Page 228 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

Figure 14-4 Two "high" frequency signals that are combined and squared,
resulting in a modulating waveform. The Xaxis shows time, whereas the
Yaxis shows the amplitude.
So, clearly, a nonlinear device causes a modulation effect, which, in turn, causes a
mixing effect. If we just substitute two sinusoidal signals of frequencies Fl and F2

into a squaring function, we get the following:

[ 0 (21T It) + (2'7T 2t)]2 = [ 0 (2'7T It)]2 + [2 (2'7T It) 0 (2'iT 2t)] + [ 0 (2'lT 2t)]2
(14-2)
Note that the first and third terms, [cos(2~Flt)f and [cos(2IJF2~f, will generate
second harmonics of each of the two input signals, and more important, the middle

term shows multiplication of the two input signals.
From a trigonometric identity, 2[cos(a)][cos(~)] = cos(a + ~) + cos(a - ~) and in
particular, that middle term

[2 (27T It .. 27T 2t)] = 0 27T 1 - 2}t] + . [2'iT( + 2)t] (14-3)
Note that the squaring function provides both a difference-frequency term (Fl -
F2) and a summing-frequency term (Fl + F2). And it should be noted that signals