Applied Electronics and Instrumentation

LESSON 12. Transistor amplifier- h parameter-benefits-h parameter equivalent circuit for CE configurates- comparison.

 Definitions of h – parameter

The parameters in the above equation are defined as follows:

    h₁₁ =       = input resistance with output short – circuited, in ohms..

    h₁₂ =        = Fraction of output voltage at input with input open circuited.

                               This parameter is ratio of similar quantities, hence unitless

    h₂₁ =        = Forward current transfer ratio or current gain with output

                                short   circuited.

                               This parameter is a ratio of similar quantities, hence unitless.

     h₂₂ =        = Output admittance with input open-circuited, in mhos.

From the above discussion we can say that, these four parameters are not same. They have different units. In other words, they are mixture of different units and hence referred to as hybrid parameters. As we use small letter for ac analysis, these are commonly known as h-parameters. The standard notations can be given as

i = 11= input                                o = 22 = output

f = 21 = forward transfer             r = 12 = reverse transfer

Thus we can write h-parameters as follows.

a) With output short circuited :   

h₁₁ = h_i  : Input resistance

h₂₁ = h_f  : Short circuit current gain

b) With input open circuited :   

h₁₂ = h_r  : Reverse voltage transfer ratio

h₂₂ = h_o  : output admittance.

H- parameter equivalent circuit for transistor is shown in the following figure

           

In order to analyze transistorized amplifier circuit and calculate its input impedance, output impedance, current gain and voltage gain, it is necessary to replace transistor circuit with its equivalent. The equivalent circuit can be drawn with the help of two equations, as shown in Fig. 1.10.

                                       V_i = h_i I_i + h_r V_o          I_o = h_f I_i + h_o V_o

Many transistor models have been proposed, each one having its advantages and disadvantages. The transistor model used in this text is in terms of h-parameters. 

Benefits of h-parameters

1. Real numbers at audio frequencies.

2. Easy to measure.

3. Can be obtained from the transistor static characteristics curves.

4. Convenient to use in circuit analysis and design.

5. Most of the transistor manufacturers specify the h-parameters.

H – parameters equivalent circuit for CE configuration in the following figure

             Simple common emitter configuration

To see how we can derive a hybrid model for a transistor, let us consider the common emitter configuration as shown in the above figure.. The variables I_b, I_c, V_b and V_c represent total instantaneous currents and voltages.

                    I_b = input current

                    I_c = output current

                    V_be = input voltage

                    V_ce = output voltage.

The following figure shows the h-parameter equivalent circuit for the common emitter configuration.

h-parameter equivalent circuit for the common emitter configuration

 

      From the h-parameter equivalent circuit of the common emitter configuration we can write,

                  V_be = h_ie I_b + h_re V_ce                                                …(7)

                     I_c = h_fe I_b + h_oe V_ce                                               …(8)

The quantities ∆V_BE (V_be), ∆V_CE (V_ce), ∆_IB (I_b) and ∆_IC (I_c) represent the small change in base and collector voltages and currents.

H-parameters for all three configurations

As mentioned earlier, transistor can be represented as a two port network by making any one terminal common between input and output. Since there are three possible configurations in which a transistor can be used, there is a change in terminal voltage and current for different transistor configurations. For different configurations the relation between input parameters and output parameters also differs. Therefore, one needs to define different set of h-parameters for different configurations. To designate the type of configuration another subscript is added to the h-parameters.

       For example :

       h_ie = h_11e = input resistance in common emitter configuration.

       h_fb = h_21b = short-circuit current gain in common base configuration.

       The following table summarizes the h-parameters for all the three configurations.

parameter	CB	CE	CC
Input resistance	hib	hie	hic
Reverse voltage gain	hrb	hre	hrc
Forward transfer current gain	hfb	hfe	hfc
Output admittance	hob	hoe	hoc