RF Blockset™

S-Parameters Mixer - Model mixer and local oscillator using S-parameters

Library

Mixer sublibrary of the Physical library

Description

The S-Parameters Mixer block models the nonlinear mixer described in the block dialog box, in terms of its frequency-dependent S-parameters, the frequencies and reference impedance of the S-parameters, noise data (including phase noise data), and nonlinearity data.

Network Parameters

The S₂₁ parameter values describe the conversion gain as a function of frequency, referred to the mixer input frequency. The other S-parameters also refer to the mixer input frequency.

The S-Parameters Mixer block interpolates the given S-parameters to determine their values at the modeling frequencies the Output Port block calculates. For more details about how the Output Port block calculates the modeling frequencies, see RF Blockset Algorithms.

RF Blockset software computes the reflected wave at the mixer input ( ) and at the mixer output ( ) from the interpolated S-parameters as

where

and are the mixer input and output frequencies, respectively.
and are the incident waves at the mixer input and output, respectively.

The interpolated S₂₁ parameter values describe the conversion gain as a function of frequency, referred to the mixer input frequency.

Active Noise

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

Spot noise data in the S-Parameters Mixer block dialog box.
Noise figure, noise factor, or noise temperature value in the S-Parameters Mixer 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.

Phase Noise

The S-Parameters Mixer block applies phase noise to a complex baseband signal. The block first generates additive white Gaussian noise (AWGN) and filters the noise with a digital FIR filter. It then adds the resulting noise to the angle component of the input signal.

The blockset computes the digital filter by:

Interpolating the specified phase noise level to determine the phase noise values at the modeling frequencies.
Taking the IFFT of the resulting phase noise spectrum to get the coefficients of the FIR filter.

Note If you specify phase noise as a scalar value, the blockset assumes the phase noise is constant at all modeling frequencies and does not have a 1/f slope. This assumption differs from that made by the Mathematical Mixer block.

Nonlinearity

If power data exists in the data source, the block extracts the AMAM/AMPM nonlinearities from the power data. Power data determines both IP3 and 1 dB gain compression power.

If the data source contains no power data, then you can enter either OIP3 or IIP3 data as a scalar value for nonlinearity in the S-Parameters Mixer block dialog box. You can also specify the 1 dB gain compression power and the output saturation power in the S-Parameters Mixer block dialog box.

If you do not specify the 1 dB gain compression power, the block ignores the output saturation power specification. The block computes and adds the nonlinearity from the OIP3 or IIP3 value for each specified frequency point by:

Converting the specified value into IIP3 (if needed)
Using the third-order input intercept point value in dBm to compute the factor, f, that scales the input signal before the S-Parameters Mixer block applies the nonlinearity:
Computing the scaled input signal by multiplying the mixer input signal by f.
Limiting the scaled input signal to a maximum value of 1.
Applying an AM/AM conversion to the mixer gain, according to the following cubic polynomial equation:

where u is the magnitude of the scaled input signal, which is a unitless normalized input voltage.

If you specify the 1 dB gain compression power, the block computes and adds the nonlinearity to the input signal by:

Converting the specified third-order intercept value into OIP3 (if needed).
Converting the gain, OIP3, and 1dB compression data to linear, unitless values, normalized to 1 volt and the reference impedance Z₀ (which is specified in the data source):

where
- GAIN is the mixer power gain, which is derived from the network parameters.
- OIP3 is the output third-order intercept point.
- PCOMP is the output power at the 1 dB compression point.
Computing the coefficients of the polynomial, , that determines the AM/AM conversion for the input signal s:
Computing the input power at which the output saturates, if it is not specified, according to the following function:

This value is the input power above which the block replaces the AM/AM conversion model with a constant output power value A_sat.
Applying the AM/AM conversion to the input signal

Dialog Box

Main Tab

S-Parameters

S-parameters for a nonlinear mixer in a 2-by-2-by-M array. M is the number of S-parameters.

