11.14: Mixer

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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

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