# Signal Modulation with Carrier Wave?

Image B shows the frequency of an FM signal is changing, yet I know a single broadcast station on FM is specific to a single frequency. Is the pictured FM signal again modulated with another fixed frequency carrier representing the station frequency?

In Image A is the spectrum of an AM broadcast. Why are the side bands so large compared to the carrier? Is this somehow to accommodate the audio bandwidth over a frequency range?

A:

B:

• doing various operations on sinewaves works back to trigonometry - it just happens that for radio we exploit these mathematical properties. Read up on Fourier. Using the fourier transform you can view the function as time or frequency. Commented May 28, 2022 at 13:38

yet I know FM is specific to a single frequency

That is incorrect. The frequency of the carrier varies in FM, which stands for FREQUENCY MODULATION. There does not need to be another carrier which the signal shown in B under FM modulates. That signal, labeled FM, is modulated. That's what frequency modulation looks like.

The image B shows correctly how an FM signal works. The frequency of an FM signal varies with the modulating signal. The maximum variation either way is set by regulation if the FM signal is broadcast. When the modulating signal is at zero amplitude, the frequency of the FM signal is at its midpoint or nominal frequency.

In Image A is the spectrum of an AM broadcast. Why are the side bands so large compared to the carrier? Is this somehow to accommodate the audio bandwidth over a frequency range?

The bandwidth of an AM signal is twice the highest frequency of the modulating (usually audio) signal. In the center is the carrier, and above and below that are sidebands.

• An FM receiver has filters that severely attenuate all signals other than those from the FM station that is to be received. But it passes a band of frequencies, not a single frequency. Also, I did not say that image B was wrong, but that it was correct. Commented May 27, 2022 at 19:28
• @Nick Math didn't say that image B was wrong. Only that you probably referenced the wrong image in your question: "In Image B is the spectrum of an AM broadcast." makes more sense when talking about image A. Commented May 27, 2022 at 19:51

For your first question, FM means frequency modulation of the carrier wave. For a zero modulating signal the carrier wave is at the nominal frequency. For minimum and maximum modulating signal, the carrier frequency deviates by the allocated bandwidth of the signal, for example FM radio modulates the carrier by +/- 75 kHz.

For your second question why the carrier frequency is so narrow in the diagram compared to the bandwidth of the modulated signal is that the carrier is a single point of frequency, so it is infinitely narrow, basically it has no width at all.

• I understand FM using the bandwidth for its variable frequency channel (3x sampling rate it seems). AM sidebands confuse me. I know there’s a modulated audio signal, but it’s frequency is constant, so why all that bandwidth. Is it the same signal duplicated on different frequencies?
– Nick
Commented May 27, 2022 at 23:08
• Don't know where "sampling rate" comes from: nothing here is sampled. And 3x never ever occurs in these equations. It seems you're just randomly picking statements without respect for any context. If anything is modulated, it cannot be constant. That is literally what "modulated" means. Nothing is duplicated. Commented May 27, 2022 at 23:30
• If you have any signal that has a bandwidth (such as speech) and multiply that with a carrier sine wave then that is what you get, upper side band that matches the spectrogram of the original audio, and lower sideband that is mirrored. Try multiplying a fixed amplitude sine wave with a carrier and see the result. Audio/speech is just a collection of varying amplitude sine waves at varying frequencies than vary over time. Commented May 28, 2022 at 6:40
• If the carrier is modulated by +/- 75 kHz, I'm curious if you know how this compares to CD quality sound which is 16 bits modulated at 48 kHz? Maybe a comparison is not possible because its digital modulation.
– Nick
Commented Nov 11, 2022 at 5:11
• CD quality is not 48 KHz but 44.1 kHz and it is the sampling rate, not modulation. FM radio is analog. CD has bandwidth to 20 kHz with 96 dB range and FM radio 15 kHz and according to some sources around 70 dB range. Commented Nov 11, 2022 at 5:50

Radio stations (AM or FM) are actually allocated a narrow band of frequencies centered on their advertised frequency.

The extra bandwidth is used to accomodate the sidebands generated when you modulate the carrier.

The FM radio channel is a rather more complex mix of "sub-carrier" signals modulated on an FM carrier. Perhaps commercial equipment uses an Intermediate Frequency before converting to the selected channel with a local oscillator and IF to RF output. The designated FM Channel uses 100 kHz BW. The 150 kHz spacing allows a guard band to prevent adjacent channel crosstalk.

Back in the day when I was sending TV and DS1 over coax in 1970, we would listen to the mono broadcast FM on a spectrum analyzer just tuning the bandpass slightly off center so the FM gets converted to AM and we could hear it with an amplifier on the output with zero frequency sweep thus tuned slightly off-peak and the FM goes up and down like AM.

The AM carrier BW is only 7 kHz so the span looks wide with the break in the x Axis to zero. Adjacent channel crosstalk is more common on AM with weak and strong signals near each other or even using the same carrier frequency but both weak signals in opposite directions.