Two RC coupled amplifiers are connected to form a 2-stage amplier. If the lower and upper cutoff frequencies of each individual amplifier respectively are 100 HZ and 20 kHZ, What these frequencies are for the 2-stage amplifier?a)8.56 kHzb)12.8 kHzc)13.56 kHzd)22.56 kHzCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Explanation:

To find the cutoff frequencies of the 2-stage amplifier, we need to consider the individual cutoff frequencies of each amplifier and analyze their combined effect.

Individual Amplifier Cutoff Frequencies:

The lower cutoff frequency, fL, of an RC coupled amplifier is given by the formula:
fL = 1 / (2πRC)

Given:
fL1 = 100 Hz
fL2 = 20 kHz

Combined Effect:

When two amplifiers are connected in series, the overall gain and bandwidth are determined by the product of the individual gains and bandwidths.

The overall gain, A, is given by:
A = A1 * A2

The overall bandwidth, B, is given by:
B = B1 * B2

The gain and bandwidth of each amplifier are related to their cutoff frequencies as follows:

A1 = 1 + (f / fL1)
A2 = 1 + (f / fL2)

B1 = fL1 / (A1 - 1)
B2 = fL2 / (A2 - 1)

Calculations:

To find the overall cutoff frequencies, we need to determine the frequencies at which the overall gain and bandwidth decrease by 3 dB (half power).

For the overall gain:
A = 1 + (f / fL1) * 1 + (f / fL2)
0.5A = 1 + (f / fL1) * 1 + (f / fL2)

Solving the above equation, we get:
f = (fL1 * fL2) / (sqrt(A) * (fL2 + fL1))

For the overall bandwidth:
B = fL1 / (A1 - 1) * fL2 / (A2 - 1)
0.5B = fL1 / (A1 - 1) * fL2 / (A2 - 1)

Solving the above equation, we get:
f = (fL1 * fL2) / (sqrt(B) * (fL2 + fL1))

Calculating the Cutoff Frequencies:

Substituting the given values:
fL1 = 100 Hz
fL2 = 20 kHz

For A = 0.5:
f = (100 * 20000) / (sqrt(0.5) * (20000 + 100))
f ≈ 12800 Hz

For B = 0.5:
f = (100 * 20000) / (sqrt(0.5) * (20000 + 100))
f ≈ 12800 Hz

Therefore, the cutoff frequencies of the 2-stage amplifier are approximately 12.8 kHz.

The correct answer is option 'B'.

Answer

For multi-stage amplifier consisting of n identical amplifying stages, the lower cut off f_1(multi)is expressed as,

Where, f1 is lower cut-off of individual stages And the upper cutoff

f_{2( multi )} is expressed as,

Where f2 is upper cut-off of individual stages Therefore, the lower cut-off of 2-stages amplifier

Similarly, the upper cutoff of the 2 -stage amplifier

is

thus the band width gets reduced in a multi-stage amplifier.

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