### Wave Quantities and Ratios

The elements of the S-, Z- and Y-matrices represent fixed ratios of complex wave amplitudes. As long as the assumption of linearity holds, the S-, Z- and Y-parameters are independent of the source power.

The network analyzer provides two additional sets of measurement parameters which have a unambiguous meaning even if the DUT is measured outside its linear range:

- Wave Quantities
  provide the power of any of the transmitted or received waves.

- Ratios
  provide the complex ratio of any combination of transmitted or received wave amplitudes.

In contrast to S-, Z- and Y-parameters, wave quantities and ratios are not system-error corrected. A power calibration can be applied to wave quantities and ratios; see Data Flow
.

#### Wave Quantities

A wave quantity measurement provides the power of any of the transmitted or received waves. The power can be displayed in voltage (e.g. V or dBmV) or equivalent power units (e.g. W or dBm).

Examples for using wave quantities

The wave quantities provide the power at the different receive ports of the analyzer. This is different from an S-parameter measurement, where the absolute power of a linear device is cancelled. Wave quantities are therefore suitable for the following measurement tasks:

- Analysis of non-linearities of the DUT.

- Use of the analyzer as a selective power meter.

The notation for wave quantities includes the direction and the test port number. Additionally, the source port must be specified. The letter a indicates a transmitted wave, b a received wave.

Examples:

- a1 Src Port 1 is the outgoing wave at test port 1. In a standard S-parameter
  measurement, this wave is fed to the input port (port 1) of the DUT (forward measurement).

- b1 Src Port 1 is the incoming wave at test port 1. In a standard S-parameter measurement, this is the reflected wave at port 1 of the DUT (forward measurement).

#### Ratios

A ratio measurement provides the complex ratio of any combination of transmitted or received wave amplitudes. Ratios complement the S-parameter measurements, where only ratios of the form bi/aj (ratio of the incoming wave to the outgoing wave at the test ports i and j of the DUT) are considered.

Examples for using ratios

A measurement of ratios is particularly suitable for the following test scenarios:

- The test setup or some of its components (e.g. active components or non-reciprocal devices) do not allow a system error correction so that a complete S-parameter measurement is not possible.

- The test setup contains frequency-converting components so that the transmitted and the received waves are at different frequencies.

- A ratio of two arbitrary waves that is not an element of the S-matrix (e.g. a ratio of the form ai/aj) is needed.

The notation for ratios includes the two waves with their directions and test port numbers. Additionally, the source port must be specified. In analogy to wave quantities
, the letter a indicates an outgoing wave, b an incoming wave.

Examples:

- b2/a1 Src Port 1 is the ratio of the incoming wave at port 2 and the outgoing wave at port 1 b2 and a1 and corresponds to the S-parameter S21 (forward transmission coefficient).

- b1/a1 Src Port 1 is the ratio of the wave quantities b1 and a1, measured at PORT 1, and corresponds to the S-parameter S11 (input reflection coefficient).