Page 234 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

1M2 = ( lcn740/ Icn38)A,A,/A, = 19A, = 19(0.01 3) = 0.25 = 25 percent = 25%
(1 4-1 5)
Note: (I 740/I 38) = (IcQ/I cQ ) (740/38) = 1(740/38) = 19
cQ
cQ
But what does this 25 percent of 1M2 distortion mean? This means that the 1M2
distortion components have an equivalent transconductance of 25 percent of the
small-signal transconductance. So, if the transistor is biased at 1 mA, the
transconductance for generating the sum- or difference-frequency signal is 25%(gm
= 25%(0.0384) A/V, or 9.5 mA/V.

So, for example, for an oscillator signal of 0.013 volt peak sinusoidal waveform
added or combined with a small-signal RF signal V RF into the base and emitter
junction of a bipolar transistor amplifier operating at 1 mA, the IF signal current

IS;9-IF with the difference frequency is

ISI~I F = V Rf X 25%(glll) = V X 9.5 rnA/ V
Rf
Note that the conversion transconductance is IS;9_IF/VRF. And for a O.013-volt peak
sinusoidal oscillator signal into the mixer, the conversion transconductance is
25%(gm).
Equation (14-15) shows that the conversion gain or IF signal transconductance is

controlled by the oscillator's signal amplitude. But it should be noted that increasing
the oscillator's peak amplitude A, beyond O.013-volt will raise that 25 percent
number to something higher that is no longer linear or proportional. By using other
mathematical techniques that are more accurate than the power-series expansion

[e.g., Equation (14-8) or (14-9)], it is found that if the oscillator signal is raised to
26 mV peak, or 2 3 13 mV peak, we get 45%(gm) instead of 50%(gm) for the
conversion gain.
In previous chapters concerning the superheterodyne radio, it was mentioned that
the oscillator voltage into the mixer or converter is in the range of about 200 mV to
300 mV peak to peak or 100 mV to 150 mV peak. The next section will explore a

more accurate model for bipolar mixer circuits with large oscillator voltages that are
beyond 13 mV peak.
Another technique to more accurately characterize the behavior of a simple
transistor mixer is to view the transistor as having a time-varying transconductance

that depends on the oscillator signal. Recall that the small-signal transconductance
gm = I /(0.026 volt). Usually we define a small-signal transconductance as gmQ =
cQ
I /(0.026 volt), where ICQ is a constant DC current, which then makes gmQ a
cQ
constant small-signal transconductance.
But when an oscillator voltage is added with the bias voltage, the collector current

is actually time-varying, and thus the transconductance is changing with time in
relation to the amplitude and frequency of the oscillator signal. Therefore, the
output collector current as a function of time can be thought of as