Midband analysis of BJT Single Stage Amplifiers

Midband analysis of BJT Single Stage Amplifiers:

Consider the basic amplifier circuit. To form a transistor amplifier only is is necessary to connect an external load and signal source along with proper biasing.

We can replace the transistor circuit as shown in the following figure.

Let us analyze the hybrid model to find current gain, input resistance, voltage gain and output resistance.

Current gain (A_i):

It is defined as the ratio of output to input current. It is given by,

Here I_L and I₂ are equal in magnitude but opposite in sign. I_L = -I₂

From above circuit

Current gain (AIS):  

It is given by, 

From above figure, using current divider rule, 

Input Impedance (Z_i):

R_i is the input resistance looking into the amplifier input terminals ( 1, 1’). It is given by,

From the input circuit,

Substituting V₂ = -I₂R_L = A_i I₁ R_L in the above equation,

Dividing numerator and denominator by R_L we get,

From this equation, note that the input impedance is a function offload impedance.

Voltage gain (A_v):

It is the ratio of output voltage to input voltage. It is given by,

By substituting V₂ = -I₂R_L = A_i I₁ R_L

Voltage gain (A_vs):

It is voltage gain including the source. It is given by,

From above figure, applying potential divider rule, then we get,

Substituting the value of V₁/V_s in the equation of

Output Admittance (Y_o):

It is the ratio of output current to output voltage. It is given by,

Dividing above equation by V₂, We get,

From transistor amplifier in h-parameter model circuit, with V_s = 0,

R_sI₁ + h_iI₁ +h_rV₂ = 0 

(R_s + h_i) I ₁ = -h_r V₂

Substituting the value of I₁/V₂ from above equation in the equation of Y_o. We obtain,

From this equation, note that the output admittance is a function of source resistance.

Power gain (Ap):

It is the ratio of average power delivered to the load to the input power. Output power is given as,

Since the input power is P₁ = V₁I₁

The operating power gain A_p of the transistor is given as,

Relation between A_vs and A_IS

From equation,

Taking ratio of above two equations we get,

Method for analysis of a transistor circuit:

The analysis of transistor circuits for small signal behaviour can be made by following simple guidelines. These guidelines are,

1.     Draw the actual circuit diagram

2.     Replace coupling capacitors and emitter bypass capacitor by short circuit

3.     Replace D.C. source by a short circuit

4.     Mark the points B, E, C on the circuit diagram and locate these points as the start of the equivalent circuit

5.     Replace the transistor by its h-parameter model

Problem 1:

For the common base circuit shown in figure, transistor parameters are h_ib = 22Ω,

h_fb = -0.98, h_ob = 0.49µA/V, h_rb = 2.9*10 ^-4. Calculate the values of input resistance, output resistance, current gain and voltage gain for the given circuit.

Solution:

Change the given figure into h-parameter equivalent model.

R_o' = R_o || R_L’ = 1.21M || 5.45K = 5.425KΩ

Problem 2:

Consider a single stage CE amplifier with Rs = 1KΩ, RL = 1.2KΩ. Calculate A_i, R_i,  A_v, A_is, power gain and R_o if hie = 1.1k, h_re = 2.5*10^-4, h_fe = 50 and h_oe = 25µA/V.

Solution:

Problem 3:

Consider a single stage CE amplifier with R_s = 1k, R₁ = 50k, R₂ = 2k, R_c = 2k, R_L =  2K, h_ie = 1.1k, h_oe = 25µA/V, h_fe = 50 and hre = 2.5*10^-4 as shown in the figure.

Find A_i, R_i, A_v, A_i, A_vs and R_o.

Solution:

Since h_oe R_L' = 25*10-6*(2K || 2K) = 0.25, which is less than 0.1, so use approximate analysis.

Consider the simplified hybrid model for the given circuit.

Comparison of Transistor Configurations: