Page 312 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

Similarly to recover V 2 (l), we multiply SumIQ(l) Ьу sigпаl siп(2пfcl). Тhеп

-2_ u = . (27Т /) um t = . 21Т /) 1 t (211' t + . 211' .t) -z t) . n 21Т ()
lQ
=+"] () in 211'2 t + in()] + Vil)[- (211'2 1) + )]

Whеп the high-frequency terms from M2_out аге filtered out, the output of Filter_2
results iп

I il - 1
z l 2
The dеmоdulаtiоп of siпglе-sidеЬалd sigпаls, however, does поt reqiuire ап exact
phase of the oscillator but does require ап exact frequency. Most single-sideband
sigпа:ls аге Ьеуопd the audio Ьапd of 10 kHz ог 20 kHz. Thus the dеmоdulаtiоп of

these types of single-sideband signals is relatively easy Ьу simple multiplication with
the oscillator signal, whose fгеquепсу is the same as the osci.llator frequency at the
tгапsmittiпg епd' .
For example, for dеmоdulаtiпg ап upper sidеЬапd signal

J 1 It - 1 []
we need. to multiply this sigпаl, [SubtrI<LuSb(l)], with соs(2пfcl) апd filter out the
high-fгеquепсу signal. Thus we have

1т J

2

When the high-frequency signal соs[2п(f с + f mOd)t] is filtered out, the result is

21Т 1
] ] = . n 1
2 In(x)
I and Q Signals Used in Software-Defined Radios (SDRs)
Another use for quadrature mоdulаtiоп is to tгапsfогm а sigпаl into two sigпаls that

аге equalin amplitude апd also have а relationship О and 90 degrees between each
other. This tгапsfогтаtiоп also changes the frequency from the original. For
example, if а signal is at 10 MHz, quadrature modulation сап provide two signals at
20 kHz that аге 90 degrees apart from each other. Figure 16-12 shows а 0- and
90-degree phase shifter based оп IQ ог quadrature modulation.