## Nonlinearities and Noise in Idealized Baseband Amplifier Block

Use the Idealized Baseband Amplifier block to simulate nonlinearities and noise in your RF system design. The Amplifier block provides four nonlinearity models and three options to represent noise.

### Nonlinearity Models in Idealized Amplifier Block

#### Cubic Polynomial

The `Cubic polynomial` model uses linear power gain to determine the linear coefficient of a third-order polynomial and either IP3, P1dB, or Psat to determine the third - order coefficient of the polynomial. The general form of cubic nonlinearity models the AM/AM characteristics as

`${\text{F}}_{\text{AM/AM}}{\text{(|u|)=c}}_{\text{1}}\text{×|u|+}\frac{\text{3}}{\text{4}}{\text{c}}_{\text{3}}{\text{×|u|}}^{\text{3}}$`

where `FAM/AM(|u|)` is the magnitude of the output signal, |u| is the magnitude of the input signal, c1 is the coefficient of the linear gain term, and c3 is the coefficient of the cubic gain term. The results for IIP3, OIP3, IP1dB, OP1dB, IPsat and OPsat are taken from [1]. The coefficient c3 are given in this table.

Nonlinearity TypeEquations
Input third-order intercept point, IIP3 (dBm)
`${c}_{3}=-\frac{4{c}_{1}}{3×{10}^{\left[\left(IIP3-30\right)/10\right]}}$`

where IIP3 is given in dBm.

Output third-order intercept point,OIP3 (dBm)
`${c}_{3}=-\frac{4{c}_{1}^{3}}{3×{10}^{\left[\left(OIP3-30\right)/10\right]}}$`

where OIP3 is given in dBm.

Input 1 dB gain compression power,IP1dB (dBm)
`${c}_{3}=-\frac{2{c}_{1}\left({10}^{19}{20}}-10\right)}{15×{10}^{\left[\left(IP1dB-30\right)/10\right]}}$`

where IP1dB is given in dBm.

Output 1 dB gain compression power, OP1dB (dBm)
`${c}_{3}=-\frac{2{c}_{1}^{3}\left({10}^{19}{20}}-10\right)}{15×{10}^{\left[\left(OP1dB-30-LGdB+1\right)/10\right]}}$`

where OP1dB is given in dBm, and LGdB is the linear gain in dB

Input saturation power, IPsat (dBm)
`${c}_{3}=-\frac{4{c}_{1}}{9×{10}^{\left[\left(IPsat-30\right)/10\right]}}$`

where IPsat is given in dBm.

Output saturation power, OPsat (dBm)
`${c}_{3}=-\frac{16{c}_{1}^{3}}{81×{10}^{\left[\left(OPsat-30\right)/10\right]}}$`

where OPsat is given in dBm.

#### AM/AM-AM/PM

The `AM/AM-AM/PM` model uses a lookup table to specify the amplifier power characteristics. The table returns interpolated or extrapolated values using linear interpolation. Each row in the table expresses the relationship between output power or phase change as a function of input power.

`${u}_{\text{out}}=Tabl{e}_{AM/AM}\left(u\right)×{e}^{\left(\left(Tabl{e}_{AM/PM}\left(u\right)+\angle u\right)×i\right)}$`

where `uout` is the output signal and u is the magnitude of input signal.

#### Saleh

The `Saleh` model is based on normalized transfer function. Use the input / output scaling parameters to adjust signal levels from their normalized values. For `Saleh`, the AM/AM parameters alphaAM/AM and betaAM/AM are used to compute the amplitude gain for an input signal using the following equation:

`${F}_{AM/AM}\left(u\right)=\frac{alph{a}_{AM/AM}×|u|}{1+bet{a}_{AM/AM}×|u{|}^{2}}$`

where |u| is the magnitude of the scaled signal and `u` is calculated as:

`$u=InputScale×{u}_{\text{in}}$`

For `Saleh`, the AM/PM parameters alphaAM/PM and betaAM/PM are used to compute the phase change for an input signal using the following equation:

`${F}_{AM/PM}\left(u\right)=\frac{alph{a}_{AM/PM}×|u{|}^{2}}{1+bet{a}_{AM/PM}×|u{|}^{2}}+angle\left(u\right)$`

where |u| is the magnitude of the scaled signal and angle is a MATLAB® function that returns the phase angle of u.

