Question

The expression for resonant frequency of the op-amp

(a) fp = 1/[2π×√(LC)].

(b) fp = (2π×√L)/C

(c) fp = 2π×√(LC)

(d) fp = 2π/√(LC)

The question was asked by my school teacher while I was bunking the class.

I'd like to ask this question from Peaking Amplifier topic in portion Operational Amplifier Applications of Linear Integrated Circuits

Answer 1

The correct answer is:

(a) fp=12πLCf_p = \frac{1}{2\pi \sqrt{LC}}fp​=2πLC​1​

Explanation:

The expression for the resonant frequency fpf_pfp​ of a circuit, specifically for an LC circuit (inductor-capacitor), is given by:

fp=12πLCf_p = \frac{1}{2\pi \sqrt{LC}}fp​=2πLC​1​

Where:

• $L$ is the inductance in henries (H),
• $C$ is the capacitance in farads (F),
• fpf_pfp​ is the resonant frequency in hertz (Hz).

This formula applies to a series or parallel LC circuit, which is often used in peaking amplifiers to set the frequency response of the amplifier.

Why not the other options?

• (b) fp=2πLCf_p = \frac{2\pi \sqrt{L}}{C}fp​=C2πL​​: This is incorrect as it doesn't follow the standard resonant frequency formula.
• (c) fp=2πLCf_p = 2\pi \sqrt{LC}fp​=2πLC​: This formula has the wrong dimensions and doesn't correspond to the correct resonant frequency formula.
• (d) fp=2πLCf_p = \frac{2\pi}{\sqrt{LC}}fp​=LC​2π​: This is a misrepresentation of the formula; it incorrectly places the $2\pi$ factor.