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Model mixer in RF systems

**Library:**RF Blockset / Circuit Envelope / Elements

The Mixer block performs signal frequency translation and nonlinear amplification.

For a given RF input signal, *V*_{RF} = *A*_{RF}cos(*ω*_{RF}t) and an LO input signal *V*_{LO} = *A*c_{LO}cos(*ω*_{LO}t), the mixer multiplies the signals at the input ports:

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

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.

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