Page 276 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

whose frequency exceeds ('/2)f 5 is the equivalent of sampling another signal of the

same amplitude but with а frequency of (f - fin) ог If - finl. This also implies that if
s
5
the output of the sampling circuit includes а capacitor to form а sample-and-hold
circuit, the actual conversion gain will Ье almost lossless when I f s - fin I < < (5 О (See
the sample-and-hold ciгcuit in Fig'uгe 12-36.)

For example, if а mixer is to translate amplitude-modulated (АМ) radio signal at
990 kHz (f iп ) to а low IF signal such as 10 kHz, then the mixing ог sampling
frequency сап Ье 1,000 kHz (f ), and thus so the sampling mixer will have almost
5
lossless conversion. That is, the 10-kНz IF signal will have almost the same

amplitude as the incoming АМ radio signal.

«
'1 1 -
Generally, the phase of the IF signal is not that important. However, the fact that
there is ап identifying phase (noninverting ог inverting) in the sampling ог

multiplying mixer when the incoming RF signal is аЬоуе ог below the ,mixing ог
sampling frequency provides added information. This added (phase) information is
actually used in constructing ап image-reject mixer (note that image-reject mixers
will Ье covered in Chapter 21).
Before we move оп to multiplexing mixers, I/d like to add а word ог two about what

is really inside the sine ог cosine functions. That is, when we look at sin(x), what is
х? The variabIe х has to Ье ап angle. 50, when you see siп(2пft), the term 2пft is
ап angle that varies with time. In addition,

- 'П I =

where w is the frequency ,п гаdiапs рег second, and tis time measured in seconds.
Therefore,
.

1
and thus

11' ) - ~
And it is known that

/ l = h 1 U n in 1 i n t n 1 -1
Thus ll<p(t)/ llt = w in radians рег second, which is indeed the radial frequency of

the sinusoidal waveform.
When studying frequency mоdulаtiоп (FM), дер ( f)/ llt, the frequency, is handy to
keep in mind because the change in phase divided Ьу the change in time results in
the (instantaneous) frequency of the signal.