# Mixer Image Frequency

When a mixer is used to translate a signal either up or down in frequency, it does so for every spectral component that lies within the bandwidth of its circuitry. Due to the nonlinear nature of the mixer - a feature necessary for mixing - harmonics of the input frequencies are generated that also translate up and down with every other frequency present.

The result is the translation of the fundamental inputs (the local oscillator and the signal of interest), and also the intermodulation products. Intermod products are covered in another page on RF Cafe, but here we are concerned with the special case of frequency components that generate what are termed "image products."

An image frequency is one which lies equidistant from the LO frequency, but on the opposite side, as shown in the drawing below (down-conversion shown). In this case, we assume the frequency band desired to be translated down to a lower frequency is the one represented by the orange triangle. It can be seen from the dashed lines from each of the band regions (orange triangle and green rectangle) that unless some means is provided to prevent the process, both bands will be translated down to the same set of down-converted frequencies.

Image Frequency in a Down-conversion

Equations label the lines to indicate the origin of each product. Notice that a negative image of the "positive" frequencies is shown to the left of 0 Hz (DC). Negative frequencies are often used in order to make the equations easier to visualize (substitute fLO=-fLO and FImage=-FImage). It prevents the equations from needing to indicate subtracting a negative number, which is the equivalent of addition.

The fundamental equation for calculating the resulting frequencies from the presence of a local oscillator (fLO), the intended RF signal (fRF), and the unintended image (FImage), are as follows:

f = fLO - fRF

f = FImage - fLO = fRF + 2fIF

Ok, then how do you prevent the image frequency from ending up in the IF band? There are two methods that can be used alone or together, depending on your system requirements. The first is to use a filter to prevent the image frequency from ever getting to the mixer input. The other is to use a mixer whose construction is such that a phasing technique is used to cancel out the image frequency (an image-reject mixer).

See A Graphical Approach to Mixer Spurious Analysis for more information.