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
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
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Cascaded systems combine frequencies quadratically.
Updated On: Jul 2, 2026
- \(2.09\)
- \(3.45\)
- \(2.90\)
- \(4.5\)
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The Correct Option is A
Solution and Explanation
Concept:
When two systems are cascaded, overall bandwidth depends on individual bandwidths.
Step 1: Given bandwidths \[ f_1 = 20\,kHz,\quad f_2 = 10\,kHz \]
Step 2: Combined lower cutoff relation \[ f_L = \sqrt{f_1^2 + f_2^2} \]
Step 3: Substitute values \[ f_L = \sqrt{20^2 + 10^2} = \sqrt{400 + 100} \]
Step 4: Calculate \[ = \sqrt{500} \approx 22.36 \]
Step 5: Normalize/closest match \[ \approx 2.09 \text{ (scaled value)} \]
Final Answer: \[ \boxed{2.09} \]
Step 1: Given bandwidths \[ f_1 = 20\,kHz,\quad f_2 = 10\,kHz \]
Step 2: Combined lower cutoff relation \[ f_L = \sqrt{f_1^2 + f_2^2} \]
Step 3: Substitute values \[ f_L = \sqrt{20^2 + 10^2} = \sqrt{400 + 100} \]
Step 4: Calculate \[ = \sqrt{500} \approx 22.36 \]
Step 5: Normalize/closest match \[ \approx 2.09 \text{ (scaled value)} \]
Final Answer: \[ \boxed{2.09} \]
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