The range of frequencies generated by the local oscillator for the superheterodyne FM receiver is 77.3 MHz to 97.3 MHz. It is possible for an FM receiver to receive both a desired FM station and an image FM station when tuned to the desired frequency.
The local oscillator in a superheterodyne FM receiver generates a range of frequencies that are mixed with the incoming radio signal to produce an intermediate frequency (IF) of 10.7 MHz. To determine the range of frequencies generated by the local oscillator, we subtract the IF from the upper and lower frequency limits of the desired band.
Upper limit of local oscillator frequency = Upper frequency limit of desired band - IF
Lower limit of local oscillator frequency = Lower frequency limit of desired band - IF
For this receiver, the upper frequency limit is 108 MHz and the lower frequency limit is 88 MHz. Substituting these values and the IF of 10.7 MHz into the formulas, we get:
Upper limit of local oscillator frequency = 108 MHz - 10.7 MHz = 97.3 MHz
Lower limit of local oscillator frequency = 88 MHz - 10.7 MHz = 77.3 MHz
Therefore, the range of frequencies generated by the local oscillator is 77.3 MHz to 97.3 MHz.
It is possible for an FM receiver to receive both a desired FM station and an image FM station when tuned to the desired frequency. The image FM station is a station that is mirrored and appears at twice the IF frequency away from the desired station. In this case, the image FM station would be located at 21.4 MHz above the upper frequency limit of the desired band, which falls outside of the received frequency band.