Radio Receivers
The controlled oscillator synthesizer is sometimes preferred over the direct one because

It is a simpler piece of equipment
It is relatively free of spurious frequency
It does not require crystal oscillator
Its frequency stability is better

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Radio Receivers
In a broadcast superheterodyne receiver, the

RF amplifier normally works at 455 kHz above the carrier frequency
Local oscillator frequency is normally double the IF
Mixer input must be tuned to the signal frequency
Local oscillator operates below the signal frequency

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