Page 244 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

2
l_ r I 't" if _ r
Now let's take a look at the harmonic conversion transconductance of the
differential-pair mixer. For mixing at the fundamental frequency, Equation (14-18)
states

I 1 I F = [I : 'in 21T 2 t [; -'in 21T l)t = F ;, ['in(21T! 1 t ['in 21T 2)t ·.14-

But we can modify this equation for any Mh harmonic by factoring N, which leads
to

I 1_1l'.J - l .. in 'ITl· 2 LJ[; ~ in 21T lJ -

T f-[ in 27Tl 1 l[ in 27l' 2 t]I 1 -1
!
And this leads to a modification of Equation (14-19):

T ,1_11' = 1 R F ~ 1 - 2 t] - + 2 t } 1-2
{
And for an Mh harmonic, where N is an odd number, the output signal is

_
I .1 IF _ = Il<l' ~f { 1 - I 2 tl - 1 + 2 tl } ] -21)
11
And thus the conversion transconductance is
1 -
n
1T
where gm3 = IEEjO.026 volt.
For example, for harmonic mixing based on the fifth harmonic to provide an output
signal whose frequencies are SFOSC ± F Rf , the conversion transconductance is

.~ 1
t ) -
1i
where gm3 = IEEjO.026 volt the small-signal transconductance of Q3 in Figure 14-9.

Mixer Oscilllator Circuits
At this point of writing this chapter I am glad to leave the world of complicated

equations, So back to circuits!
In essence, some oscillator circuits can double as a mixer circuit as well. You have
seen these circuits in Chapters 8 and 10, and they are called converter circuits. The
conversion gain analysis is the same as in the preceding section for a one-transistor
mixer. Typically, the self-oscillating voltage is usually set for about 100 mV to 200
mV peak into the base-emitter junction for the converter circuit, so the conversion

transconductance for simple mixing will be about the same as the small-Signal
tra nscond uctance.