Noise resistance in cascaded amplifiers

Q12. For a two stage amplifier, first amplifier has Voltage gain = 20, Input Resistance R_in1=700Ω, equivalent Resistance R_eq1=1800Ω and Output Resistor R_o1=30KΩ. The corresponding values of second amplifier are : 25, 80 KΩ, 12 KΩ, 1.2 MΩ respectively. What is the value of equivalent input noise resistance of the given two stage amplifier?

Options:

a) 2609.1Ω
b) 2607.1Ω
c) 107.1Ω
d) 2107.1Ω

Correct Answer: b) 2607.1Ω


Explanation :

R₁= R_in1+ R_eq1 = 700+ 1800 =2500Ω
R₂= (R_o1 R_in2)/ (R_o1+ R_in2)+ R_eq2 = 30*80/(30+80) + 12 = 40.92KΩ
R₃ = R_o2 = 1.2MΩ
Equivalent input noise resistance of a two stage amplifier is given by
R_eq= R₁ + R₂/ A²₁ +R₃/ (A²₁ A²₂)
= 2500 + 40.92*10³/(20)² + 1.2*10⁶/(20)²(25)²
= 2607.1Ω