Frequency (Hz)

Frequencies of the S-parameters as an M-element vector. The order of the frequencies must correspond to the order of the S-parameters in S-Parameters. All frequencies must be positive. The following figure shows the correspondence between the S-parameters array and the vector of frequencies.

Reference impedance (ohms)

Reference impedance of the S-parameters as a scalar or a vector of length M. The value of this parameter can be real or complex. If you provide a scalar value, then that value is applied to all frequencies.

Interpolation method

The method used to interpolate the network parameters. The following table lists the available methods describes each one.

Method	Description
`Linear` (default)	Linear interpolation
`Spline`	Cubic spline interpolation
`Cubic`	Piecewise cubic Hermite interpolation

Mixer Type

Type of mixer. Choices are Downconverter (default) and Upconverter.

LO frequency (Hz)

Local oscillator frequency. If you choose Downconverter, the blockset computes the mixer output frequency, , from the mixer input frequency, , and the local oscillator frequency, , as . If you choose Upconverter, .

Note The mixer output frequency must be positive. This means that if you choose a downconverting mixer, must be greater than . Otherwise, an error appears.

Noise Data Tab

Phase noise frequency offset (Hz): Vector specifying the frequency offset.
Phase noise level (dBc/Hz): Vector specifying the phase noise level.
Noise type: Type of noise data. The value can be Noise figure, Spot noise data, Noise factor, or Noise temperature. This parameter is disabled if the data source contains noise data.
Noise figure (dB): Scalar ratio, in decibels, of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (S_i/N_i)/(S_o/N_o). This parameter is enabled if Noise type is set to Noise figure.
Minimum noise figure (dB): Minimum scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (S_i/N_i)/(S_o/N_o). This parameter is enabled if Noise type is set to Spot noise data.
Optimal reflection coefficient: Optimal mixer source impedance. This parameter is enabled if Noise type is set to Spot noise data.
Equivalent normalized resistance: Resistance normalized to the resistance used to take the noise measurement. This parameter is enabled if Noise type is set to Spot noise data.
Noise factor: Scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (S_i/N_i)/(S_o/N_o). This parameter is enabled if Noise type is set to Noise factor.
Noise temperature (K): Equivalent temperature that produces the same amount of noise power as the amplifier. This parameter is enabled if Noise type is set to Noise temperature.

Nonlinearity Data Tab

IP3 type: Type of third-order intercept point. The value can be IIP3 (input intercept point) or OIP3 (output intercept point). This parameter is disabled if the data source contains power data or IP3 data.
IP3 (dBm): Value of third-order intercept point. This parameter is disabled if the data source contains power data or IP3 data. Use the default value, Inf, if you do not know the IP3 value. This parameter can be a scalar (to specify frequency-independent nonlinearity data) or a vector (to specify frequency-dependent nonlinearity data).
1 dB gain compression power (dBm): Scalar output power value at which gain has decreased by 1 dB. This parameter is disabled if the data source contains power data or 1 dB compression point data. Use the default value, Inf, if you do not know the 1 dB compression point. This parameter can be a scalar (to specify frequency-independent nonlinearity data) or a vector (to specify frequency-dependent nonlinearity data).
Output saturation power (dBm): Scalar output power value the amplifier produces when fully saturated. This parameter is disabled if the data source contains output saturation power data. The block uses this value only if you specify 1 dB gain compression power (dBm). Use the default value, Inf, if you do not know the saturation power. This parameter can be a scalar (to specify frequency-independent nonlinearity data) or a vector (to specify frequency-dependent nonlinearity data).
Frequency (Hz): Scalar or vector value of frequency points corresponding to the third-order intercept and power data. This parameter is disabled if the data source contains power data or IP3 data. If you use a scalar value, the IP3 (dBm), 1 dB gain compression power (dBm), and Output saturation power (dBm) parameters must all be scalars. If you use a vector value, one or more of the IP3 (dBm), 1 dB gain compression power (dBm), and Output saturation power (dBm) parameters must also be a vector.

Visualization Tab

For information about plotting the amplifier parameters, see Plotting Model Data.