Go to www.awrcorp.com
Back to search page Click to download printable version of this guide.

Nonlinear Amplifier System Model (Closed Form): NL_AMP2

Symbol

Summary

NL_AMP2 is a sophisticated model, and some aspects of its behavior may be different from expected. Therefore, you should read this entire section before using this model. NL_AMP2 offers improved accuracy of nonlinear characteristics and full noise and S parameters over NL_AMP.

Equivalent Circuit

Parameters

Name Description Unit Type Default
ID Element ID   AM1
NFMIN Minimum noise figure dB 3.0
RN_NORM Normalized noise resistance   0.5
GOPT_MAG Source reflection coefficient magnitude at optimum NF   0.0
GOPT_ANG Source reflection coefficient angle at optimum NF Angle 0.0
IP2H Mid-band output IP2 (harmonic) dB Power 40
IP3 Mid-band output IP3 dB Power 20
P1DB Output 1-db compression point dB Power 10
*S11MAG Input reflection coefficient magnitude   0.0
*S11ANG Input reflection coefficient phase angle Angle 0.0
*S21MAG Transmission coefficient magnitude   3.1623
*S21ANG Transmission coefficient phase angle Angle 180.0
*S12MAG Reverse transmission coefficient magnitude   0.0
*S12ANG Reverse transmission coefficient phase angle Angle 0.0
*S22MAG Output reflection coefficient magnitude   0.0
*S22ANG Output reflection coefficient phase angle Angle 0.0
*Z0 Port Impedance Resistance 50.0

* indicates a secondary parameter

Linear Behavior

The linear behavior of the amplifier is modeled by a controlled current source (the linear part of f(v) in the equivalent circuit) and input and output impedances. The parameters of the controlled current source are derived from the user-specified gain and impedances, so the transducer gain is always the value specified. The gain, therefore, is the gain with the specified values of S11 or S22. Changing S11 or S22 does not change the transducer gain, as long as the source and load impedances remain at Z0.

The gain is entered by S21. Note that the transducer power gain, when the source and load impedances equal Z0, is S21MAG2.

Nonlinear Behavior

IP3 and Compression

It is important to recognize that IP3 and the 1-dB compression point are not independent. If compression is caused by the small-signal nonlinearities of the device, expressed in the equation below, the 1 dB compression point must be approximately 10 dB below IP3. However, if compression is caused by clipping the large-signal drain or collector waveforms, saturation can occur at a lower level, and need not be related to IP3. This is why amplifiers that are highly linear, in terms of IP3, often do not obey the "10 dB" rule.

The Nonlinear Model

Nonlinearities are modeled by a polynomial and a clipping function. This provides the correct saturation and intermodulation characteristics, regardless of the relative values of IP3 and P1DB. The controlled current source f(v) is modeled by a polynomial:

This polynomial models intermodulation distortion through third order. The values of the coefficients are derived from the specified intercept points.

The one-dB compression point is more problematic to model. One cause of compression in an amplifier is clipping of the waveforms when dc bias power is inadequate to provide output. This can happen, in theory, even if the amplifier is perfectly linear for small signals; that is, when a2 = a3 = 0 in the polynomial. Compression can also be caused by the inherent small-signal nonlinearities in f(v). In this case, a cubic polynomial is not adequate to model compression, and unless other means are used, the model becomes very poor above the 1-dB compression point.

To avoid these difficulties, the amplifier model calculates the 1 dB compression point according to both criteria and uses the one that represents the lower of the two compression levels. If the amplifier's compression is caused by clipping, a clipping function is used with the value set appropriately. However, if compression is caused by the nonlinearities in f(v), these are allowed to provide compression. The clipping level is then set somewhat higher, to provide the correct behavior in hard saturation.

The transition between these two conditions is approximately 10 dB below the third-order intercept point, IP3. Therefore, if P1DB < IP3 - 10, the amplifier saturates on clipping, while, for higher values, the nonlinearities of f(v) dominate.

The clipping function is symmetrical, so it affects only third-order intermodulation. The second-order IM level saturates gracefully, but does not exhibit the sudden increase in level that is observable in the third-order.

As with linear characteristics, the calculation of the coefficients of the polynomial includes the effect of S11 and S22. Therefore, if the value of load and source resistance is Z0, changing S11 or S22 does not affect the calculated IM levels.

Layout

This element does not have an assigned layout cell. You can assign artwork cells to any element. See “Assigning Artwork Cells to Layout of Schematic Elements” for details.

Reference

This model was developed under research performed at Cadence Design Systems, Inc. The full set of details of the implementation are proprietary.

Legal and Trademark Notice