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

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

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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 operates below the signal frequency
Mixer input must be tuned to the signal frequency
Local oscillator frequency is normally double the IF

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