# Solved Problems on Multistage Transistor Amplifiers

### Q1. Find the gain in db in the following cases : (i) Voltage gain of 30 (ii) Power gain of 100.

### Solution :

(i) Voltage gain = 20 log_{10 }30 db = 29.54 db

(ii) Power gain = 10 log_{10} 100 db = 20 db

### Q2. Express the following gains as a number : (i) Power gain of 40 db (ii) Power gain of 43 db.

### Solution :

(i) Power gain = 40 db = 4 bel

If we want to find the gain as a number, we should work from logarithm back to the original number.(ii) Power gain = 43 db = 4.3 bel

### Q3. A three-stage amplifier has a first stage voltage gain of 100, second stage voltage gain of 200 and third stage voltage gain of 400. Find the total voltage gain in db .

### Solution :

First-stage voltage gain in db = 20 log_{10} 100 = 20 × 2 = 40

Second-stage voltage gain in db = 20 log_{10} 200 = 20 × 2.3 = 46

Third-stage voltage gain in db = 20 log_{10} 400 = 20 × 2.6 = 52

∴ Total voltage gain = 40 + 46 + 52 = 138 db

### Q4. (i) A multistage amplifier employs five stages each of which has a power gain of

30. What is the total gain of the amplifier in db ?

(ii) If a negative feedback of 10 db is employed, find the resultant gain.

### Solution :

Given : Absolute gain of each stage = 30

No. of stages = 5

(i) Power gain of one stage in db = 10 log_{10} 30 = 14.77

∴ Total power gain = 5 × 14.77 = 73.85 db

(ii) Resultant power gain with negative feedback = 73.85 − 10 = 63.85 db

### Q5. In an amplifier, the output power is 1.5 watts at 2 kHz and 0.3 watt at 20 Hz,

while the input power is constant at 10 mW. Calculate by how many decibels gain at 20 Hz is below that at 2 kHz ?

### Solution :

**db power gain at 2 kHz :**

At 2 kHz, the output power is 1.5 W and input power is 10 mW.

**db power gain at 20 Hz:**

At 20Hz, the output power is 0.3 W and input power is 10 mW.

Fall in gain from 2 kHz to 20 Hz = 21.76 − 14.77 = 6.99 db

### Q6. A certain amplifier has voltage gain of 15 db. If the input signal voltage is 0.8V,

what is the output voltage ?

### Solution :

### Q7. An amplifier has an open-circuit voltage gain of 70 db and an output resistance

of 1.5 kΩ. Determine the minimum value of load resistance so that voltage gain is not more than 67db.

### Solution :

### Q8. An amplifier feeding a resistive load of 1kΩ has a voltage gain of 40 db. If the

input signal is 10 mV, find (i) output voltage (ii) load power.

### Solution :

### Q9. An amplifier rated at 40W output is connected to a 10Ω speaker.

(i) Calculate the input power required for full power output if the power gain is 25 db.

(ii) Calculate the input voltage for rated output if the amplifier voltage gain is 40 db.

### Solution :

(i)

(ii)

### Q10. In an amplifier, the maximum voltage gain is 2000 and occurs at 2 kHz. It falls

to 1414 at 10 kHz and 50 Hz. Find : (i) Bandwidth (ii) Lower cut-off frequency (iii) Upper cut-off frequency.

### Solution :

(i) Referring to the frequency response in Fig. 1, the maximum gain is 2000.

Then 70.7% of this gain is 0.707 × 2000 = 1414

It is given that gain is 1414 at 50 Hz and 10 kHz.

As bandwidth is the range of frequency over which gain is equal or greater than 70.7% of maximum gain,

**∴ Bandwidth = 50 Hz to 10 kHz**

(ii) The frequency (on lower side) at which the voltage gain of the amplifier is exactly 70.7% of the maximum gain is known as lower cut-off frequency.

Referring to Fig. 1, it is clear that :

**Lower cut-off frequency = 50 Hz**

(iii) The frequency (on the higher side) at which the voltage gain of the amplifier is exactly 70.7% of the maximum gain is known as upper cut-off frequency.

Referring to Fig. 1, it is clear that:

**Upper cut-off frequency = 10 kHz**

### Q11. A single stage amplifier has a voltage gain of 60. The collector load RC = 500Ω and the input impedance is 1kΩ. Calculate the overall gain when two such stages are cascaded through R-C coupling.

### Solution :

The gain of second stage remains 60 because it has no loading effect of any stage.

However, the gain of first stage is less than 60 due to the loading effect of the input impedance of second stage.

### Q12. Fig. 2 shows two-stage RC coupled amplifier. If the input resistance Rin of each stage is 1kΩ, find : (i) voltage gain of first stage (ii) voltage gain of second stage (iii) total voltage gain.

Fig. 2

### Solution :

### Q13. A single stage amplifier has collector load R_{C} = 10 kΩ; input resistance R_{in} =1kΩ and β = 100. If load R_{L} = 100Ω, find the voltage gain.

### Solution :

Effective collector load, R_{AC} = R_{C} || R_{L} = 10 kΩ || 100 Ω = 100 Ω