Also known as: Z, characteristic impedance, Z0
Impedance is the total opposition a circuit, component, or transmission line presents to an alternating current, written as a complex number Z = R + jX in ohms (Ω).1 The real part R is resistance and the imaginary part X is reactance, which stores and returns energy through capacitance or inductance. In radio, most sources, cables, and antennas are built around a common characteristic impedance of 50 Ω so that power flows between them without reflection.
How it works
For a resistor, opposition is purely real and independent of frequency. Capacitors and inductors add reactance: an inductor’s reactance is X = 2πfL and rises with frequency, while a capacitor’s is X = −1/(2πfC) and falls with frequency. Because these reactances shift the current’s phase relative to the voltage, the combined effect is captured by a complex number whose magnitude gives the amplitude ratio and whose angle gives the phase shift.
A transmission line such as coaxial cable has a characteristic impedance Z0 set by its geometry and dielectric — the ratio of voltage to current for a wave travelling along it. For a lossless line Z0 = √(L/C) from the per-metre inductance and capacitance. Crucially, Z0 is not a resistance you can measure with an ohmmeter; it is the impedance the line looks like to a signal propagating down it.
The reason impedance dominates RF engineering is the matching condition. When a source of impedance Zs drives a load ZL through a line of impedance Z0, maximum power transfers and no energy reflects only when the impedances are equal (for the line, when ZL = Z0). A mismatch sends part of the wave back toward the source, creating standing waves — the subject of the reflection coefficient, return loss, and standing-wave ratio.
In practice
The 50 Ω convention is a historical compromise: coaxial lines carry peak power near 30 Ω and lowest loss near 77 Ω, and 50 Ω sits usefully between them while giving convenient dimensions. Video and broadcast gear instead standardised on 75 Ω. An antenna’s feedpoint impedance rarely lands exactly on 50 Ω across a band, so an antenna tuner or a matching network transforms it back toward the system reference. Matching is done with reactive elements — series or shunt inductors and capacitors, quarter-wave line sections, or transformers — chosen to cancel the load’s reactance and rotate its resistance to the target value. The Smith chart is the classic graphical tool for this, plotting normalised impedance so matching moves become geometric steps.
Relevance to SDR
Every software-defined radio front end presents a nominal 50 Ω input at its antenna connector, and the low-noise amplifier, filters, and mixer behind it are all designed around that reference. If the antenna or feedline is badly mismatched, part of the received signal reflects instead of reaching the ADC, degrading sensitivity; on a transmit-capable SDR the reflected power can also stress the power amplifier. This is why receivers benefit from a resonant, reasonably matched antenna rather than a random length of wire, even though a receive-only mismatch mainly costs signal rather than damaging hardware.
GopherTrunk is a pure-software decoder that operates on the digital IQ stream after the SDR’s analog front end, so it does not measure or correct impedance itself — that work happens in the hardware and cabling. Understanding impedance still matters to GopherTrunk users because a good antenna match improves the signal-to-noise ratio the decoder ultimately sees, and poor matching is a common cause of weak control-channel reception that no amount of DSP can recover.
Sources
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Electrical impedance — Wikipedia, the complex R + jX definition, reactance, and phase relationships. ↩