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Unformatted text preview: (ωLO = ωc + ωIF ). Since ωLO > ωc , the results for ωLO > ωRF are applicable in this case. If the signals
are summed at the output of the mixer then according to equation 1 the output will be zero. If the signals
are diﬀerenced, then according to equation 2 the output will be A cos[(2ωc + ωIF )t] + A cos(ωIF t). The ﬁrst
term will be blocked by the IF ﬁlter, and the second term will be passed. Thus, we should use the − sign in
the combiner in order to produce the desired frequency conversion.
d. The image signal is at ωRF = ωc + 2ωIF . For the image signal, ωLO < ωRF , so if the signals are summed
the output will be A cos(ωIF t). If the signals are diﬀerenced the output is A cos[(2ωc + 3ωIF )t]. Thus, when
the signals are diﬀerenced, as required to produce the required output when the desired signal is input to
the mixer, the image signal produces a ﬁnite output from the mixer, but the frequency of the output signal
will be much higher than ωIF . Hence the response due to the image signal is easily rejected by the IF ﬁlter,
so the image signal will not produce any output after the IF ﬁlter. 4...
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- Spring '08