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Question: How does a radio change stations and volume?
To answer these questions I have to explain a little bit about communications engineering and electrical circuits, both fundamental design areas for electrical engineers.
To answer the first question, we must first describe how radio signals are transmitted as electromagnetic waves. Since the frequencies present in audio signals cannot be transmitted over long distances as electromagnetic waves, the audio signals are first converted to much higher frequencies using either amplitude modulation (AM) or frequency modulation (FM). Each AM station and each FM station in a particular region is assigned a specific center frequency and occupies an allotted bandwidth. As you may know the Federal Communications Commission (FCC) assigns these frequencies, using the range 535 kHz to 1600 kHz for AM stations, and the range 88.1 MHz to 108.1 MHz for FM stations. To then answer your question about changing stations, the radio electronics are used to "tune" the radio to a specific narrow frequency band of frequencies corresponding to the specific station that is desired.
Tuning, which is the heart of your first question, is accomplished with what electrical engineers call a resonant circuit. This is a little easier to explain using the electrical-mechanical methods that were used in the earlier days of radio and which continued to be used up until about the 1980s. The tuner is a resonant circuit built with two electrical elements called an inductor and a capacitor. This circuit creates an electrical output only for those frequencies, which are very close to the resonant frequency, which depends on both the inductor value and capacitor value. It turns out to be quite easy to make an adjustable capacitor, with the capacitance value changed with a tuning knob. Thus, if you want to listen to FM station 92.5, you actually adjust the variable capacitor so that the tuned resonant circuit responds only to the narrow band around 92.5 MHz. The selected high frequency signal is then converted back to the original audio frequency band, using a demodulation circuit. The demodulation methods are quite different for AM and FM stations.
As electronics technology as progressed, electrical engineers figured out how to build tunable circuits without any mechanical moving parts. Thus modern radios often no longer have a tuning knob, but rather just push in buttons that cause an electronic circuit to change a capacitance value. The electronics can also be used to select the precise capacitance values needed for the stations that the user is interested in. Many other refinements, such as station presets, can be incorporated. However, the principle of a resonant circuit with an adjustable center frequency is still used. Since modern electrical parts are more reliable than mechanical moving parts, modern radios can be much more reliable and function better than older radios.
As to your second question, about changing the volume, a circuit called an adjustable gain amplifier is used. One component in the circuit, usually a resistor, controls the gain and can be adjusted using a control knob or button on the front of the radio. The output of the amplifier is connected to a speaker, and the radio plays at the desired level. The radio engineers also have to consider that the strength of the radio signal varies greatly due to the weather conditions and the location of the radio, especially a radio in a car. To compensate for these different signals levels, another circuit called automatic gain control (AGC), is used to make the radio signal a constant amplitude before it is passed to the final volume control stage. The AGC circuit works by examining the strength of the radio signal and then automatically increasing or decreasing the gain of the AGC so that its output level is independent of the initial radio signal strength. Engineers use feedback control to build the AGC stages of radios.
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