Resonant Frequency Calculator

Resonant Frequency (f):

Angular Frequency (ω):

1. What is a Resonant Frequency Calculator?

Definition: This calculator computes the resonant frequency (f) and angular frequency (ω) of an LC circuit, which consists of an inductor (L) and a capacitor (C) in series or parallel.

Purpose: It is used in electronics to determine the natural oscillation frequency of LC circuits, essential for designing filters, oscillators, and radio tuners.

2. How Does the Calculator Work?

The calculator uses the following equations:

\( f = \frac{1}{2\pi \sqrt{LC}} \)
\( \omega = 2\pi f \)

Where:

\( f \) is the resonant frequency (Hz)
\( L \) is the inductance (H)
\( C \) is the capacitance (F)
\( \omega \) is the angular frequency (rad/s)
\( \pi \) is approximately 3.14159

Steps:

Enter capacitance (C) and inductance (L)
Convert inputs to base units (F for capacitance, H for inductance)
Calculate \( f \) and \( \omega \) using the formulas
Display results with appropriate units (Hz/kHz/MHz for f, rad/s/krad/s/Mrad/s for ω)

3. Importance of Resonant Frequency Calculation

The resonant frequency determines the frequency at which an LC circuit oscillates most efficiently, critical for applications like radio receivers, transmitters, and signal processing.

4. Using the Calculator

Examples:

For \( C = 220 \, \text{pF} \), \( L = 1 \, \text{mH} \):
- \( f = \frac{1}{2\pi \sqrt{0.001 \cdot 2.2 \times 10^{-10}}} = 339.32 \, \text{kHz} \)
- \( \omega = 2\pi \cdot 339320 = 2.13185 \, \text{Mrad/s} \)
For \( C = 100 \, \text{nF} \), \( L = 10 \, \text{µH} \):
- \( f = \frac{1}{2\pi \sqrt{10 \times 10^{-6} \cdot 100 \times 10^{-9}}} = 159.15 \, \text{kHz} \)
- \( \omega = 2\pi \cdot 159150 = 999.03 \, \text{krad/s} \)

5. Frequently Asked Questions (FAQ)

Q: What is an LC circuit?
A: An LC circuit is a resonant circuit with an inductor (L) and capacitor (C), used to generate or select specific frequencies.

Q: What is the difference between f and ω?
A: \( f \) is the frequency in cycles per second (Hz), while \( \omega \) is the angular frequency in radians per second (rad/s), related by \( \omega = 2\pi f \).

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