Mixer

A mixer is a three port circuit element that takes two input signals and creates an output signal that is a combination of both the RF In and LO. In this design, the mixer multiplies the unknown input signal (frequency = f_sig) with the known local oscillator (frequency = f_LO).

The resultant output is composed of the original RF signal (f_sig), the local oscillator signal (f_LO), and both the sum-and-difference of the RF and LO inputs ( f_LO-f_sig and f_LO+f_sig , respectively), and the sum-and-difference of higher harmonics, such as (2f_LO-f_sig/2f_sig-f_LO and 2f_LO+f_sig/2f_sig+f_LO).

The diagram below shows the fundamental mixed products, and ignores the higher harmonics for clarity:

Tech Note: The output frequency from the mixer is called the Intermediate Frequency (IF)

Example

RFin = 10MHz

LO = 2GHz

What are the values of the downconverted and upconverted IF outputs?

Downconverted Signals are calculated by:

IF_down = f_LO-f_RF

f_LO = 2GHz = 2e⁹ Hz f_RF = 10MHz = 10e⁶ Hz

IF_down = (2e⁹ Hz) - (10e⁶ Hz) = 1.99e⁹ Hz = 1.99GHz

Upconverted Signals are calculated by:

IF_up = f_LO+f_RF

IF_up = (2e⁹ Hz) + (10e⁶ Hz) = 2.01e⁹ Hz = 2.01GHz

In reality, there can be multiple mixer stages used in series to provide the right balance of resolution and operational frequency range. To provide fine frequency resolution, we need to have narrow bandwidth filters. But, we want the filter to operate over a large range of frequencies. These two requirements often seem to be at odds because narrow bandpass filters are not effective over large frequency ranges and adding filters increases the cost and complexity of a design.

Multiple IF Stages

By adding multiple IF stages, you can maximize the frequency resolution and extend the operating range. Multistage IF sections can upconvert ("step up") or downconvert ("step down") the f_LO to a different range where they can be filtered to remove unwanted frequencies at each step as shown below:

The use of multiple mixing stages allows the instrument to have superior sensitivity, good frequency stability and high frequency selectivity that enable the instrument to have a wide operating frequency range with the ability to differentiate signals that have frequencies that are close together.

The below video shows a mixer output on a Spectrum Analyzer