The wave going out meets a wave coming back
A short wire connected to a battery can usually be treated as one electrical potential. At radio frequencies, propagation takes an appreciable part of an oscillation cycle. A disturbance launched now is still traveling toward the load as an earlier reflection returns toward the source.
The inner and outer conductors of a coaxial cable guide this traveling field. The forward voltage and current waves have a characteristic ratio called the line impedance. Many RF systems use fifty ohms. A load that matches the line accepts the arriving wave; a different impedance generally sends part of it back.
The word vector says that the instrument retains phase as well as amplitude. Phase records position within an oscillation cycle. Coherent receivers share an oscillating reference, distinguish incident and outgoing waves, and compare their complex amplitudes. Each frequency point then describes how much wave comes back and its timing relative to the incident wave.
A hundred-ohm load reflects one ninth of the incident power
Place the observation plane directly at a resistor connection. An ideal fifty-ohm line terminated by a hundred-ohm resistor returns a voltage wave one third as large as the incident wave. Power follows amplitude squared, so one ninth, about 11.1 percent, returns. The remaining power enters the resistor as heat. This power comparison uses a common real reference impedance.
Let denote the load impedance and the real line reference. The reflection coefficient is the outgoing-to-incident wave ratio. A load close to the reference makes its numerator small.
An ideal open admits no load current and has reflection coefficient plus one. A short forces the terminal voltage to zero, so its reflected voltage reverses sign and its coefficient is minus one. Both return all incident power, with a half-cycle difference in reflection phase.
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Move the observation plane and the reflection travels twice
Move the observation plane twenty-five centimetres back toward the source. The incident wave travels down the added cable to reach the resistor. Its reflection travels back through the same cable. The resistor is unchanged, but the reflection phase includes two propagation paths.
For a chosen ideal matched cable with propagation speed two hundred million metres per second, a hundred-megahertz wave has a two-metre wavelength. Twenty-five centimetres is one eighth of a wavelength: forty-five degrees of lag each way and ninety degrees on the reflection round trip. A lossy cable also reduces the returning amplitude.
Calibration fixes a reference plane at a physical connection. The analyzer measures an open, a short and a known load there to determine leakage, wave tracking and source mismatch. The intervening cable response becomes part of that correction. Subsequent reflection results refer to the plane where those standards were connected.
Real opens have fringing capacitance and shorts have connection inductance. A calibration kit specifies these departures from ideal behavior and the frequency range of its definitions. Incorrect definitions can still fit the three observations. A separate known load tests the correction against an additional observation.
A filter has a second way for energy to leave
A filter normally has two measured ports. A wave incident on the first port can return there or emerge from the second. Exciting the other port measures reverse transmission and the other reflection. These four complex wave ratios form the scattering parameters.
A low-pass filter transmits lower frequencies. At higher frequencies, its inductors and capacitors change the port voltage-current relations, transmission falls and reflection often rises. Reduced transmission alone does not show how much power became heat. Reflection and dissipation must also be considered.
Each receiver channel has its own amplitude and phase response. Mismatch at either port feeds back through the device. A known through connection relates the two channels for transmission calibration. Commercial two-port calibration also accounts for changes introduced by switching the excitation between ports and for unwanted leakage.
If a known matched spacer remains beyond the calibration plane, its propagation model can shift the reported plane farther toward the device. Replacing or moving a test cable requires checking the calibration again. The corrected reflection and transmission then describe a clearly identified physical section.