Z-Parameters Amplifier

Model nonlinear amplifier using Z-parameters

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Libraries:
RF Blockset / Equivalent Baseband / Amplifiers

Description

The Z-Parameters Amplifier block models the nonlinear amplifier described in the block dialog box, in terms of its frequency-dependent Z-parameters, the frequencies of the Z-parameters, noise data, and nonlinearity data.

Parameters

Main

Z-Parameters — Z-parameters for nonlinear amplifier

[0.0200,0;-0.0400, 0.0200] (default) | 2-by-2-by-M array

Z-parameters for a nonlinear amplifier, specified as a 2-by-2-by-M array where M is the number of Z-parameters.

Frequency (Hz) — Frequency of Z-parameters

2.0e9 (default) | M-element vector

Frequency of Z-parameters, specified as M-element vector with each element unit in hertz.

Interpolation method — Method to interpolate network parameters

Linear (default) | Spline | Cubic

Method to interpolate the network parameters, specified as one of the following:

Method	Description
Linear	Linear interpolation
Spline	Cubic spline interpolation
Cubic	Piecewise cubic Hermite interpolation

Noise Data

Noise type — Type of noise data

Noise figure (default) | Spot noise data | Noise factor | Noise temperature

Type of noise data, specified as one of the following:

• Noise figure

• Spot noise data

• Noise factor

• Noise temperature

This parameter is disabled if the data source contains noise data.

Noise figure (dB) — Available signal-to-noise ratio at the input to available signal-to-noise ratio at the output

0 (default) | scalar ratio | vector of ratios

Available signal-to-noise ratio at the input to available signal-to-noise ratio at the output, specified as a scalar ratio or a vector of ratios.

Dependencies

To enable this parameter, select Noise figure in Noise type.

Minimum noise figure — Minimum ratio of available signal-to-noise ratio at input to available signal-to-noise ratio at output

0 (default) | scalar ratio | vector of ratios

Minimum ratio of available signal-to-noise ratio at the input to available signal-to-noise ratio at the output, specified as a scalar ratio or a vector of ratios.

Dependencies

To enable this parameter, select Spot noise data in Noise type.

Optimal reflection coefficient — Optimal source impedance

1+0i (default) | complex scalar | complex vector

Optimal source impedance, specified as a complex scalar or a complex vector.

Dependencies

To enable this parameter, select Spot noise data in Noise type.

Equivalent normalized noise resistance — Normalized resistance values used to take noise measurement

1 (default) | positive scalar | positive vector

Normalized resistance values used to take noise measurement, specified as a positive scalar or a positive vector.

Dependencies

To enable this parameter, select Spot noise data in Noise type.

Noise factor — Ratio of available signal-to-noise power at input to available signal-to-noise power at output

1 (default) | scalar ratio | vector of ratios

Ratio of available signal-to-noise power at the input to available signal-to-noise power at the output, specified as a scalar ratio or a vector of ratios.

Dependencies

To enable this parameter, select Noise factor in Noise type.

Noise temperature (K) — Equivalent temperature that produces the same amount of noise as amplifier

0 (default) | nonnegative scalar | nonnegative vector

Equivalent temperature that produces the same amount of noise as the amplifier, specified as a nonnegative scalar in kelvins or nonnegative vector with each element unit in kelvins.

Dependencies

To enable this parameter, select Noise temperature in Noise type.

Frequency (Hz) — Domain of frequencies to express noise data

2.0e9 (default) | nonnegative scalar | nonnegative vector

Domain of frequencies to express noise data, specified as a nonnegative scalar in hertz or nonnegative vector with each element unit in hertz. If you provide a scalar value for your noise data, the block ignores the Frequency (Hz) parameter and uses the same noise data for all frequencies. If you provide a vector of values for your noise data, it must be the same size as the vector of frequencies. The block uses the Interpolation method specified in the Main tab to interpolate noise data.

Nonlinearity Data

IP3 type — Type of third order intercept

OIP3 (default) | IIP3

Type of third order intercept, specified as OIP3 (output intercept point) or IIP3 (input intercept point). This parameter is disabled if the data source contains power data or IP3 data.

