Page 232 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

equation holds up very well in determining harmonic distortion. Higher-amplitude

sinusoidal waveforms of 50 mV or more peak will cause gain compression, and
predicting the harmonic distortion will become inaccurate. Therefore, for the higher
amplitude Signals, modified Bessel functions are used instead of the power series
expansion in equation (14-9).
Before moving on to how harmonic and intermodulation distortion is calculated, we
should review Equation (14-9):

le = leQ [l + (38/ v)V". + (740/ v' )V,i,.+ (9 ,467/ v:l)V;:.+ .. '1 (1 4-9)

Spreading out the terms, we get

(14-10)
Now let's look at the first four terms and see what they represent.
1. ICQ 1 = ICQ is DC collector current or bias current.

2. I CQ(38/v)VSig = is the linear amplification term. The small-signal
transconductance gm = ICQ (38). For example, at 1 mA of Ico, the DC collector
current results in 38 mA/V for the small-signal transconductance. And 100 ~A of ICQ

results in 3.8 mA/V of small-signal transconductance.
3. ICQ(740/y' )V/Si9 is the square-law term that generates a DC offset plus
second-order harmonic and intermodulation distortion. Second-order
intermodulation distortion from two signals of frequencies F1 and F2 results in

output signals with frequencies of (F1 1 F2) and (Fl - F2).
3
4. IcQ(9,467/v )V'3Sig is the cubic term, which produces third-order harmonic and
intermodulation distortion. For two signals at the input of Fl and F2, the third-order

intermodulation signals are more complicated than the second-order
intermodulation components. The third-order intermodulation distortion products
for the two input signals will generate signals that have frequencies of (2F1 - F2),
(2F2 - Ft), (2Fl 1 F2), and (2F2 1 Fl).
To calculate distortion, such as second- or third-order distortion, Vsig is set to a

single or multiple sinusoidal signals. For mixing purposes, there are generally two
signals at the input of the mixer, the RF signal and the local oscillator signal. Thus,
for now, we will not concern ourselves with harmonic distortion but just
concentrate on second-order intermodulation distortion because it is this distortion
product that generates the difference-frequency signal (Fl - F2).

Consider the input two sinusoidal waveforms from Equation (14-2):

[cos(2'lTFlt) + cos(2'lTF2tW = V,i = [cos(2'lTFlt)]' +
g
[2 cos(2'lTF lt) cos(2'lTF2t)] + [COS(21TF2tW (14-2)

Let's generalize the amplitudes of each input signal with A, and A, such that