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Nexxim Simulator >
Nexsys Discrete Time Domain Analysis >
Overview of Discrete Time Domain Analysis >
Discrete Time Simulation of Nonlinear Behavioral Components

Discrete Time Simulation of Nonlinear Behavioral Components

The nonlinear discrete time simulation technique described here is used for processing bandpass modulated signals through nonlinear behavioral components (e.g., amplifiers, mixers, frequency multipliers). Generally, nonlinear behavioral components are not only power dependent, but also frequency and/or temperature dependent. An equivalent model is used for nonlinear components in discrete time simulation to separate the power dependent characteristics from frequency and temperature dependent characteristics.

All nonlinear behavioral two-port components are assumed unidirectional (i.e., S₁₂ = 0). Each nonlinear component is partitioned into three segments: a linear electrical (active) input component, a nonlinear functional component, and a linear electrical (passive and noiseless) output component. This arrangement is shown in Figure 2 below.

In this model, the power dependent characteristics of S₁₁, S₁₂and S₂₂ are ignored. The frequency and temperature dependent small signal S₁₁ and NF are associated with the input linear electrical component. The power dependent characteristics of S₂₁ are associated with the nonlinear functional component. The frequency and temperature dependent small signal S₂₁ and S₂₂ are associated with the output linear electrical component.

For discrete time simulation, the linear electrical input and output components are associated with other connected linear electrical components and simulated as a linear electrical sub-design as discussed in the previous section.

The nonlinear characteristic of a two-port component in Designer is described by its nonlinear figures-of-merit or nonlinear measured data. Only the nonlinear characteristic of S₂₁ is considered in discrete time analysis techniques even though S₁₁, S₁₂and S₂₂ may possibly be power dependent too.

Note

For the two-port nonlinear mixer model, the arrangement in Figure 2 still holds. In addition, the nonlinear functional component is associated with the actual frequency conversion and discrete time phase noise simulation. As a result of that, the input linear electrical component in Figure 2 is associated with the mixer’s input frequency while the output linear electrical component is associated with the mixer’s output frequency.

Modeling Nonlinearity with Polynomial Power Series

It is always assumed that nonlinear measurements are obtained when the input and output ports of the nonlinear component are terminated in 50Ω. Nonlinear measurements of a two-port component typically include the AM-AM and AM-PM effects. This nonlinear relationship between S₂₁ and P₁ (the available input power) or, equivalently, between P_out and P₁ is represented by the following power series polynomials:

where

P₁ = the available input power from the source (with RS = 50Ω)

= the output load power (assuming RL = 50Ω)

S₂₁_ss = the small signal gain.

The coefficients a₁, a₃, a₅,... and b₁, b₃, b₅,... are calculated using a least-squares curve fitting technique based on the user-supplied measurements P₁ - P_out data or P₁ - S-parameters data. For example, a set of coefficients can be obtained based on the following power amplifier P₁ - P_out measured data (in 50ohm terminations).

RTH_PA 2-port

POUT dBm

P1 dBm, FREQ = 900MHz

* P1	Pout	Phase (degrees)
5.00	25.68	88.75
7.00	27.67	88.75
9.00	29.66	88.75
11.00	31.64	88.75
13.00	33.61	88.75
15.00	35.56	88.75
17.00	37.48	88.76
19.00	39.35	88.76
21.00	41.16	88.76
23.00	42.86	88.75
25.00	44.38	88.71
27.00	45.65	88.66
29.00	46.53	88.76
31.00	47.17	91.85
33.00	47.50	97.08
35.00	47.66	102.81

Note	If the error obtained using the least squares curve fitting technique for the a and b coefficients exceeds 1e-5, an alternate approach based on cubic spline interpolation will be used to compute the output power level for a given input signal power
Note	If the input signal power to the nonlinear component exceeds the maximum supplied measured input power P1, the simulator will assume the last supplied output power entry in the measured data to be the saturation power.
Note	The above mentioned data is given at FREQ = 900MHz. Additional nonlinear measured data at other frequencies may be provided as well. The discrete time analysis is capable of locating the actual operating point using multi-dimensional data interpolation. For more information, please refer to the Nonlinear RF Component Models documentation.

If the user chooses to provide the nonlinear figures-of-merit (OIP3 or P1dB and Psat) instead of measurement data, the power series coefficients are approximated by

a_i = 0, i = 5,7, ...

b_i = 0, i = 1,3,5, ...

where:

S₂₁ is the linear small signal gain

OIP3 is the output power at the third order intercept point.

In this case, the simulations tend to be less accurate.

Calculating a Nonlinear Output Voltage

Assuming a bandpass modulated input signal of the form:

where

V_s(t) is the baseband input voltage

is the phase of the input modulated signal

= In-phase envelope of the input signal

= Quadrature-phase envelope of the input signal

, where f_c is the carrier frequency.

The nonlinear output voltage is calculated as:

where:

with

and

The source resistance Rinand the load resistance Rout are always defaulted to 50Ω, but they can be individually specified for each input and output, respectively.

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