IP3 (dBm) — IP3 value

inf (default) | scalar | vector

IP3 value, specified as a scalar in dBm for frequency independent nonlinear data or a vector with each element unit in dBm for frequency dependent nonlinear data. This parameter is disabled if the data source contains power data or IP3 data.

1dB gain compression power (dBm) — Output power value at which gain has decreased by 1 dB

inf (default) | scalar | vector

Output power value ($$P_{1dB,out}$$) at which the gain has decreased by 1 dB, specified as a scalar in dBm for frequency independent nonlinear data or vector with each element unit in dBm for frequency dependent nonlinear data. This parameter is disabled if the data source contains power data or IP3 data.

Output saturation power (dBm) — Output power value that amplifier produces when fully saturated

inf (default) | scalar | vector

Output power value ($$P_{sat,out}$$) that the amplifier produces when fully saturated, specified as a scalar in dBm for frequency independent nonlinear data or a vector with each element unit in dBm for frequency dependent nonlinear data. This parameter is disabled if the data source contains output saturation power data.

Gain compression at saturation (dB) — Decrease in gain value

3 (default) | scalar | vector

Decrease in gain value ($$G{C}_{sat}$$) when the power is fully saturated, specified as a scalar in dB for frequency independent nonlinear data or a vector with each element unit in dB for frequency dependent nonlinear data.

Frequency (Hz) — Frequency points corresponding to third-order intercept or power data

2.0e9 (default) | positive scalar | positive vector

Frequency points corresponding to third-order intercept or power data, specified as a positive scalar or positive vector in units of hertz. This parameter is disabled if the data source contains power data or IP3 data.

Dependencies

• If you specify the frequency as a scalar, then the IP3 (dBm), 1 dB gain compression power (dBm), and Output saturation power (dBm) parameters must all be scalars.

• If you specify the frequency as a vector, then or more of the IP3 (dBm), 1 dB gain compression power (dBm), and Output saturation power (dBm) parameters must also be a vector.

Visualization

Source of frequency data — Frequency data source

Same as the Z-Parameters (default) | User-specified

Frequency data source, specified as Same as the Z-Parameters or User-specified.

Frequency data (Hz) — Frequency data range

[1.9e9:1.0e8:2.2e9] (default) | vector

Frequency data range, specified as a vector with each element unit in hertz.

Dependencies

To enable this parameter, set Source of frequency data to User specified.

Reference impedance (ohms) — Reference impedance

50 (default) | nonnegative scalar

Reference impedance, specified as a nonnegative scalar in ohms.

Plot type — Type of data plot

X-Y plane (default) | Composite data | Polar plane | Z Smith chart | Y Smith chart | ZY Smith chart

Type of data plot to visualize using the given data, specified as one of the following:

• X-Y plane — Generate a Cartesian plot of the data versus frequency. To create linear, semilog, or log-log plots, set the Y-axis scale and X-axis scale accordingly.

• Composite data — Plot the composite data. For more information, see Create Plots Using Equivalent Baseband Library Blocks.

• Polar plane — Generate a polar plot of the data. The block plots only the range of data corresponding to the specified frequencies.

• Z smith chart, Y smith chart, and ZY smith chart — Generate a Smith^® chart. The block plots only the range of data corresponding to the specified frequencies.

Y parameter1 — Type of parameters to plot

S11 (default) | S12 | S21 | S22 | GroupDelay | OIP3 | IIP3 | NF | ...

Type of parameters to plot, specified as one of the following:

S11	S12	S21	S22
GroupDelay	GammaIn	GammaOut	VSWRIn
VSWROut	OIP3	IIP3	NF
NFactor	NTemp	TF1	TF2
TF3	Gt	Ga	Gp
Gmag	Gmsg	GammaMS	GammaML
K	Delta	Mu	MuPrime

Note

Y parameter1 is disabled when you select Plot type to Composite data.

Y parameter2 — Type of parameters to plot

S11 (default) | S12 | S21 | S22 | GroupDelay | OIP3 | IIP3 | NF | ...

