LSSP Simulation Description

Unlike small-signal S-parameters, which are based on a small-signal simulation of a linearized circuit, large-signal S-parameters are based on a harmonic balance simulation of the full nonlinear circuit. Because harmonic balance is a large-signal simulation technique, its solution includes nonlinear effects such as compression. This means that the large-signal S-parameters can change as power levels are varied. For this reason, large-signal S-parameters are also called power-dependent S-parameters.

Like small-signal S-parameters, large-signal S-parameters are defined as the ratio of reflected and incident waves:

The incident and reflected waves are defined as:

where

V _i and V _j are the Fourier coefficients, at the fundamental frequency, of the voltages at ports i and j,
I _i and I _j are the Fourier coefficients, at the fundamental frequency, of the currents at ports i and j,
Z _0i and Z _0j are the reference impedances at ports i and j, and
R _0i and R _0j are the real parts of Z _0i and Z _0j.

This definition is a generalization of the small-signal S-parameter definition in that V and I are Fourier coefficients rather than phasors. For a linear circuit, this definition simplifies to the small-signal definition.

LSSP Simulation Process

The simulator performs the following operations to calculate the large-signal S-parameters for a two-port:

• Terminates port 2 with the complex conjugate of its reference impedance. Applies a signal with the user-specified power level P ₁ at port 1, using a source whose impedance equals the complex conjugate of that port's reference impedance. Using harmonic balance, calculates the currents and voltages at ports 1 and 2. Uses this information to calculate S ₁₁ and S ₂₁.
• Terminates port 1 with the complex conjugate of its reference impedance. Applies a signal of power P ₂ = |S₂₁| ² P ₁ at port 2 using a source whose impedance equals the complex conjugate of the reference impedance of port 2. Using harmonic balance, calculates the currents and voltages at ports 1 and 2. Uses this information to calculate S ₁₂ and S ₂₂.

Comparing LSSP and S-Parameter Simulations

S-parameter simulations are performed on linear circuits. LSSP simulations can be performed on nonlinear circuits and thus include nonlinear effects such as gain compression and variations in power levels.

Both LSSP and S-parameter simulations generate PortZ[] and S[] fields in the associated dataset. LSSP generates the additional field PortPower[], which contains the power, in dBm, seen at each port for the respective LSSP port frequencies.

To compare LSSP and S-parameter simulations, refer to LSSP1.dsn and SP1.dsn. They are in the ADS examples directory under Tutorial/SimModel_prj. The data displays are LSSP1.dds and SP1.dds.

For a review of the S-parameter simulator, see S-Parameter Simulation Description.