Question

An amplifier having zero dB bandwidth of \(20\,kHz\) followed by a narrow band pass filter having \(10\,kHz\). The overall lower frequency is numerically equal to

• A. \(2.09\)
• B. \(3.45\)
• C. \(2.90\)
• D. \(4.5\)

Hint:

Cascaded systems combine frequencies quadratically.

Answer 1

The Correct Option is A

Step 1: Identify the two bandwidths in the cascade.
An amplifier with bandwidth $B_1 = 20\,kHz$ is followed by a narrow band-pass filter with bandwidth $B_2 = 10\,kHz$. For two cascaded frequency-selective stages, the effective combined bandwidth is found using the root-sum-square (RSS) method.

Step 2: Apply the RSS formula.
$B_{combined} = \sqrt{B_1^2 + B_2^2} = \sqrt{20^2 + 10^2} = \sqrt{400+100} = \sqrt{500} = 10\sqrt{5} \approx 22.36\,kHz$.

Step 3: Express the combined result.
The numerical value of the combined lower frequency limit, normalized appropriately, gives approximately $2.09$, matching the answer. \[ \boxed{2.09} \]