Small Signal Amplifier Performance In terms of h-parameters

Small Signal Amplifier Performance In terms of h-parameters

AU : May-03, 05, 09, 15, 16, Dec.-05, 06, 14, 16

• The Fig. 6.4.1 shows basic amplifier circuit. It represents a transistor in any one of the three possible configurations.

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

Step 1 : Draw the hybrid equivalent circuit

• The Fig. 6.4.2 shows hybrid equivalent circuit for the amplifier circuit. It is obtained by replacing the transistor by its h-parameter model.

Step 2 : Obtain expression for current gain (A_I )

• For transistor amplifier, A_I is defined as the ratio of output to input currents. It is given by,

A_I = I_L / I₁ = - I₂ / I₁ ...(6.4.1)

• Here IL and I2 are equal in magnitude but opposite in sign, i.e. I_L= - I₂

• From the circuit of Fig. 6.4.2 We have,

I₂ = h_f I₁  + h_o V₂  … (6.4.2)

• Substituting V₂ = - I₂ R_L in Equation (6.4.2) we obtain,

Current Gain (A_Is ) :

• It is the current gain taking into account the source resistance, R s if the model is driven by the current source instead of voltage source. It is given by

• Looking at Fig. 6.4.3 (b) and using current divider equation we get

Step 3 : Obtain expression for input resistance (R_i)

• As shown in the Fig. 6.4.1, Ri is the input resistance looking into the amplifier input terminals (1, 1'). It is given by,

R_i = V₁ / I₁   ... (6.4.6)

• From the input circuit of Fig. 6.4.2, we have

• Dividing numerator and denominator by R_L we get

Important Concept

From this equation we can note that input impedance is a function of the load impedance.

Step 4 : Obtain expression for voltage gain (A_V)

• It is the ratio of output voltage V₂ to the input voltage V₁ It is given by

A_V = V₂ / V₁ … (6.4.1)

From equation (6.4.9) we have,

Voltage Gain (A_vs) : It is voltage gain including the source. It is given by,

Looking at Fig. 6.4.4 and applying potential divider theorem we can write,

• Substituting value of V₁ / V_s in equation (6.4.16) We get,

Step 5 : Obtain expression for output admittance (Y_o)

• It is the ratio of output current I₂ to the output voltage V₂. It is given by,

Y_o = I₂ / V₂ with V_s = 0 ... (6.4.19)

• From equation (6.4.2), we have,

I₂ = h_f I₁ + h_o V₂ … (6.4.19)

• Dividing above equation by V₂ we get,

• Applying KVL to the input loop of Fig. 6.4.2 we have,

• Substituting value of from equation (6.4.22) in equation (6.4.20), we obtain,

Important Concept

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

Step 6 : Obtain expression for power gain (A_P)

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

P₂ = V₂ I_L = -V₂I₂  ... (6.4.24)

• Since the input power is p = V₁I₁ the operating power gain A_P of the transistor is defined as

Relation between A_Vs and A_Is :

• From equations (6.4.18) and equation (6.4.5) we have

• Taking ratio of above two equations we get,

• Table 6.4.1 summarizes small-signal analysis of a transistor amplifier

Important Concept

The above formulae is applicable to all transistor configuration. Only we have added the appropriate subscript to h-parameters corresponding to the transistor configuration in the expression of A_I,A_v,R_i    Y_o

• Table 6.4.2 shows the typical values of h parameters for three different configurations at normal room temperature and at quiescent operating point IEQ = 7.3 mA

Ex. 6.4.1 Derive the expressions for A_I, A_V, R_i and R_o for CE amplifier using h-parameter model.

AU : Dec.-14, 16, May-15, Marks 16

Sol. : The Fig. 6.4.5 shows the CE amplifier and its h-parameter equivalent circuit.

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

Step 1 : Obtain expression for current gain (A_I )

Current gain (A_I) =        I_L / I_b = I_c / I_b  ... (1)

From the circuit of Fig. 6.4.5 (b) we have,

Step 2 : Obtain expression for input resistance (R_i)

Input resistance (R_i) = V_b / I_b … (4)

From the input circuit of Fig. 6.4.5 (b) we have,

Step 3 : Obtain expression for voltage gain (A_V )

Voltage gain (A_V ) =

Step 4 : Obtain expression for output admittance (Y_o)

Output admittance (Y_o) = I_c / V_c with V_s = 0  … (8)

From equation (6.4.2), we have,

I_c = h_fe I_b + h_oe V_c

Dividing above equation by V_c we get,

Y_o = I_c / V_c = h_fe I_b  / V_c + h_oe     

From Fig. 6.4.5 (b), with V_s = 0 we can write,

Substituting value of I_b / V_c from equation (10) in equation (9), we obtain,

 

Ex. 6.4.2 Consider a single stage CE amplifier with Rs = 1 K and RL = 1.2 k Ω. Calculate Ai, Ri, Av, AIs, power gain and Ro if hie = 1.1 K, hre = 2.5 × 10-4, hfe = 50 and hoe = 25 µA/V.

Sol.

 

Ex. 6.4.3 Derive the expressions for current gain, voltage gain, input impedance and output impedance for an emitter follower circuit.

AU : ECE : May-03,05,09, Marks 10; Dec.-06

Sol. : The Fig. 6.4.6 shows the emitter follower (CC) amplifier circuit and its h-parameter equivalent circuit.

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

Current Gain (A_i) = I_L / I_b = - I_e / I_b ... (1)

From the circuit of Fig. 6.4.6 (b) we have,

From the input circuit of Fig. 6.4.6 (b), we have,

Substituting value of I_b / V_e from equation (11) in equation (10), we obtain,

 

Ex. 6.4.4 In the common collector in Fig. 6.4.7, the transistor parameters are hfc = 1.2 K, h_fc = -101, h_rc = 1 and hoc = 25 µA/V. Calculate the , Ri, A_I = I_L / I_s, A_D, A_GS = Vo / Vs , Ro for the circuit.

Sol. : Fig. 6.4.7 shows the h-parameters equivalent model for the given circuit,

a) Current gain

 

Ex. 6.4.5 Derive the expressions for A^, Ay, Rt and Ro for CB amplifier using h-parameter model.

AU : ECE : Dec.-05, May-16, Marks 8

Sol. : The Fig. 6.4.8 shows the CB amplifier and its h-parameter equivalent circuit

From the circuit of Fig. 6.4.8 (b) we have,

From the input circuit of Fig. 6.4.8 (b) we have

 

Ex. 6.4.6 For the common base circuit in Fig. 6.4.9, the transistor parameters are hib =22 Ω, hfc =- 0.98, hob = 0.49 µA/V, hrb = 2.9 × 10-4. Calculate the values of the input resistance, output resistance, current gain and voltage gain for the given circuit.

Sol. : Fig. 6.4.9 (a) shows the h-parameter equivalent model for the given circuit.

Review Question

1. Derive the expressions for the current gain, input impedance, voltage gain and output admittance of a small signal CE transistor amplifier in terms of the h-parameters.