Also known as: resonant frequency, tuned circuit, tank circuit
Resonance is the condition at which a system stores and exchanges energy most readily at a particular frequency, so a small periodic drive produces a large response.1 In an electrical LC circuit it occurs where the inductive and capacitive reactances become equal and cancel, leaving a purely resistive impedance, at the resonant frequency f₀ = 1/(2π√(LC)). Resonance is the mechanism behind tuning a radio, the sharpness of a filter, and the operation of an antenna, and its selectivity is quantified by the Q factor.
How it works
An inductor’s reactance rises with frequency (XL = 2πfL) while a capacitor’s falls (XC = 1/(2πfC)). At one frequency these are equal in magnitude and, because they have opposite sign, they cancel. That crossover is resonance, and setting XL = XC and solving gives f₀ = 1/(2π√(LC)). At that point the reactive parts of the impedance vanish and the circuit looks purely resistive, so voltage and current fall back into phase and the system exchanges energy most efficiently with its drive.
The two canonical topologies behave as mirror images:
- Series resonance — L and C in series present minimum impedance at f₀, so a series-resonant branch passes the resonant frequency and blocks others. Used to short unwanted frequencies to ground or to pass a wanted one.
- Parallel resonance (a “tank”) — L and C in parallel present maximum impedance at f₀, so a tank develops a large voltage there and rejects that frequency from a series path. Used as the frequency-selecting element in oscillators and filters.
Mechanically the same idea appears as a struck bell or a plucked string: energy sloshes between two stores (kinetic and potential, or magnetic and electric) at a natural frequency, and driving it there builds a large amplitude.
In practice
How sharp the resonance is depends on loss, captured by the Q factor: high Q gives a tall, narrow peak that selects one frequency tightly, low Q a broad hump that responds over a wider span. Resonators are realised in many forms with wildly different Q — lumped LC circuits, quartz crystals, coaxial cavities, dielectric pucks, and mechanical/SAW structures — chosen for the stability and bandwidth an application needs. An antenna is itself a resonant structure: a half-wave dipole resonates where its length matches half the signal’s wavelength, which is why antennas are cut for a target band.
Relevance to SDR
Resonance underlies the analog scaffolding around any SDR. Preselector and RF filter stages use resonant elements to pass the wanted band and reject strong out-of-band energy before it can overload the front end, and the local oscillator that the receiver mixes against is stabilised by a high-Q resonant reference. Even the antenna and its matching network are resonant devices tuned to the band of interest. The purity and selectivity these resonators provide set the quality of the samples the SDR digitises.
In GopherTrunk the frequency selection that a physical tuned circuit performs is done downstream in software: the digital channelizer and channel filters isolate the wanted channel from the wideband IQ stream, playing the role a resonant filter plays in analog radios. The analog resonances upstream (in the preselector and reference oscillator) still bound what reaches the ADC, so GopherTrunk depends on good physical resonance even though it does not implement it.