Short note: AM radio receiver

The standard AM radio receiver is the superheterodyne receiver. It converts every received station frequency to a fixed intermediate frequency (IF) of 455 kHz, where most of the gain and selectivity are provided.

 Antenna
   |
 [RF amp]->[Mixer]->[IF amp]->[Envelope]->[Audio]->Spkr
   ^          ^      455 kHz   [detector]  [ amp ]
   |          |                    |
   +-gang-[Local osc]          AGC -> RF/IF amps
         fLO = fs + 455 kHz

Stages

1. RF amplifier: tuned to the station $f_s$ (535–1605 kHz); improves sensitivity and rejects the image frequency.
2. Mixer + local oscillator: produces $f_{LO} - f_s = 455$ kHz. LO and RF tuning are ganged (tracking).
3. IF amplifier: fixed-tuned, high-gain stages with sharp filters; give most of the selectivity (adjacent-channel rejection).
4. Detector: diode envelope detector recovers the audio.
5. AGC: DC part of detector output controls the gain of RF/IF stages, keeping output level constant for strong and weak stations.
6. Audio amplifier drives the loudspeaker.

Image frequency: $f_{si} = f_s + 2f_{IF}$, rejected mainly by the RF stage. Image rejection ratio $\alpha = \sqrt{1 + Q^2\rho^2}$, $\rho = \frac{f_{si}}{f_s} - \frac{f_s}{f_{si}}$.

Advantages: uniform selectivity and gain across the band, high sensitivity, stable operation.