characteristic impedance

When a wave first sets off down a transmission line, the line presents it with a fixed ratio of voltage to current, and that ratio is the characteristic impedance, written Z0. Think of pushing water into a hose of a particular bore: for a given push you get a particular flow, and that relationship is a property of the hose itself, not of what is at the far end. Crucially, Z0 is set entirely by the line's geometry and materials, not by its length, and the famous value in RF is 50 ohms.

Mathematically, for a lossless line Z0 = square root of (L/C), where L and C are the inductance and capacitance per unit length. A coax cable with thin centre conductor and wide shield has more inductance and less capacitance, giving a higher Z0; a fat centre conductor close to the shield gives a lower Z0. While the forward wave alone is travelling, the line really does look like a pure Z0 resistor to the source, even though no actual resistor is present, because the energy is leaving down the line rather than being dissipated. The 50 ohm standard is an engineering compromise: in air-dielectric coax, lowest loss occurs near 77 ohms and highest power handling near 30 ohms, and 50 is a practical middle ground.

Characteristic impedance is the number everything in RF is matched to. Sources are built for 50 ohms, instruments have 50 ohm ports, cables are 50 ohms, and a load is called matched when it equals Z0 so the wave is absorbed with no reflection. Honest caveat: Z0 is not a resistor you can measure with an ohmmeter, a DC meter on a 50 ohm cable reads near zero ohms or open, depending on the far end. Z0 only reveals itself to a travelling wave, and only a properly matched, long-enough line behaves as that clean resistance.