The scaled output signal, uout is calculated as:

`${u}_{\text{out}}={F}_{AM/AM}×{e}^{\left({F}_{AM/PM}×i\right)}×OutputScale$`

#### Modified Rapp

The `Modified Rapp` model is based on normalized transfer functions. Use the input and output scaling parameters to adjust the signal levels from their normalized values. The AM/AM characteristics for `Modified Rapp` are given by:

`${F}_{AM/AM}\left(u\right)=\frac{{g}_{lin}×|u|}{{\left(1+|\frac{{g}_{lin}×u}{{V}_{sat}}{|}^{2p}\right)}^{1}{2p}}}$`

where |u| is the magnitude of input signal, glin is 10(Linear Gain (dB)/20), and is the amplitude gain of the amplifier, Vsat is Output saturation level (V), and p is Magnitude smoothness factor.

The AM/PM characteristics for `Modified Rapp` is given by

`${F}_{AM/PM}\left(u\right)=\frac{Α×|u{|}^{q}}{{\left[1+\left(\frac{|u|}{B}\right)\right]}^{q}}+angle\left(u\right)$`

where u is the input signal, A is the Phase gain (rad), B is Phase saturation, q is Phase smoothness factor and angle is a MATLAB function which returns phase angle of `u`.

The output signal uout is calculated as:

`${u}_{\text{out}}={F}_{AM/AM}\left(u\right)×{e}^{\left({F}_{{}_{AM/PM}}\left(u\right)×i\right)}$`

### Plot Power Characteristics

To visualize the functionality of Plot power characteristics button, you can set the parameters of the Amplifier block as listed in the table.

ModelParametersPower Characteristics Plot
Cubic Polynomial

Main tab:

• Linear power gain (dB): `7`

• Type of Non-linearity: `IIP3`

• IIP3 (dBm): `33`

• Simulate using: `Code generation`

Noise tab:

• Specify noise type: `Noise temperature`

• Noise temperature: `290`

• Seed source: `Auto`

AM/AM - AM/PM

Main tab:

• Lookup table (Pin(dBm), Pout(dBm), deg): `[-25, 5, -1; -10, 20, -2; 0, 27, 5; 5, 28, 12]`

• Simulate using: `Code generation`

Noise tab:

• Specify noise type: `Noise temperature`

• Noise temperature: `290`

• Seed source: `User specified`

• Seed : `67987`

Modified Rapp

Main tab:

• Linear power gain (dB): `7`

• Output saturation level (V): `1`

• Magnitude smoothness factor: `2`

• Phase gain (rad): `-.45`

• Phase saturation: `0.88`

• Phase smoothness factor: `3.43`

• Simulate using: `Code generation`

Noise tab:

• Specify noise type: `Noise temperature`

• Noise temperature: `290`

• Seed source: `User specified`

• Seed : `67987`

Saleh

Main tab:

• Input scaling (dB): `0`

• AM/AM parameters [alpha beta]: `[ 2.1587, 1.1517 ]`

• AM/PM parameters [alpha beta]: `[ 4.0033, 9.1040 ]`

• Output scaling (dB): `0`

• Simulate using: `Interpreted execution`

Noise tab:

• Specify noise type: `Noise figure`

• Noise figure: `10 * log10( 2 )`

• Seed source: `Auto`

### Application of Nonlinearities

All four subsystems for the amplifier nonlinearity models apply a memoryless nonlinearity to the complex baseband input signal. Each model

1. Multiplies the signal by a gain factor.

2. Splits the complex signal into its magnitude and angle components.

3. Applies an AM/AM conversion to the magnitude of the signal, according to the selected nonlinearity model, to produce the magnitude of the output signal.

4. Applies an AM/PM conversion to the phase of the signal, according to the selected nonlinearity model, and adds the result to the angle of the signal to produce the angle of the output signal.

### Thermal Noise Simulations in Idealized Amplifier Block

According to the Specify noise type parameter, you can specify the amount of thermal noise in three ways,

• `Noise temperature` — Specifies the noise in kelvin.

• `Noise factor` — Specifies the noise by using the equation:

• `Noise figure` — Specifies the noise in decibels relative to a noise temperature of 290 kelvin. In terms of noise factor

Note

Some RF Blockset™ blocks require the sample time to perform baseband modeling calculations. To ensure accuracy in these calculations, the Input Port block, as well as the mathematical RF blocks compare the input sample time to the sample time you provide in the mask. If these times do not match, or if the input sample time is missing because the blocks are not connected, an error message appears.

To learn how to use the idealized baseband library Amplifier block to amplify a signal with nonlinearity and noise, see Idealized Baseband Amplifier with Nonlinearity and Noise.

## References

[1] Kundert, Ken.“ Accurate and Rapid Measurement of IP2 and IP3,“ The Designer Guide Community, May 22, 2002.