Frequency of the carrier wave changed during amplitude modulation

In summary: FM and the frequency of the carrier wave remains unchanged in AM.In summary, frequency modulation (FM) maintains a constant amplitude of the carrier wave and additional circuitry is used to ensure this. On the other hand, amplitude modulation (AM) produces two new frequencies called sidebands, resulting in a zone of frequency (bandwidth) depending on the rate of increase or decrease in amplitude. Mathematically, FM represents multiplication while AM represents addition of two waves. When studying the concept of beats in physics, this phenomenon can be compared to AM. In FM, the modulating frequency is not present, while in AM, the amplitude of the modulating frequency is added to the carrier frequency.
  • #1
Pranav Jha
141
1
While reading about frequency modulation, I found that it was clearly written that the amplitude of the carrier wave remains unchanged. However, i didn't find a statement stating that the frequency of the carrier wave remains unchanged for amplitude modulation. So, is the frequency of the carrier wave changed during amplitude modulation? Also, please explain the relation between the frequency of the modulated wave and the frequency of the information signal (the sidebands confused me)
 
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  • #2
During transitions in amplitude, the frequency "appears" to change. An increase in amplitude while the amplitude itself is also increasing appears to be an increase in frequency and vice versa for the other combinations, with the end result that during a change in amplitude, the result is a fuzzy zone of frequency (bandwidth) that gets wider depending the rate of increase or decrease. This is the reason why morse code transmitters ramp up the amplitude over a few milliseconds instead of instantly turning the signal on and off.
 
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  • #3
While reading about frequency modulation, I found that it was clearly written that the amplitude of the carrier wave remains unchanged. However, i didn't find a statement stating that the frequency of the carrier wave remains unchanged for amplitude modulation. So, is the frequency of the carrier wave changed during amplitude modulation? Also, please explain the relation between the frequency of the modulated wave and the frequency of the information signal (the sidebands confused me)

1) Not only is the amplitude of an FM signal theoretically constant, additional stabilising circuitry is employed to keep it so in better equipment.

2) When amplitude modulation is employed, 2 new frequencies appear, that were not in either the original carrier or the modulating signal. These are called sidebands. I don't know if you have studied yet beats in physics but this is the same phenomenon. When two waves of nearly equal frequency combine, beats occur at the difference between their frequencies. You can here this in the thrumming of engines in an enclosed space, and the beat occurs in the audio spectrum.
With radio transmission the modulating audio signal and the carrier frequencies are quite different so the effect is given a different name.

The amplitude (the quantity we wish to vary) of the carrier is

[tex]v = {V_c}\sin \left( {{\omega _c}t} \right)[/tex]

If we add a modulating signal to Vc this becomes

[tex]v = \left( {{V_c} + {V_m}\sin \left( {{\omega _m}t} \right)} \right)\sin \left( {{\omega _c}t} \right)[/tex]

A bit of trigonometry turns this into

[tex]v = {V_c}\sin \left( {{\omega _c}t} \right) + \frac{{{V_m}}}{2}\cos \left( {{\omega _c} - {\omega _m}} \right)t - \frac{{{V_m}}}{2}\cos \left( {{\omega _c} + {\omega _m}} \right)t[/tex]

This shows that a sinusoidal wave, sinusoidally modulated contains three frequencies.

The original carrier

[tex]{f_c} = {\omega _c}/2\pi [/tex]

The lower side frequency or sideband

[tex]{f_c} - {f_m} = \left( {{\omega _c} - {\omega _m}} \right)/2\pi [/tex]

the upper side frequency or sideband

[tex]{f_c} + {f_m} = \left( {{\omega _c} + {\omega _m}} \right)/2\pi [/tex]

The modulating frequency is not present.

It is worth noting that amplitude modulation represents addition of two waves, frequency modulation represents multiplication.

go well
 
  • #4
Studiot said:
The amplitude (the quantity we wish to vary) of the carrier is

[tex]v = {V_c}\sin \left( {{\omega _c}t} \right)[/tex]

If we add a modulating signal to Vc this becomes

[tex]v = \left( {{V_c} + {V_m}\sin \left( {{\omega _m}t} \right)} \right)\sin \left( {{\omega _c}t} \right)[/tex]

It is worth noting that amplitude modulation represents addition of two waves, frequency modulation represents multiplication.

go well

A minor clarification.

