Resonant Frequency
Understanding Resonant Frequency
Resonance is one of the most important phenomena in RF engineering. Every filter, oscillator, antenna, and resonator operates at or near resonance. Understanding and controlling resonant frequency is fundamental to RF circuit design.
Resonance Conditions
- Series resonance: Impedance is minimum (= R, the loss resistance). Current is maximum. Series RLC circuits become short circuits at resonance.
- Parallel resonance: Impedance is maximum. Current is minimum. Parallel RLC circuits become open circuits at resonance.
- Quarter-wave resonance: Transmission line stub resonates at odd multiples of lambda/4.
f0 = 1 / (2 pi sqrt(L C))
Examples:
L=10nH, C=1pF: f0 = 1.59 GHz
L=1nH, C=1pF: f0 = 5.03 GHz
L=0.5nH, C=0.5pF: f0 = 10.07 GHz
Frequently Asked Questions
What is resonant frequency?
Resonant frequency is where a circuit stores equal electric and magnetic energy, producing purely resistive impedance. For LC: f0 = 1/(2*pi*sqrt(LC)). At resonance, energy oscillates between L and C. Every filter, oscillator, and antenna uses resonance.
What determines antenna resonance?
An antenna resonates when its physical length is a multiple of half a wavelength (for dipoles) or quarter wavelength (for monopoles). At resonance, the input impedance is purely resistive, making matching to the feed line easiest.
What is the relationship between resonance and Q?
Q (quality factor) describes how sharp the resonance is. Higher Q = sharper peak, narrower bandwidth. BW = f0/Q. A Q of 100 at 10 GHz gives a 100 MHz bandwidth. Resonance frequency sets the center; Q sets the width.