ELECTRONICS | hybrid parameters

What is hybrid parameter?

Hybrid parameters (also known as h parameters) are known as ‘hybrid’ parameters as they use Z parameters, Y parameters, voltage ratio, and current ratios to represent the relationship between voltage and current in a two port network.

Hybrid parameter or h parameter – Every linear two port circuit having input and output terminals can be analysed by four parameters having mixed dimension. These parameters are called hybrid parameter.

Explanation :

In a two port device i/p (input) and o/p (output) signal currents are i1 and i2.

i/p and o/p voltages are v1 and v2.

Here the dependent variables are v1 and i2.

and the independent variables are i1 and v2.

They are expressed by two linear equations with hybrid parameter as

h-parameters are defined as-

Input impedance when output is short circuited.

Unit of h11 – ohm

Reverse voltage amplification factor when input is open circuited.

Unit of h12 – unit-less

Forward current gain when o/p is short circuited.

Unit of h21 – unit-less.

Output admittance when input is open circuited.

Unit of h22 mho.

 

Hybrid parameters of a transistor in CE mode –

Here independent variables are –

input current (IB)

output voltage (VCE)

Here dependent variables are –

output current (IC)

input voltage (VBE)

Thus

Again

 

Definition of four hybrid parameters :

called input impedance when output is short circuited.

Definition – The ratio of change in input voltage (VBE) to the corresponding change in input current (IB) when the output is short circuited.

 

called reverse voltage amplification factor when input is open circuited.

Definition – The ratio of change in input voltage (VBE) to the corresponding change in output voltage (VCE) when input is open circuited.

called forward current gain when input is short circuited.

Definition – The ratio of the change in output current (IC) to the corresponding change in input current (IB) when output is short circuited.

 

called output admittance when the input is open circuited.

Definition – The ratio of the change in output current (IC) to the corresponding change in output voltage (VCE) When the input is open circuited.

 

Equivalent circuit of a transistor in CE configuration :

We know in the CE Configuration, the Emitter terminal of the transistor will be connected common between the output and the input terminals. The variation of emitter current(I_B) with Base-Emitter voltage(V_BE), keeping Collector Emitter voltage(V_CE) constant.

Hybrid equations of a transistor in CE configuration –

 

Graphical determination of CE h parameters :

(i) Determination of the parameters hie and hre:

The Q point is first found on the input characteristic curves. A horizontal line AB is drawn through the Q-point to establish a line IB = constant (indicated IBO)

Now from the definition,

Now we draw a tangent to the curve at Q-point.

So, now from the definition,

 

(II) Determination of the parameter hfe and hoe :

The Q point is first found on the output characteristic curves. A vertical line XY is drawn through the Q point to establish a line VCE = constant (indicated VCEO)

From the derivation,

Now we draw a tangent to the given curve at the Q point.

From the definition,

 

Analysis of a CE transistor amplifier using hybrid model to calculate-

1. Current gain
2. Voltage gain
3. Input impedance
4. Output impedance
5. Power gain

A basic  common emitter amplifier circuit –

We can find its hybrid parameter equivalent circuit using two linear equations

Thus CE transistor amplifier circuit using hybrid model,

 

A) Current gain :

Current gain defined as the ratio of the load current I_L to the input current I_b. Thus,

From the output loop

Including the effect of source resistance,we consider the Norton’s equivalent  for the source as

Now current gain

From figure

 

B) Input impedance (Zi) :

This is the impedance between the input terminals B and E looking into the amplifier as shown in Figure  and is, therefore, given by,

From the input loop

 

C) Voltage gain (Av) :

It is the ratio of the output voltage to the input voltage . Thus,

 

Including the effect of source resistance,

 

D) Output impedance :

The output impedance is the ratio of change in output voltage to change in load current.

From output circuit,

From input circuit, applying KVL ( Kirchhoff’s Voltage Law)

 

E) Power gain ( Ap) :

From the circuit of Figure , the average power delivered to the load imprudence, is given by

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