Electronic Devices and Circuits Engineering Sciences 154

Mixer Circuit

Using the Shockley Diode Equation we can write

This is a pretty complicated expression, but we can get a reasonable and useful result with a bit algebra and analysis.  Let us assume that there are dc biases on the signals (usual case) so that

where are fluctuations around the bias values .
Putting these expressions the Shockley equation we get

Using a standard (Taylor) expansion of the exponential for small argument - viz.

Thus we obtain the following exact transcendental equation relating the bias voltages:

which, in turn, allows us to write the following approximate equation for the voltage fluctuations

This is still a pretty complicated affair, we can handle it if write plug in to the equation above

If we ignore terms ,  or higher, we get

or

Finally, we see that for

we have

Notice that we can enhance these two coefficients by chosing the right bias!  In particular, the maximum value  occurs when  or .