Important Solved Problems of Multistage Amplifiers and Differential Amplifier

SOLVED PROBLEMS

Problem 3.4

An amplifier has the voltage gains of A_V1 = 10, A_V2 = 20 and A_V3 = 40. Find the overall voltage gain.

Given:

A_V1 = 10,

A_V2 = 20,

A_V3 = 40

To Find:

Overall voltage gain

Solution:

Overall voltage gain A_V = A_V1 . A_V2 . A_V3 = 10 . 20 . 40

A_V = 8000

To find voltage gain in dB = 20 log10 8000 = 78 dB

Another Method:

Voltage gain of stage 1, G_V1 = 20 log₁₀ A_V1 = 10 log₁₀ 10 = 20 dB

Voltage gain of stage 2, G_V2 = 20 log₁₀ A_V2 = 20 log₁₀ 20 = 26 dB

Voltage gain of stage 3, G_V3 = 20 log₁₀ A_V3 = 20 log₁₀ 40 = 32 dB

Total dB voltage gain, G_V = G_V1 + G_V2 + G_V3 = 20 + 26 + 32 = 78 dB

Problem 3.5

Three amplifier stages are connected in cascade with 0.05 V peak-to-peak input providing 150 V peak-to peak output. If the voltage gain of the first stage is 20 and input to the third stage is 15 V peak to peak, determine

(a) The overall voltage gain

(b) Voltage gain of second and third stages

(c) Input voltage of second stage

Given:

No of stages = 3

Input to the first stage V_in1 = 0.05 V_P-P

Output of third stage V_out3 = 150 V_P-P

Voltage gain of first stage A_V1 = 20

Input to third stage V_in3 = 15 V_P-P

To find:

(a) Overall voltage gain

(b) Voltage gain of second and third stage

(c) Input voltage of second stage

Solution:

(a) Overall Voltage Gain

(b) Voltage gain of second and third stage

Let us find voltage gain of third stage

Overall voltage gain = 3000

i.e., A_V1 A_V2 A_V3 = 3000

20. A_V2. 10 = 3000

A_V2 = 3000/200

A_V2 = 15

(c) Input voltage of second stage

We know that voltage gain of second stage A_V2 = 15

Problem 3.6

Calculate the bandwidth between the half-power points of circuit which resonates at 1 MHz and has a Q of 100.

Given:

f_O = 1 MHz,

Q_O = 100

To Find:

Bandwidth

Solution:

Problem 3.7

A tuned amplifier has maximum gain at a frequency of 2 MHz and bandwidth of 50 KHz. Calculate the Q-factor.

Given:

f_O = 2 MHz

BW = 50 KHz

To Find:

Q-Factor

Solution:

We know that

Problem 3.8

A circuit is resonant at 455 KHz and has 10 KHz bandwidth. The inductive reactance is 1255 Ω. What is the parallel impedance of the circuit at resonance?

Given:

f_O = 455 KHz = 455 × 10₃ Hz

BW = 10 KHz = 10 ×10₃ Hz

X_L = 1255 Ω

To Find:

Impedance at resonance, Z

Solution:

We know that

 

Problem 3.9

A certain power transistor meant for class A operation has zero signal power dissipation of 20 W. If the ac output power is 5 W. Find (a) collector efficiency (b) power rating of the transistor.

Given:

P_d.c = 20 W

P_O = 5 W

To Find:

(a) Collector efficiency

(b) Power rating of transistor

Solution:

(a) Collector Efficiency

(b) Power rating of Transistor

Zero signal condition implies the maximum power dissipation of the transistor.

Power rating of transistor = 20 W

Problem 3.10

An amplifier has a collector efficiency of 50% and operates from a 24 V supply. If the output power is 3.5 V, find the total power dissipated within the circuit.

Given:

V_CC = 24 V

P_O(ac) = 3.5 W

To Find:

Power dissipation P_c(dc)

Solution:

We know that

Efficiency = P_O(ac)/P_(dc)

Power of 3.5 W is dissipated in the form of heat.

Problem 3.11

A multistage amplifier has five stages each with a power gain of 30. What is the total gain of the amplifier in dB? If negative feedback of 20 dB is applied find the resultant gain.

Given:

Number of stages = 5

Gain of each stage = 30

To Find:

(i) Total power gain

(ii) Gain with 20 dB negative feedback

Solution:

(i) Total Power Gain

Power gain of one stage = 10 log ₁₀ 30

= 10 x 1.477.

= 14.77 dB

Total power gain = No. of stages x power gain of each stage

= 5 x 14.77

Total power gain = 73.85 dB

(ii) Power gain with negative feedback = total power gain - feedback gain

= 73.85 - 20

Power gain with negative feedback = 53.85 dB

 

Problem 3.12

An amplifier has a voltage gain of 15 dB. If the input signal voltage is 0.8 V, find the output voltage.

Given:

Voltage gain = 15 dB

Input voltage, V_in = 0.8 V

To Find:

Output voltage, V_out

Solution:

Problem 3.13

A tank circuit has a capacitor of 100 PF and an inductor of 100 µH. The resistance of the inductor is 5 2. Determine (a) resonant frequency (b) impedance at resonance (c) Q factor (d) bandwidth.

Given:

L = 100 μH

C = 100 PF

R = 52 Ω

To find:

(a) Resonant frequency

(b) Impedance at resonance

(c) Q-factor

(d) Bandwidth

Solution:

(a) Resonant Frequency

(b) Impedance at Resonance

(c) Q-Factor

(d) Bandwidth

Problem 3.14

A circuit has a coil of inductance 120 μH and resistance of 15.7 Ω, which is connected in series with a capacitor of 211 PF. determine a) resonant frequency b) voltage drop across R, L, C c) Quality factor.

Given:

L = 120 H

C = 211 PF

R = 15.72 Ω

To Find:

(a) Resonant frequency

(b) Voltage drop across R, L, C

(c) Quality factor

Solution:

(a) Resonant Frequency

(b) Voltage across R, L, C

(c) Quality Factor