# 11.14: Mixer

• • Michael Steer
• Lampe Distinguished Professor (Electrical and Computer Engineering) at North Carolina State University

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

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