Model mixer in RF systems

Elements

The Mixer block performs signal frequency translation and nonlinear amplification.

For a given RF input signal *V _{RF}* =

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

This mixing converts the frequency of RF signal
to *ω _{RF}* +

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 a_{1}.
A Voltage Controlled Voltage Source (VCVS), specified with a polynomial,
implements nonlinear amplification. The polynomial includes saturation
automatically and produces additional intermodulation frequencies.

**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, a_{1}. 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, a_{1}.`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, [,`a`

_{0},`a`

_{1}, …,`a`

_{2}], the polynomial it represents is`a`

_{9}*V*_{out}=*a*_{0}+*a*_{1}*V*_{in}+*a*_{2}*V*_{in}^{2}+ ⋯ +*a*_{9}*V*_{in}^{9}. In this case,*a*_{1}represents the linear gain term, and the modeling of higher-order terms is done according to [1].For example, the vector [

*a*_{0},*a*_{1},*a*_{2},*a*_{3}] specifies the relation*V*_{out}=*a*_{0}+*a*_{1}*V*_{in}+*a*_{2}*V*_{in}^{2}+ ⋯ +*a*_{3}*V*_{in}^{3}.Trailing zeroes are omitted; if

*a*_{3}= 0, [*a*_{0},*a*_{1},*a*_{2}] defines the same polynomial as [*a*_{0},*a*_{1},*a*_{2}, 0]. The default value of this parameter is [0 1], corresponding to the linear relation*V*_{o}=*V*_{i}.

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 ω

_{IM}= ω_{LO}+ (ω_{LO}– ω_{RF}).Noise Convention Signal at RF Frequency Signal at IM Frequency Mixer Block Supports This Model? Single-sideband noise (SSB) *S*+*N*, signal with noise*N*, noise onlyYes IEEE definition of single-sideband noise (SSB _{IEEE})*S*+*N*, signal with noiseNo signal No; 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.

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

*a*_{1}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`

.

The example, Validating IP2/IP3 Using Complex Signals, verifies the nonlinear modeling capabilities of the Amplifier block.

The example, Impact of an RF Receiver on Communication System Performance, performs quantitative noise analysis of the noise from an RF cascade.

The section, Create a Low-IF Receiver Model, uses an amplifier in an IF receiver with specified gain and noise figure.

The section, Model an RF Mixer, steps through setting up an RF mixer in the SimRF™ environment.

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

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