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# Mixer

Model mixer in RF systems

Elements

## Description

The Mixer block performs signal frequency translation and nonlinear amplification.

For a given RF input signal VRF = ARFcos(ωRFt) and an LO input signal VLO = ALOcos(ωLOt), the mixer multiplies the signals at the input ports:

$\begin{array}{c}{V}_{in}{V}_{LO}={A}_{in}\mathrm{cos}\left({\omega }_{in}t\right){A}_{LO}\mathrm{cos}\left({\omega }_{LO}t\right)\\ \frac{{A}_{in}{A}_{LO}}{2}\mathrm{cos}\left[\left({\omega }_{in}+{\omega }_{LO}\right)t\right]+\frac{{A}_{in}{A}_{LO}}{2}\mathrm{cos}\left[\left({\omega }_{in}-{\omega }_{LO}\right)t\right]\end{array}$

This mixing converts the frequency of RF signal to ωRF + ωLO and ωRF – ωLO. For the mixer to perform this operation correctly, you must include the frequencies ωRF + ωLO or ωRF – ωLO in the simulation frequencies the Configuration block calculates.

The Power gain specification for this block relates the power of a single-sideband (SSB) to the input.

After mixing the RF and LO signals, the mixer block performs amplification. To model linear amplification, the mixer scales the signals by the coefficient a1. A Voltage Controlled Voltage Source (VCVS), specified with a polynomial, implements nonlinear amplification. The polynomial includes saturation automatically and produces additional intermodulation frequencies.

## Dialog Box and Parameters

### Main Tab

Source of conversion gain

Specify the source parameter of the conversion gain as:

• Available power gain — The block uses the value of the Available power gain parameter to calculate the linear voltage gain term of the polynomial VCVS, a1. This calculation assumes a matched load termination for the mixer.

• Open circuit voltage gain — The block uses the value of the Open circuit voltage gain parameter as the linear voltage gain term of the polynomial VCVS, a1.

• Polynomial coefficients — The block implements a nonlinear voltage gain according to the polynomial you specify. The order of the polynomial must be less than or equal to 9 and the coefficients are ordered in ascending powers. If a vector a has 10 coefficients, [a0, a1, a2, …, a9], the polynomial it represents is Vout = a0 + a1 Vin + a2 Vin2+ ⋯ + a9 Vin9. In this case, a1 represents the linear gain term, and the modeling of higher-order terms is done according to [1].

For example, the vector [a0, a1, a2, a3] specifies the relation Vout = a0 + a1 Vin + a2 Vin2 + ⋯ + a3 Vin3.

Trailing zeroes are omitted; if a3 = 0, [a0, a1, a2] defines the same polynomial as [a0, a1, a2, 0]. The default value of this parameter is [0 1], corresponding to the linear relation Vo = Vi.

The default value of this parameter is Available power gain.

Available power gain

When Source of conversion gain is Available power gain, specify the linear gain of the mixer. Specify the units from the corresponding drop-down list. The default value of this parameter is 0 dB.

Open circuit voltage gain

When Source of conversion gain is Open circuit voltage gain, specify the open circuit voltage gain of the mixer. Specify the units from the corresponding drop-down list. If you specify the units as None, the gain must be positive. The default value of this parameter is 0 dB.

Input impedance (ohms)

Specify the scalar impedance at the In port of the mixer. The default value of this parameter is 50 Ω.

Output impedance (ohms)

Specify the scalar impedance at the Out port of the mixer. The default value of this parameter is 50 Ω.

LO impedance (ohms)

Specify the scalar impedance at the LO port of the mixer. The default value of this parameter is Inf Ω.

Noise figure (dB)

Specify the single-sideband (SSB) noise figure of the mixer. The default value of this parameter is 0 dB.

To model noise in circuit envelope model with a Noise, Amplifier, or Mixer block, you must select the Simulate noise check box in the Configuration block dialog box.

The following table summarizes the two competing definitions for specifying SSB noise, where the image frequency (IM) is defined as ωIM = ωLO + (ωLO – ωRF).

Noise ConventionSignal at RF FrequencySignal at IM FrequencyMixer Block Supports This Model?
Single-sideband noise (SSB)S + N, signal with noiseN, noise onlyYes
IEEE definition of single-sideband noise (SSBIEEE)S + N, signal with noiseNo signalNo; you can create an equivalent model using an ideal filter created from an S-parameters block.

Ground and hide negative terminals

Select this option to internally ground and hide the negative terminals. Clear this to expose the negative terminals. By exposing these terminals, you can connect them to other parts of your model.

By default, this option is selected.

### Nonlinearity Tab

The specification is identical to that of the Amplifier block, except that it includes a scaling factor of 2 to account for the SSB mixer conversion gain.

Nonlinear polynomial type

Specify either an Even and odd order or Odd order polynomial nonlinearity. The default value is Even and odd order.

• When you select Even and odd order, the amplifier can produce second- and third-order intermodulation frequencies in addition to a linear term.

• When you select Odd order, the amplifier generates only odd order intermodulation frequencies.

The linear gain determines the linear a1 term. The block calculates the remaining terms from the specified parameters. These parameters are IP3, 1-dB gain compression power, Output saturation power, and Gain compression at saturation. The number of constraints you specify determines the order of the model.

The preceding figure shows the graphical definition of the nonlinear amplifier parameters.

Intercept points convention

Specify either an Input-referred or Output-referred convention. Use this specification for the intercept points, 1-dB gain compression power, and saturation power.

The default value is Output.

IP2

When Nonlinear polynomial type is Even and odd order, specify the second-order intercept point of the amplifier.

The default value is inf dBm, which corresponds to an unspecified point.

IP3

Specify the third-order intercept point of the amplifier. The default value is inf dBm, which corresponds to an unspecified point.

1-dB gain compression power

When Nonlinear polynomial type is Odd order, specify the 1-dB gain compression point. The 1-dB gain compression point must be less than the output saturation power.

The default value is inf dBm, which corresponds to an unspecified point.

Output saturation power

When Nonlinear polynomial type is Odd order, specify the output saturation power. The block uses this value to calculate the voltage saturation point used in the nonlinear model. In this case, the first derivative of the polynomial is zero, and the second derivative is negative.

The default value is inf dBm, which corresponds to an unspecified point in the polynomial model.

Gain compression at saturation

When Nonlinear polynomial type is Odd order, specify the gain compression at saturation. This parameter cannot be set unless Output saturation power is specified.

The default value is inf dBm.

## References

[1] Grob, Siegfried and Lindner, Jurgen, "Polynomial Model Derivation of Nonlinear Amplifiers", Department of Information Technology, University of Ulm, Germany.