Page 242 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

I ,) = lI ' · + I , in(21T ' 2)l]{ .5 + ~[ in(21T 1)l + ~. in(21T ' 1)l + ~ in(21T ;~ 1)1
Rt
+ f in 211'7 1 t + . . ·n 1 -1 )

If the harmonics are ignored, we have

, = .[ _ + in 21T 2 t + 2 , in 2'TT 1 t 14 1 7
.. 1 I _ Rf T;'
Since the RF signal at frequency F2 and oscillator signal at frequency Fl can be
filtered out, let's just look at the relevant product term related to the IF signal,
which is a signal at frequency Fl - F2 or F1 1 F2. Therefore,

le) I~' = [IIU' in 21T 2 t][~ in 21T 1 )t] = I , M in(21T 1 t][ in(21T 2)t]
Rf
1 - 2 t] - + 2 t] } 14-1

= I RF~ -21T[ - 2)t] - 211')[ 1 + 2 t] } (1 -1
And if the RF signal voltage is small, such as less than 10 mV peak,

x
1
where gm3 = IEEjO.026 volt and V in is the amplitude of the RF signal, then

ill X , ! { . 2)t] - 27T)l" lJ}
:1 II' 271" [ 4} -
The conversion transconductance is gm3( l/p). So, if lEE = 1 mA, then the

conversion transconductance is 0.0384/p = 0.0122 mho.
One should note that the square-wave signal from the differential-pair mixer
consists of odd harmonics that are attenuated by a factor of 1/ N, where N is the
odd harmonic. So, for example, the third harmonic is one-third the amplitude of the
fundamental frequency and the eleventh harmonic is one-eleventh the amplitude of

the fundamental frequency. Therefore, the conversion transconductance for mixing
with the harmonic of frequency Fl is just multiplied by a factor of 1/ N.
Thus the differential-pair mixer equation (14-16) shows that the RF signa;1 current
also multiplies with signals whose frequencies are odd multiples of Fl. This then
means that mixes with the harmonics of Fl and thus provides harmonic mixing.

Harmonic Mixer Circuits

In the previous two circuits, the one-transistor mixer and differential-pair mixer, we
were concerned only with the mixers generating a sum- or difference-frequency
signal l, with frequency (F1 - F2) or (Fl + F2). But we also have seen that both the
Single-transistor and differential'-pair mixer circuits generate signals with harmonics
of the oscillator frequency.
If we define the frequency Fl as Fosc and frequency F2 as F RF , then we can show

examples of simple mixing (sum and difference frequencies) and harmonic mixing
in Table 14-3.