Type of parameters to plot, specified as one of the following:

S11	S12	S21	S22
GroupDelay	GammaIn	GammaOut	VSWRIn
VSWROut	OIP3	IIP3	NF
NFactor	NTemp	TF1	TF2
TF3	Gt	Ga	Gp
Gmag	Gmsg	GammaMS	GammaML
K	Delta	Mu	MuPrime

Note

Y parameter2 is disabled when you select Plot type to Composite data.

Y format1 — Plot format

Magnitude (decibels) (default) | Mag | Magnitude (linear) | Angle | Real | Imaginary | ...

Plot format, specified as one of the following.

Y parameter1	Y format1
S11, S12, S21, S22, GammaIn, GammaOut, TF1, TF2, TF3, GammaMS, GammaML, and Delta.	dB, Magnitude (decibels), Abs, Mag, Magnitude (linear), Angle, Angle(degrees), Angle(radians), Real, Imag, and Imaginary.
GroupDelay	ns, us, ms, s, and ps.
VSWRIn and VSWROut.	Magnitude (decibels) and None.
OIP3 and IIP3.	dBm, W, and mW.
NF	dB and Magnitude (decibels).
NFactor, K, Mu, and MuPrime.	None
NTemp	Kelvin
Gt, Ga, Gp, Gmag, and Gmsg.	dB, Magnitude (decibels), and None.

Dependencies

To enable Y format1, set Plot type to X-Y plane.

Y format2 — Plot format

Magnitude (decibels) (default) | Mag | Magnitude (linear) | Angle | Real | Imaginary | ...

Plot format, specified as one of the following.

Y parameter2	Y format2
S11, S12, S21, S22, GammaIn, GammaOut, TF1, TF2, TF3, GammaMS, GammaML, and Delta.	dB, Magnitude (decibels), Abs, Mag, Magnitude (linear), Angle, Angle(degrees), Angle(radians), Real, Imag, and Imaginary.
GroupDelay	ns, us, ms, s, and ps.
VSWRIn and VSWROut.	Magnitude (decibels) and None.
OIP3 and IIP3.	dBm, W, and mW.
NF	dB and Magnitude (decibels).
NFactor, K, Mu, and MuPrime.	None
NTemp	Kelvin
Gt, Ga, Gp, Gmag, and Gmsg.	dB, Magnitude (decibels), and None.

Dependencies

To enable Y format2, set Plot type to X-Y plane.

X parameter — Frequency plot

Freq (default)

Frequency plot, specified as Freq.

X format — Frequency plot format

Hz (default) | Auto | kHz | MHz | GHz | THz

Frequency plot format, specified as one of the following.

Auto	Hz	kHz	MHz
GHz	THz

Y scale — Y-axis scale

Linear (default) | Log

Y-axis scale, specified as Linear or Log.

Dependencies

To enable this parameter, set Plot type to X-Y plane.

X scale — X-axis scale

Linear (default) | Log

X-axis scale, specified as Linear or Log.

Dependencies

To enable this parameter, set Plot type to X-Y plane.

Plot — Plot specified data

button

Plot specified data using the plot button.

More About

Network Parameters

In the Z-Parameters field of the block dialog box, provide the Z-parameters for each of the M frequencies as a 2-by-2-by-M array. In the Frequency field, specify the frequencies for the Z-parameters as an M-element vector. The elements of the frequencies vector must be in the same order as the Z-parameters. All frequencies must be positive. For example, the following figure shows the correspondence between the Z-parameters array and the vector of frequencies.

The Z-Parameters Amplifier block uses the RF Toolbox™ z2s function to convert the Z-parameters to S-parameters, and then interpolates the resulting S-parameters to determine their values at the modeling frequencies. See Map Network Parameters to Modeling Frequencies for more details..

