Scattering parameters

The S-parameters are members of a family of similar parameters, other examples being: Y-parameters,[1] Z-parameters,[2] H-parameters, T-parameters or ABCD-parameters.

[3][4] They differ from these, in the sense that S-parameters do not use open or short circuit conditions to characterize a linear electrical network; instead, matched loads are used.

Contrary to popular belief, the quantities are not measured in terms of power (except in now-obsolete six-port network analyzers).

Modern vector network analyzers measure amplitude and phase of voltage traveling wave phasors using essentially the same circuit as that used for the demodulation of digitally modulated wireless signals.

Many electrical properties of networks of components (inductors, capacitors, resistors) may be expressed using S-parameters, such as gain, return loss, voltage standing wave ratio (VSWR), reflection coefficient and amplifier stability.

The term scattering matrix was used by physicist and engineer Robert Henry Dicke in 1947 who independently developed the idea during wartime work on radar.

It may also include many typical communication system components or 'blocks' such as amplifiers, attenuators, filters, couplers and equalizers provided they are also operating under linear and defined conditions.

[18] In this case the relationship between the outgoing ('reflected'), incident waves and the S-parameter matrix is given by: Expanding the matrices into equations gives: and Each equation gives the relationship between the outgoing (e.g. reflected) and incident waves at each of the network ports, 1 and 2, in terms of the network's individual S-parameters,

In case the two measurement ports use the same reference impedance, the insertion loss (IL) is the reciprocal of the magnitude of the transmission coefficient |S21| expressed in decibels.

It is the extra loss produced by the introduction of the device under test (DUT) between the 2 reference planes of the measurement.

A reflection coefficient with a magnitude greater than unity, such as in a tunnel diode amplifier, will result in a negative value for this expression.

Many specifications of high speed differential signals define a communication channel in terms of the 4-Port S-Parameters, for example the 10-Gigabit Attachment Unit Interface (XAUI), SATA, PCI-X, and InfiniBand systems.

Note the format of the parameter notation SXYab, where "S" stands for scattering parameter or S-parameter, "X" is the response mode (differential or common), "Y" is the stimulus mode (differential or common), "a" is the response (output) port and b is the stimulus (input) port.

Understanding mode conversion is very helpful when trying to optimize the design of interconnects for gigabit data throughput.

The fourth quadrant is the lower right 4 parameters and describes the performance characteristics of the common-mode signal SCCab propagating through the device under test.

determines the level of feedback from the output of an amplifier to the input and therefore influences its stability (its tendency to refrain from oscillation) together with the forward gain

Most practical amplifiers though will have some finite isolation allowing the reflection coefficient 'seen' at the input to be influenced to some extent by the load connected on the output.

Suppose the output port of a real (non-unilateral or bilateral) amplifier is connected to an arbitrary load with a reflection coefficient of

An amplifier is unconditionally stable if a load or source of any reflection coefficient can be connected without causing instability.

This condition occurs if the magnitudes of the reflection coefficients at the source, load and the amplifier's input and output ports are simultaneously less than unity.

[24] Instability can cause severe distortion of the amplifier's gain frequency response or, in the extreme, oscillation.

To be unconditionally stable at the frequency of interest, an amplifier must satisfy the following 4 equations simultaneously:[25] The boundary condition for when each of these values is equal to unity may be represented by a circle drawn on the polar diagram representing the (complex) reflection coefficient, one for the input port and the other for the output port.

This serves to readily show the regions of normalised impedance (or admittance) for predicted unconditional stability.

The T-parameter matrix is related to the incident and reflected normalised waves at each of the ports as follows: However, they could be defined differently, as follows : The RF Toolbox add-on to MATLAB[26] and several books (for example "Network scattering parameters"[27]) use this last definition, so caution is necessary.

In this way the incident power wave for each of the unused ports becomes zero yielding similar expressions to those obtained for the 2-port case.

The S-parameter test data may be provided in many alternative formats, for example: list, graphical (Smith chart or polar diagram).

[clarification needed] Any 2-port S-parameter may be displayed on a Smith chart using polar co-ordinates, but the most meaningful would be

Most VNAs provide a simple one-port calibration capability for one port measurement to save time if that is all that is required.

VNAs designed for the simultaneous measurement of the S-parameters of networks with more than two ports are feasible but quickly become prohibitively complex and expensive.

One risk of this approach is that the return loss or VSWR of the loads themselves must be suitably specified to be as close as possible to a perfect 50 Ohms, or whatever the nominal system impedance is.