Analysis of a Transistor Amplifier Circuit Using H-Parameters | Analog and Digital Electronics - Electrical Engineering (EE) PDF Download

ANALYSIS OF A TRANSISTOR AMPLIFIER USING H-PARAMETERS: 
 

To form a transistor amplifier it is only necessary to connect an external load and signal source as indicated in fig. 1 and to bias the transistor properly.

Consider the two-port network of CE amplifier. R_S is the source resistance and Z_L is the load impedance. The h-parameters are assumed to be constant over the operating range. The ac equivalent circuit is shown in fig. 2. (Phasor notations are used assuming sinusoidal voltage input). The quantities of interest are the current gain, input impedance, voltage gain, and output impedance.
 

Current gain: 

For the transistor amplifier stage, A_i is defined as the ratio of output to input currents.

1.3.2 Input impedance:

The impedance looking into the amplifier input terminals ( 1,1' ) is the input impedance Z_i
                                 
 

Voltage gain: 

The ratio of output voltage to input voltage gives the gain of the transistors.

Output Admittance: 

It is defined as
 

A_v is the voltage gain for an ideal voltage source (R_v = 0).

Consider input source to be a current source I_S in parallel with a resistance R_S as shown in fig. 3.

In this case, overall current gain A_IS is defined as

                                   

h-parameters:

 To analyze multistage amplifier the h-parameters of the transistor used are obtained from manufacturer data sheet. The manufacturer data sheet usually provides h-parameter in CE configuration. These parameters may be converted into CC and CB values. For example fig. 4 h_rc in terms of CE parameter can be obtained as follows. 

Fig. 4 

For CE transistor configuaration 

V_be = h_ie I_b + h_re V_ce 

I_c = h_fe I_b + h_oe V_ce 

The circuit can be redrawn like CC transistor configuration as shown in fig. 5. 

V_bc = h_ie I_b + h_rc V_ec 

I_c = h_fe I_b + h_oe V_ec 
 

Hybrid model for transistor in three different configurations
 

Typical h-parameter values for a transistor:
 

Analysis of a Transistor amplifier circuit using h-parameters

A transistor amplifier can be constructed by connecting an external load and signal source and biasing the transistor properly.
 

The two port network of Fig. 1.4  represents a transistor in any one of its configuration. It is assumed that h-parameters remain constant over the operating range.The input is sinusoidal and I₁,V­₁,I₂ and V₂ are phase quantities.
 

                            Fig. 1.5  Transistor replaced by its Hybrid Model

Current Gain or Current Amplification (A_i)

For transistor amplifier, the current gain A_i is defined as the ratio of output current to input current,i.e,

A_i =I_L /I₁ = -I₂ / I₁

From the circuit of Fig 1.5

I₂= h_f I₁ + h_oV₂

Substituting V₂ = I_LZ_L =  -I₂Z_L

            I₂= h_f I₁- I₂Z_L h_o

            I₂ + I₂Z_L h_o = h_f I₁    

 
               I₂( 1+ Z_L h_o) = h_f I₁

                A_i =  -I₂ / I₁ = - h_f / ( 1+ Z_L h_o)

            Therefore,

            A_i = - h_f / ( 1+ Z_L h_o)

Input Impedance (Z_i)

In the circuit of Fig 1.5, R_S is the signal source resistance .The impedance seen when looking into the amplifier terminals (1,1^’) is the amplifier input impedance  Z_i,

Z_i = V₁/I₁

From the input circuit of Fig   V₁ = h_i I₁ + h_rV₂

Z_i = ( h_i I₁ + h_rV₂) / I₁

     = h_i + h_r V₂ / I₁

Substituting

V₂ = -I₂ Z_L = A₁I₁Z_L

 Z_i = h_i + h_r A₁I₁Z_L / I₁

     = h_i + h_r A₁Z_L

Substituting for A_i

Z_i = h_i - h_f h_r Z_L / (1+ h_oZ_L)

    = h_i - h_f h_r Z_L / Z_L(1/Z_L+ h_o)

Taking the Load admittance as Y_L =1/ Z_L

Z_i  = h_i - h_f h_r  / (Y_L + h_o)
 

Voltage Gain or Voltage Gain Amplification Factor(A_v)

The ratio of output voltage V₂ to input voltage V₁ give the voltage gain of the transistor i.e,

A_v = V₂ / V₁

Substituting

            V₂ = -I₂ Z_L = A₁I₁Z_L

            A_v = A₁I₁Z_L / V₁ =  A_iZ_L / Z_i

Output Admittance (Y_o)

Y_o is obtained by setting V_S to zero, Z_L to infinity and by driving the output terminals from a generator V_2. If the current is I₂ then Y_o= I₂/V₂ with V_S=0 and R_L= ∞.

From the circuit of fig 1.5

I₂= h_f I₁ + h_oV₂

Dividing by V_2,

I₂ / V₂ = h_f I₁/V₂ + h_o

With V₂= 0, by KVL in input circuit,

R_SI₁ + h_i I₁ + h_rV₂ = 0

(R_S + h_i) I₁ + h_rV₂ = 0

Hence,     I₂ / V₂ = -h_r / (R_S + h_i)

                            = h_f (-h_r/( R_S + h_i)+h_o

Y_o= h_o- h_f h_r/( R_S + h_i)

The output admittance is a function of source resistance. If the source impedance is resistive then Y_o is real.

