# 11.14: Mixer

Frequency conversion or mixing is the process of converting information centered at one frequency (present in the form of a modulated carrier) to another frequency. The second frequency is either higher, in the case of frequency up-conversion, where it is more easily transmitted; or lower when mixing is called frequency down-conversion, where it is more easily captured, see Figure 11.8.4.

Conversion loss, $$L_{C}$$: This is the ratio of the available power of the input signal, $$P_{\text{in}}(\text{RF})$$, to that of the output signal after mixing, $$P_{\text{out}}(\text{IF})$$:

$\label{eq:1}L_{C}=\frac{P_{\text{in}}(\text{RF})}{P_{\text{out}}(\text{IF})}$

Example $$\PageIndex{1}$$: Mixer Calculations

A mixer has an LO of $$10\text{ GHz}$$. The mixer is used to down-convert a signal at $$10.1\text{ GHz}$$ and has a conversion loss, $$L_{c}$$ of $$3\text{ dB}$$ and an image rejection of $$20\text{ dB}$$. A $$100\text{ nW}$$ signal is presented to the mixer at $$10.1\text{ GHz}$$. What is the frequency and output power of the down-converted signal at the IF?

Solution

The IF is at $$100\text{ MHz}$$. $$L_{c} = 3\text{ dB} = 2$$ and from Equation $$\eqref{eq:1}$$ the output power at IF of the intended signal is

$\label{eq:2}P_{\text{out}}=P_{\text{in}}(\text{RF})/L_{c}=100\text{ nW}/2=50\text{ nW}=-43\text{ dBm}$