Amplitude modulation involves the the multiplication of the modulation frequency plus a constant offset (to produce the carrier), and the carrier frequency.
 
  • #5
Studiot said:
1) Not only is the amplitude of an FM signal theoretically constant, additional stabilising circuitry is employed to keep it so in better equipment.

2) When amplitude modulation is employed, 2 new frequencies appear, that were not in either the original carrier or the modulating signal. These are called sidebands. I don't know if you have studied yet beats in physics but this is the same phenomenon. When two waves of nearly equal frequency combine, beats occur at the difference between their frequencies. You can here this in the thrumming of engines in an enclosed space, and the beat occurs in the audio spectrum.
With radio transmission the modulating audio signal and the carrier frequencies are quite different so the effect is given a different name.

The amplitude (the quantity we wish to vary) of the carrier is

[tex]v = {V_c}\sin \left( {{\omega _c}t} \right)[/tex]

If we add a modulating signal to Vc this becomes

[tex]v = \left( {{V_c} + {V_m}\sin \left( {{\omega _m}t} \right)} \right)\sin \left( {{\omega _c}t} \right)[/tex]

A bit of trigonometry turns this into

[tex]v = {V_c}\sin \left( {{\omega _c}t} \right) + \frac{{{V_m}}}{2}\cos \left( {{\omega _c} - {\omega _m}} \right)t - \frac{{{V_m}}}{2}\cos \left( {{\omega _c} + {\omega _m}} \right)t[/tex]

This shows that a sinusoidal wave, sinusoidally modulated contains three frequencies.

The original carrier

[tex]{f_c} = {\omega _c}/2\pi [/tex]

The lower side frequency or sideband

[tex]{f_c} - {f_m} = \left( {{\omega _c} - {\omega _m}} \right)/2\pi [/tex]

the upper side frequency or sideband

[tex]{f_c} + {f_m} = \left( {{\omega _c} + {\omega _m}} \right)/2\pi [/tex]

The modulating frequency is not present.

It is worth noting that amplitude modulation represents addition of two waves, frequency modulation represents multiplication.

go well

Thanks but could you clarify the math further. I think i am starting to get the concept.
 
  • #6
Carrock said:
A minor clarification.

Amplitude modulation involves the the multiplication of the modulation frequency plus a constant offset (to produce the carrier), and the carrier frequency.

Please state that mathematically
 

1. What is amplitude modulation and how does it work?

Amplitude modulation is a method of encoding information on a carrier wave by varying its amplitude. It works by superimposing the information signal onto the carrier wave, causing the amplitude of the carrier wave to vary in accordance with the information signal.

2. How does changing the frequency of the carrier wave affect amplitude modulation?

Changing the frequency of the carrier wave alters the characteristics of the modulated signal. It can affect the bandwidth, transmission range, and overall quality of the signal. Higher frequency carrier waves typically result in a higher quality and more efficient modulation.

3. What is the relationship between the frequency of the carrier wave and the amplitude of the modulated signal?

The relationship between the frequency of the carrier wave and the amplitude of the modulated signal is inverse. As the frequency of the carrier wave increases, the amplitude of the modulated signal decreases. This is because modulation is achieved by varying the amplitude of the carrier wave, so a higher frequency carrier wave has less time to reach its peak amplitude.

4. How do changes in the frequency of the carrier wave affect the demodulation process?

Changes in the frequency of the carrier wave can affect the demodulation process by making it more difficult to accurately retrieve the original information signal. If the frequency is too high, it can result in distortion or loss of the information signal. Demodulators must be tuned to the specific carrier frequency in order to accurately recover the information signal.

5. Can the frequency of the carrier wave be changed during transmission in amplitude modulation?

Yes, the frequency of the carrier wave can be changed during transmission in amplitude modulation. This is known as frequency shifting and can be used to change the transmission range or to avoid interference with other signals. However, it is important to ensure that the receiving demodulator is also tuned to the new carrier frequency in order to successfully recover the information signal.

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