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

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

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Radio Receivers
In a radio receiver with simple AGC

The audio stage gain is normally controlled by the AGC
An increase in signal strength produces more AGC
The faster the AGC time constant the more accurate the output
The highest AGC voltage is produced

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Radio Receivers
The local oscillator of a broadcast receiver is tuned to a frequency higher than the incoming frequency

To allow adequate frequency coverage without switching
Because otherwise an intermediate frequency could not be produced
To permit easier tracking
To help the image frequency rejection

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