output shorted ”. Similarly, h21 is the ratio of output and input current (i.e., i 2/i 1), it will be dimensionless and is called“current gain with output shorted”.

The other two h parameters (viz h12 and h22) can be found by making i

1 = 0. This can be d doneby the arrangement shown in Fig.. Here, we drive the output terminals with voltage v2,

keeping the input terminals open. With this set up, i

1 = 0 and the equations become :

v1 = h11 × 0 + h12 v2

i 2 = h21 × 0 + h22 v2

∴ h12 = v1/v2 for i1 = 0 i.e. input open

and

h22 = i2 /v2 , for i1 = 0 i.e. input open

Since h12 is a ratio of input and output voltages (i.e. v1/v2), it is dimensionless and is called “voltage

feedback ratio with input terminals open”. Similarly, h22 is a ratio of output current and output voltage

(i.e. i 2/v2), it will be admittance and is called “output admittance with input terminals open”.

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