Signal frequency spectrum down-conversion is achieved by multiplying the radio-frequency signal by a local oscillator signal in a circuit known as a mixer. This multiplication produces two signals whose frequency content lies about the sum and difference frequencies of the center frequency of the original signal and the oscillator frequency. Two signals at frequencies f1 and f2 are applied to a mixer, and it produces new signals at the sum f1 + f2 and difference f1 - f2 of the original frequencies.

A simple technique which uses a diode can be is employed for the purpose of obtaining multiplication. A diode is a non-linear (or non-ohmic) device/element, which means its response (current) is not proportional to its input (voltage). The diode therefore does not reproduce the frequencies of its driving voltage in the current through it, which allows the desired frequency manipulation. The current 'I' through an ideal diode as a function of the voltage 'V' across it is given by

And can be approximated for small x (that is, small voltages) by the first few terms of that series. Suppose that the sum of the two input signals v1 + v2 is applied to a diode, and that an output voltage is generated that is proportional to the current through the diode (perhaps by providing the voltage that is present across a resistor in series with the diode). Then, disregarding the constants in the diode equation, the output voltage will have the form

The first term on the right is the original two signals followed by the square of the sum, which can be rewritten as

.

The multiplied signal is present as the above equation shows. It represents all the higher powers of the sum which we assume to be negligible for small signals. As every multiplication produces sum and difference frequencies, from the quadratic term of the series we expect to find signals at frequencies 2f1 and 2f2 from and , and f1 + f2 and f1 f2 from the v1v2 term. Often, so the difference signal has a much lower frequency than the others; extracting this distinct signal is often the principal purpose of using a mixer in such devices as radio receivers.

Filter: -

The other terms of the above series give rise to other weaker signals at various frequencies which act as noise for the desired signal. They may be filtered out. The filter shown in the block diagram performs this purpose.

IF amplifier: -

It is an amplifying circuit in a (RF) receiver that processes and enhances a down-converted or modulated signal. A variable local oscillator is used in the receiver to hold the difference-signal center frequency constant as the receiver is tuned. The constant frequency of the down-converted signal is called the
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