Frequency transposition is carried out using a mixer circuit, which shifts a signal’s spectrum centered on the initial frequency *f* around frequency *f*_{0}.

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 *f*_{0}, 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 *f*_{LO}. 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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