Nonlinearity

You can introduce nonlinearities into your model by specifying parameters in the Nonlinearity Data tab of the Z-Parameters Amplifier block dialog box. Depending on which of these parameters you specify, the block computes up to four of the coefficients $$c_1$$, $$c_3$$, $$c_5$$, and $$c_7$$ of the polynomial $$F_{AM/AM}(s)=c_{1}s+c_3{\left|s\right|}^{2}s+c_5{\left|s\right|}^{4}s+c_7{\left|s\right|}^{6}s$$ that determines the AM/AM conversion for the input signal $$s$$. The block automatically calculates $$c_1$$, the linear gain term. If you do not specify additional nonlinearity data, the block operates as a linear amplifier. If you do, the block calculates one or more of the remaining coefficients as the solution to a system of linear equations, determined by the following method. If you provide vectors of nonlinearity and frequency data, then the block calculates the polynomial coefficients using values for the parameters interpolated at the center frequency.

1. The block checks whether you have specified a value other than Inf for:

   • The third-order intercept point ($$OIP3$$ or $$IIP3$$).

   • The output power at the 1-dB compression point ($$P_{1dB,out}$$).

   • The output power at saturation ($$P_{sat,out}$$).

   In addition, if you have specified $$P_{sat,out}$$, the block uses the value for the gain compression at saturation ($$G{C}_{sat}$$). Otherwise, $$G{C}_{sat}$$ is not used. You define each of these parameters in the block dialog box, on the Nonlinearity Data tab.

2. The block calculates a corresponding input or output value for the parameters you have specified. In units of dB and dBm,

   $$\begin{array}{c}{P}_{sat,out}+G{C}_{sat}=P_{sat,in}+G_{lin}\\ P_{1dB,out}+1=P_{1dB,in}+G_{lin}\\ OIP3=IIP3+G_{lin}\end{array}$$

   where $$G_{lin}$$ is $$c_1$$ in units of dB.

3. The block formulates the coefficients $$c_3$$, $$c_5$$, and $$c_7$$, where applicable, as the solutions to a system of one, two, or three linear equations. The number of equations used is equal to the number of parameters you provide. For example, if you specify all three parameters, the block formulates the coefficients according to the following equations:

   $$\begin{array}{c}\sqrt{P_{sat,out}}=c_1\sqrt{P_{sat,in}}+c_3{\left(\sqrt{P_{sat,in}}\right)}^3+c_5{\left(\sqrt{P_{sat,in}}\right)}^5+c_7{\left(\sqrt{P_{sat,in}}\right)}^7\\ \sqrt{P_{1dB,out}}=c_1\sqrt{P_{1dB,in}}+c_3{\left(\sqrt{P_{1dB,in}}\right)}^3+c_5{\left(\sqrt{P_{1dB,in}}\right)}^5+c_7{\left(\sqrt{P_{1dB,in}}\right)}^7\\ 0=\frac{c_1}{IIP3}+c_3\end{array}$$

   The first two equations are the evaluation of the polynomial $$F_{AM/AM}(s)$$ at the points $$(\sqrt{P_{sat,in}},\sqrt{P_{sat,out}})$$ and $$(\sqrt{P_{1dB,in}},\sqrt{P_{1dB,out}})$$, expressed in linear units (such as W or mW) and normalized to a 1-Ω impedance. The third equation is the definition of the third-order intercept point.

   The calculation omits higher-order terms according to the available degrees of freedom of the system. If you specify only two of the three parameters, the block does not use the equation involving the parameter you did not specify, and eliminates any $$c_7$$ terms from the remaining equations. Similarly, if you provide only one of the parameters, the block uses only the solution to the equation involving that parameter and omits any $$c_5$$ or $$c_7$$ terms.

If you provide vectors of nonlinearity and frequency data, then the block calculates the polynomial coefficients using values for the parameters interpolated at the center frequency.

Active Noise

You can specify active block noise in one of the following ways:

• Spot noise data in the Z-Parameters Amplifier block dialog box.

• Noise figure, noise factor, or noise temperature value in the Z-Parameters Amplifier block dialog box.

If you specify block noise as spot noise data, the block uses the data to calculate noise figure. The block first interpolates the noise data for the modeling frequencies using the specified Interpolation method. It then calculates the noise figure using the resulting values.

Version History

Introduced before R2006a