At the transmitter, the carrier wave is generated at two phase angles. One of these carriers is called the in-phase carrier (I), and the other is called the quadrature (Q) carrier because it is 90 degrees out of phase with respect to the in-phase carrier. The in-phase carrier drives a standard AM modulator that receives the sum of the left and right channels (L+R). The quadrature carrier drives a suppressed carrier modulator that receives the difference of the left and right channels (L-R), as well as a low-level 25Hz tone. A suppressed carrier modulator is an AM modulator in which the carrier nulls out when there is no modulation. The sole purpose of the 25Hz pilot tone is to identify the signal as AM stereo. Unlike the pilot used in FM stereo, the AM stereo pilot does not play any part in the decoding process.
The combined output of these two modulators is a quadrature-AM signal. This type of signal varies in phase and amplitude. Unfortunately, both the in-phase and quadrature components contribute to the amplitude of this signal, so its mono (L+R) component cannot be properly detected using the type of detector that is typically used in mono receivers. This is where the "Compatible" part comes in. The quadrature-AM is run through a circuit called a limiter. This is a high-gain amplifier that is purposely overdriven so that almost all the amplitude variations of the quadrature-AM signal are removed, leaving a signal that varies only in phase. This phase modulated carrier drives an AM modulator that receives the sum of the left and right audio. This is what makes the system compatible with regular mono receivers. A mono receiver demodulates only the audio that goes to the last AM modulator. Stereo receivers rely on the last AM modulator to reconstruct the QUAM signal that was present at the limiter input.
Decoding of C-QUAM requires three detectors (just as transmitting took three modulators). One of these is a regular AM envelope detector of the type that might be found in a mono receiver. The other two are synchronous detectors. A synchronous detector is a circuit that works by multiplying the incoming signal with a locally generated reference carrier. If the incoming signal and the reference carrier differ in phase by 90 degrees, the synchronous detector will produce no output! Synchronous detectors can also demodulate suppressed-carrier AM, whereas conventional AM detectors cannot.
A phase-locked loop generates two reference carriers that differ in phase by 90 degrees. The phase locked loop tracks long-term changes in the incoming signal phase and adjusts itself accordingly, but is does not respond to instantaneous phase changes caused by audio or by the 25Hz pilot tone. The output of the in-phase synchronous detector is expected to be identical to that of the envelope detector because the two AM modulators at the transmitter received identical input signals. Any difference between the outputs of the two detectors is amplified and fed to the gain control input of a variable-gain amplifier. The envelope detector, in-phase synchronous detector, difference amp, and the variable gain amp form a feedback loop that keeps the output of the two detectors nearly identical. This means that variable-gain amplifier is being controlled in such a way that it undoes the action of the limiter and final AM modulator at the transmitter, thereby restoring the quadrature-AM signal! The quadrature synchronous detector demodulates only the L-R audio.
Most AM stereo tuners have a 25Hz tone detector that mutes the L-R signal unless the tone is present. If the tone is present, the tone detector turns on some kind of indicator, such as an LED. The only exception to this rule that I've encountered is Sony's SRF-42 Walkman (TM) radio. In the SRF-42, L-R audio is muted only when the phase-locked loop loses its lock on the incoming signal--there is no pilot detector or stereo indicator. Most of the AM stereo tuners built during the 1980s used Motorola's MC13020 integrated circuit, which contains some rather elaborate pilot tone detection circuitry.
These frequency response requirements may be different outside of the United States. Areas where 9KHz channel spacing is used will most likely have different standards for audio frequency response.