Page 279 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

And if V RF = О volt, then both inputs of the multiplexer аге О volt. The output of the

multiplexer thus switches between О volt and О volt to provide а О volt
(square-wave) signal ог по signal. 50, when the input signal drops to О volt, there
is по caггier ог oscillator signal at the output of the multiplexer, which balances out
ог removes the oscillator signal from the output.
We thus will characterize this dual-polarity squ.are-wave signal and its Fourier series

as

(l) =.!. (21Т .l) - ."- 1т l +.!. (1 1i "l) - 7 - О 1471" [) . ..
р 1т - .. ' 51Т ... 'п (1 _ )

Notice that the bipolar square-wave signal SQbP (f) has по DC teгm. This makes
sense because there is ап equal number of positive and negative pulses from this
signal, which aveгages to О.

The output of the mixer now сап Ье characterized as

I 11 Х
L

21Тft - ~ . ) 41Т f.t . . ,]
: 311'
(15-15)
Equations (15-14) and (15-15) thus show the multiplying effect of the input RF
signal and the oscillatoг signal.
То this point, ап intuitive explanation has Ьееп presented. In practice, if опе builds
the circuit shown in Figure 15-20, а multiplication of the RF and oscillator sigлаls
will Ье verified. However, there is another way to show тоге formally why the

multiplexeг ciгcuit works as а mixer.
The signal at the А teгminal сап Ье thought of as being multiplied Ьу а
square-wave signal 5Q(f) fгom Еquаtiол (15-5) that has ал amplitude range from О
to 1. The signal at the В teгminal сап Ье thought at of as the inveгted signal from
the А teгminal multiplied Ьу а 180-degree phase-shifted version of SQ(f). The mixer

output then is the summation of these two multiplication operations.
А 180-degree phase-shifted versiOin of SQ(t) = [1 - SQ(t)]. Figure 15-21 presents а
gгaph of 5Q(f), and Figure 15-22 presents а graph of [1 - SQ(f)]. Thus, Figure
15-22 shows equivalent of the square-wave signal SQ(t), shifted Ьу 180 degгees.