Voltage Amplification Factor(A_vs) is taking into account the resistance (R_s) of the source.

Fig. 5.6 Thevenin’s Equivalent Input Circuit

This overall voltage gain A_vs is given by

            A_vs = V₂ / V_S = V₂V₁ / V₁V_S = A_v V₁/ V_S

From the equivalent input circuit using Thevenin’s equivalent for the source shown in Fig. 5.6,

V₁ = V_S Z_i / (Z_{i +} R_S)

V₁ / V_S = Z_i / ( Z_i + R_S)

Then,               A_vs =  A_v Z_i / ( Z_i + R_S)

Substituting     A_v = A_iZ_L / Z_i

                        A_vs =  A_iZ_L / ( Z_i + R_S)

                        A_vs = A_iZ_L R_S / ( Z_i + R_S) R_S

                        A_vs = A_isZ_L /  R_S

Current Amplification (A_is) taking into account the source Resistance(R_S)

Fig. 1.7  Norton’s Equivalent Input Circuit

The modified input circuit using Norton’s equivalent circuit for the calculation of A_is is shown in Fig. 1.7

Overall Current Gain, A_is = -I₂ / I_S = - I₂I₁ /I₁ I_S = A_i I₁/I_S

From Fig. 1.7                          I₁= I_S R_S / (R_S + Z_i)

                                    I₁ / I_S = R_S / (R_S + Z_i)

and hence,                   A_is = A_i R_S / (R_S + Z_i)

Operating Power Gain (A_P)

The operating power gain A_P of the transistor is defined as

A_P = P₂ / P₁ = -V₂ I₂ / V₁ I₁ = A_vA_i = A_i A_iZ_L/ Z_i

A_P = A_i²(Z_L/ Z_i)

Small Signal analysis of a transistor amplifier

Simplified common emitter hybrid model:

In most practical cases it is appropriate to obtain approximate values of A _V , A _i etc rather than calculating exact values. How the circuit can be modified without greatly reducing the accuracy. Fig. 4 shows the CE amplifier equivalent circuit in terms of h-parameters Since 1 / h_oe in parallel with R_L is approximately equal to R_L if 1 / h_oe >> R_L then h_oe may be neglected. Under these conditions,

I_c = h_fe I_B .

h_re V_c = h_re I_c R_L = h_re h_fe I_b R_L .
 

                                                                Fig. 4

Since h_fe.h_re = 0.01(approximately), this voltage may be neglected in comparison with h_ie I_b drop across h_ie provided R_L is not very large. If load resistance R_L is small than h_oe and h_re can be neglected.
 

Output impedance seems to be infinite. When V_s = 0, and an external voltage is applied at the output we find I_b = 0, I _C = 0. True value depends upon R_S and lies between 40 K and 80K.

On the same lines, the calculations for CC and CB can be done.

CE amplifier with an emitter resistor:

The voltage gain of a CE stage depends upon h_fe. This transistor parameter depends upon temperature, ageing and the operating point. Moreover, h_fe may vary widely from device to device, even for same type of transistor. To stabilize voltage gain A_V of each stage, it should be independent of h_fe. A simple and effective way is to connect an emitter resistor R_e as shown in fig. 5. The resistor provides negative feedback and provide stabilization.
                   

An approximate analysis of the circuit can be made using the simplified model

Subject to above approximation A _V is completely stable. The output resistance is infinite for the approximate model

 Comparison of Transistor Amplifier Configuration

The characteristics of three configurations are summarized in Table. Here the quantities A_i, A_v, R_i, R_o and A_P are calculated for a typical transistor whose h-parameters are given in table .The values of R_L and R_s are taken as 3KΩ.

Table: Performance schedule of three transistor configurations.
 

The values of current gain, voltage gain, input impedance and output impedance calculated as a function of load and source impedances.

Characteristics of Common Base Amplifier

1. Current gain is less than unity and its magnitude decreases with the increase of load resistance R_L,
2. Voltage gain A_V is high for normal values of R_L,
3.  The input resistance R_i is the lowest of all the three configurations, and
4.  The output resistance R_o is the highest of all the three configurations.

Applications: The CB amplifier is not commonly used for amplification purpose. It is used for

1. Matching a very low impedance source
2. As a non inverting amplifier to voltage gain exceeding unity.
3.  For driving a high impedance load.
4. As a constant current source.

 Characteristics of Common Collector Amplifier

1. For low R_L (< 10 kΩ), the current gain A_i is high and almost equal to that of a CE amplifier.
2. The voltage gain A_V  is less than unity.
3.  The input resistance is the highest of all the three configurations.
4. The output resistance is the lowest of all the three configurations.

Applications: The CC amplifier is widely used as a buffer stage between a high impedance source and a low impedance load.

Characteristics of Common Emitter Amplifier

1. The current gain A_i is high for R_L < 10 kΩ.
2. The voltage gain is high for normal values of load resistance R_L.
3.  The input resistance R_i is medium.
4. The output resistance R_o is moderately high.

Applications: CE amplifier is widely used for amplification.