Page 233 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

- 2'lT t + 'IT 2
~ 1 2
which then yields the square-law term:

[ 2 = (21TF l)f

[2 1 2 21T · 2£ ]2 14- 2
Because we are interested only in the "modulated" or multiplying term between the
two signals, the second term is of interest, which then reduces to

(2'1Tl- 1 t
1 2
+ 1'2)t 4-1 )
] 2
So now, if we return to Equation (14-10) for just the first three terms, we have

- I I / 7 2

and if we substitute for the two signals at the input for V sig and refer to equations
(14-11) and (14-12), we have

le = CQ + Xt / v)[ C (21T 21T 2t] + let! 74 / vZ){[ I 21T It 2
+ [2 11 (2n 1 t) 21T. 2e)] + [ . c 2n 2t)f}

Removing or ignoring the second-order harmonic distortion terms [Al cos(2nF1 tjf
and [A2 cos(2nF2t)f, we get

/ l J

I . / 2 [2 1 2 1T I J

And using Equation (14-13) for substitution, we arrive at

le = I :Ql + ;Q(3 Iv [ ] I 21T 1 t + 1. . 21T 2t] +
I
I . 740/ V2){ ) 2 0 [21T 1 - 2)t] + 1 2 ~ [21T( 1 + 2 t] } 4- 4)

So what does Equation (14-14) really mean? For determining the intermodulation
distortion products and the difference-frequency term, this equation is really
accurate for signals of less than about 13mV peak. Any larger signals will start to
include errors, and these errors will increase as the input signal's amplitude rises
above 26 mV peak.

Let's try the following scenario: The signal Ai cos(2nF1t) is the oscillator signal with
Al = 0.013. A2 is the RF input signal with A2 < 0.013 volt (e.g., typically = mV or
less). The second-order intermodulation distortion 1M2 as a function of one of the
input signals is