Verify Hybrid Parameters of Two-port Network

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Aim

To calculate and verify Hybrid parameters of two-port network.

Apparatus

Breadboard, Batteries or DC regulated power supply, Resistors, Digital multimeter, Connecting wires, Alligator clips.

Theory

h-Parameters of Two Port Network are also called hybrid parameters. These parameters are very useful in constructing models for transistors.

These parameters are obtained by expressing voltage at input port and the current at output port in terms of the current at the input port and the voltage at the output port.

We will get the following set of two equations by considering the variables V1 & I2 as dependent and I1 & V2 as independent. 

In equation form, above relations can be written as,

V1=h11I1+h12V2                         …(1)

I2=h21I1+h22V2                          …(2)

The coefficients of independent variables, I1 and V2, are called as h-parameters.

verify Z parameters of two-port network
Figure 1: Two-port network

In matrix form the above equations can be written as,

Verify Hybrid Parameters of Two-port Network

Assuming the short circuit condition at the output terminal, we get V2 = 0

Now putting V2 = 0 in (1), we get

V1 = h11I1

∴h11 = (V1 / I1)

 

Similarly, putting V2 = 0 in (2), we get

I2 = h21I1

∴ h21 = (I2 / I1)

 

Again, assuming input port of the two-port network to be open circuited, the input voltage will be zero i.e. I1 = 0

Now putting I1 = 0 in (1), we get

V1 = h12V2

∴ h12 = (V1 / V2)

 

Similarly putting I1 = 0 in (3), we get

I2 = h22V2

∴ h22 = (I2 / V2)

 

Thus, there are four h parameter for a two-port or four-terminal network. Their values are tabulated below.

h11

(V1 / I1)

Condition: Output port of the two-port network is short circuited i.e. V2 = 0

h21

(I2 / I1)

h12

(V1 / V2)

Condition: Input port of the two-port network is open circuited i.e. I1 = 0

h22

(I2 / V2)

 The individual h-parameters are defined as follows,

{h_{11}} = {\left. {\frac{{{V_1}}}{{{I_1}}}} \right|_{{V_2} = 0}}

This is called short circuit input impedance.

 

{h_{21}} = {\left. {\frac{{{I_2}}}{{{I_1}}}} \right|_{{V_2} = 0}}

This is called forward short circuit current gain.

 

{h_{12}} = {\left. {\frac{{{V_1}}}{{{V_2}}}} \right|_{{I_1} = 0}}

This is called reverse open circuit voltage gain.

 

{h_{22}} = {\left. {\frac{{{I_2}}}{{{V_2}}}} \right|_{{I_1} = 0}}

This is called open circuit output admittance.

 

The parameters, h12 and h21, do not have any units, since those are dimension-less. The units of parameters, h11 and h22, are Ohm and Mho respectively.

All above parameters are having different units such as ohm for short circuit impedance and mho for open circuit output admittance, the name of the parameter is hybrid parameter.

Circuit Diagram

verify Hybrid parameters of two-port network, lab manual h-parameters,
Figure 2: Circuit diagram for experimental set-up of H-Parameters

[Chose any resistor between 200Ω to 2KΩ and DC supply beween 5V to 12V]

Procedure

  1. Connect the circuit as shown in figure 2.
  2. First short the output port (port 2) and supply 10V to input port (port 1). Measure output current and input current using multi-meter.
  3. Secondly, open circuit input port and supply 5V to output port. Measure input and output voltages and output current using multi-meter.
  4. Calculate the values of h-parameters using respective formulas (Shown in calculation section).
  5. Switch ‘OFF’ the supply after taking the readings.

Precautions

  • Before circuit connection working condition of all the components must be checked.
  • All the connection should be tight.
  • Ammeter must be connected in series while voltmeter must be connected in parallel to the components (resistors).
  • The electrical current should not flow the circuit for long time, otherwise its temperature will increase and the result will be affected.

Observation table

When output port is short circuited

When input port is open circuited

V1

I1

I2

V1

V2

I2

 

 

 

 

 

 

Calculations

For Practical Values:

(a) When output is short circuited i.e. V2 = 0

       h11 = V1 / I1 = ___ Ω

       h21 = I2 / I1 = ___

(b) When input is open circuited i.e. I1 = 0

       h12 = V1 / V2 = ___

       h22 = I2 / V2 = ___ mho

 

For Theoretical Values:

[Use any method to calculate h-parameters]

       h11 = ____ Ω

       h21 = ____

       h12 = ____

       h22 = ____mho

Result

Parameter→

h11

h12

h21

h22

Theoretical

    

Practical

    

Conclusion

Calculated and practical values of h-parameters are found to be nearly equal hence h-parameters are verified.

Video Tutorial on H-Parameters

For Calculation to Verify Hybrid parameters of two-port network

Click here

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