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# Frequency Transposition

Chapter written by Jean-Luc GAUTIER.

# 3.1. Operating principles

Frequency transposition is carried out using a mixer circuit, which shifts a signal’s spectrum centered on the initial frequency f around frequency f0.

There are two types of frequency transposition:

– From lower to higher frequencies, also referred to as upconversion. The mixer is then an up-converter.
– From higher to lower frequencies or referred to as downconversion. The mixer is, in this case, a down-converter.

The mathematical operation used in frequency transposition is multiplication. If the input signal is multiplied by a sinusoidal signal at frequency f0, the output signal can be written as:

[3.1] Equation [3.1] highlights two points:

– First, the transposition uses multiplication, which is a nonlinear function. Multiplication requires two signals: the input signal to be transposed and a sinusoidal signal, which defines the shift frequency. The latter is referred to as the local oscillator signal, and the corresponding frequency is the local oscillator’s frequency fLO. In practice, an ideal multiplier circuit is not feasible in microwave frequencies. It is therefore necessary to approximate this function using the nonlinearity of several components.
– Second, multiplication generates two transposed signals, so the undesired frequency will have to be filtered out depending ...

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