What is the frequency response of the circuit in E7-3 if a capacitor is added across the feedback resistor?
The correct answer is B: Low-pass filter. When a capacitor is added across the feedback resistor in an op-amp circuit (like the inverting amplifier in Figure E7-3), the circuit becomes a low-pass filter. The capacitor provides frequency-dependent feedback that reduces gain at higher frequencies.
At low frequencies, the capacitor has high reactance and doesn't significantly affect the circuit, so the gain is determined by the resistor ratio (RF/R1). At high frequencies, the capacitor's reactance decreases, shunting the feedback resistor and reducing the gain. This creates a low-pass response - low frequencies pass through with full gain, while high frequencies are attenuated. The cutoff frequency depends on the capacitor value and feedback resistor value.
Exam Tip
Capacitor across feedback = Low-pass filter. Remember: Adding a capacitor across the feedback resistor in an op-amp creates a low-pass filter that attenuates high frequencies.
Memory Aid
"**C**apacitor **A**cross **F**eedback = **L**ow-**P**ass (think 'CAF = LP' = Capacitor Across Feedback = Low-Pass)"
Real-World Application
You're building an audio amplifier and want to filter out high-frequency noise above 3 kHz. You add a capacitor across the feedback resistor in your op-amp circuit. The capacitor creates a low-pass filter that passes audio frequencies below 3 kHz with full gain, while attenuating frequencies above 3 kHz. This reduces high-frequency noise and interference in your audio signal.
FCC Part 97.3Key Concepts
Why Other Options Are Wrong
Option A: Incorrect. A high-pass filter would require the capacitor in a different position (typically in series with the input, not across the feedback resistor).
Option C: Incorrect. A band-pass filter requires both high-pass and low-pass characteristics, typically requiring more components than just a capacitor across the feedback resistor.
Option D: Incorrect. A notch filter (band-reject) requires a more complex circuit, typically with both capacitors and inductors or multiple op-amps.
题目解析
The correct answer is B: Low-pass filter. When a capacitor is added across the feedback resistor in an op-amp circuit (like the inverting amplifier in Figure E7-3), the circuit becomes a low-pass filter. The capacitor provides frequency-dependent feedback that reduces gain at higher frequencies. At low frequencies, the capacitor has high reactance and doesn't significantly affect the circuit, so the gain is determined by the resistor ratio (RF/R1). At high frequencies, the capacitor's reactance decreases, shunting the feedback resistor and reducing the gain. This creates a low-pass response - low frequencies pass through with full gain, while high frequencies are attenuated. The cutoff frequency depends on the capacitor value and feedback resistor value.
考试技巧
Capacitor across feedback = Low-pass filter. Remember: Adding a capacitor across the feedback resistor in an op-amp creates a low-pass filter that attenuates high frequencies.
记忆口诀
**C**apacitor **A**cross **F**eedback = **L**ow-**P**ass (think 'CAF = LP' = Capacitor Across Feedback = Low-Pass)
实际应用示例
You're building an audio amplifier and want to filter out high-frequency noise above 3 kHz. You add a capacitor across the feedback resistor in your op-amp circuit. The capacitor creates a low-pass filter that passes audio frequencies below 3 kHz with full gain, while attenuating frequencies above 3 kHz. This reduces high-frequency noise and interference in your audio signal.
错误选项分析
Option A: Incorrect. A high-pass filter would require the capacitor in a different position (typically in series with the input, not across the feedback resistor). Option C: Incorrect. A band-pass filter requires both high-pass and low-pass characteristics, typically requiring more components than just a capacitor across the feedback resistor. Option D: Incorrect. A notch filter (band-reject) requires a more complex circuit, typically with both capacitors and inductors or multiple op-amps.
知识点
Low-pass filter, Op-amp filter, Capacitor feedback, Frequency response
Verified Content
Question from official FCC Extra Class question pool. Explanation reviewed by licensed amateur radio operators.