S-Parameter Simulation Description

S-parameters are used to define the signal-wave response of an n-port electrical element at a given frequency. Detailed discussions of S-parameters can be found in standard textbooks on electrical circuit theory.

Note You may find it helpful to review the publication S-Parameter Techniques for Faster, More Accurate Network Design (AN 95-1), 5952-1130, available at http://www.agilent.com/find/eesof-an95-1.

S-parameter simulation is a type of small-signal AC simulation. It is most commonly used to characterize a passive RF component and establish the small-signal characteristics of a device at a specific bias and temperature.

If the circuit contains any nonlinear devices, a DC simulation is performed first. Following the DC bias simulation, the simulator linearizes all nonlinear devices about their bias points. A linearized model captures the small incremental changes of current due to small incremental changes of voltage. These are derivatives of the transistor model equations, which are evaluated at the DC bias point. Nonlinear resistors and current sources are replaced by linear resistors whose values are set by the small signal conductance dI/dV. Current sources that depend on voltages other than the voltage across the source are replaced by linear dependent current sources dI ₁/dV ₂. Nonlinear capacitors are replaced by linear capacitors of value dQ/dV.

The linear circuit that results is analyzed as a multiport device. Each port is excited in sequence, a linear small-signal simulation is performed, and the response is measured at all ports in the circuit. That response is then converted into S-parameter data, which are in turn sent to the dataset. S-parameter simulation normally considers only the source frequency in a noise analysis. Use the Enable AC Frequency Conversion option if you also want to consider the frequency from a mixer's upper or lower sideband.

Note By selecting the appropriate option under the Parameters tab, it is possible to convert S-parameter data to Y- and Z-parameters. The S-parameter results are retained.

S-Parameter Definitions

The following is a representation of a signal wave in a two-port electrical-element.

where

a ₁ is the wave into port 1
b ₁ is the wave out of port 1
a ₂ is the wave into port 2
b ₂ is the wave out of port 2

The S-parameters for this conventional element are defined in standard microwave textbooks as follows:

b ₁ = a ₁ s ₁₁ + a ₂ s ₁₂
b ₂ = a ₁ s ₂₁ + a ₂ s ₂₂

where

s ₁₁ is the port-1 reflection coefficient: s ₁₁ = b ₁ /a ₁ ; a ₂ = 0
s ₂₂ is the port-2 reflection coefficient: s ₂₂ = _b2 /a ₂ ; a ₁ = 0
s ₂₁ is the forward transmission coefficient: s ₂₁ = b ₂ /a ₁ ; a ₂ = 0
s ₁₂ is the reverse transmission coefficient: s ₁₂ = b ₁ /a ₂ ; a ₁ = 0

These equations can be solved for b ₁ and a ₁ in terms of a ₂ and b ₂ to yield the transmission (T) parameters as follows:

b ₁ = a ₂ t ₁₁ + b ₂ t ₁₂
a ₁ = a ₂ t ₂₁ + b ₂ t ₂₂

The T-parameters are related to the S-parameters as follows:

S-parameters are defined with respect to a reference impedance that is typically 50 ohms. For 50-ohm S-parameters-with the 2-port element terminated with 50 ohms at each port – the s ₂₁ parameter represents the voltage gain of the element from port 1 to port 2.

Group Delay

Group delay is a useful measure of phase distortion in components such as amplifiers and filters. It measures the transit time, with respect to frequency, of a signal through the device under test.

The simulator calculates group delay by performing a finite difference of the phase response to obtain dΦ/dω.

group_delay = delay (2,1) = −diff(unwrap(phaserad(S21),pi))/(2pi)

The simulator sets the frequency aperture to 0.01% of the current frequency. You can override this value by modifying the value in the Group delay aperture field, under the Parameters tab. This function is similar to that found on network analyzers, like the Agilent 8710. Refer also to these functions:

delay
dev_lin_phase
diff
phasedeg
phaserad
ripple (and GpDelRip measurement equation)
unwrap
volt_gain

Descriptions are in Measurement Expressions.

Group delay results are considered with respect to the input and output ports only. Results of group delay calculations include delay(2,1) and delay(1,2), which can be viewed in the Data Display. These are absolute group delay, in seconds. For additional results data, add the measurement equations dev_lin_phase and GpDelRip to the schematic. Calculations from these equations will also be available in the Data Display.

S-Parameter Frequency Conversion

S-parameter simulation normally allows only one frequency to be considered in a noise analysis – that of the source. This can be a disadvantage in obtaining simulation results for circuits involving mixers, which are inherently frequency-translating devices involving multiple frequencies. (See Harmonic Balance for Mixers.)

As an aid in the simulation of frequencies involving mixer subnetworks, the option Enable AC Frequency Conversion (under the Parameters tab) causes the simulator to consider not only the frequency of the source but also that of one of the mixer's sidebands (which are defined by the user). Only the upper or lower sideband is considered, not both. The frequency-conversion results will appear in the dataset as for any nodes or probes placed to capture voltage or current data.

The S-parameter simulator uses the same conversion algorithm used by the AC Simulation component. For more information on this algorithm, see Enabling Frequency Conversion.