# Frequency modulation

#### mentaaal

Joined Oct 17, 2005
451
Hey guys, anyone feel like explaining the fundamental concepts of frequency modulation to me? I have been looking it up and trying to understand it but i cant find anything on the net that clears it up nicely for me.
From what i understand a carrier signal is modulated with an input signal and the resulting signals frequency deviation from the carrier wave is equal to the input signals amplitude... Well if thats the case how are the input signal's different frequencies modulated?

Cheers!

#### recca02

Joined Apr 2, 2007
1,212
even i wud be interested to know that.
i only had a very small introduction to fm so this is just an opinion.
perhaps the rate of change of carrier frequency wud be high in in case a higher frequency modulating signal is used.for a lower freq modulating signal the carrier
frequency wud change over a larger time i:e rate of change will be lower.
man i really need a brushing on this subject.the first and last time i came across it was abt 5 yrs #### antseezee

Joined Sep 16, 2006
45
Intelligence frequency is modulated by a carrier frequency. The change in output frequency contains the necessary data to transmit the wave. The wave stays at a constant frequency and suddenly speeds up. The rate of change between the speeding up contains the necessary data to transmit the FM. It's kind of confusing, but it's a very neat concept. Using frequency rate changes to transmit information. Phase modulation also plays an assisting part in the role of FM. Phase changes can occur as well to help transmit information, but PM is generally never used solely by itself due to errant phase changes occurring.

Unfortunately, that damn trig equation has been blown to hell with modulation techniques. I would love to invent my own modulation technique, and actually have it be efficient.

#### mentaaal

Joined Oct 17, 2005
451
woah so alot more complicated than i thought....
well thanks for the replies.
although i fear i am more confused than i was prior to submitting the question... so the transmitted data say for example an audio conversation is modulated through the rate of change of carrier frequency.. but how can that be when frequency deviation is respinsible for conveying the input signal's amplitude?

#### beenthere

Joined Apr 20, 2004
15,819
The rate of change encodes the frequency component of the modulating signal, the amount of deviation from the carrier frequency encodes the magnitude of the modulating signal.

#### mentaaal

Joined Oct 17, 2005
451
The rate of change encodes the frequency component of the modulating signal, the amount of deviation from the carrier frequency encodes the magnitude of the modulating signal.
well now that just summs it up nice for me. why couldnt these sites like wikipedia along with pages and pages of complicated formulas include a nice simple to understand description like that?!! kudos!

#### Ron H

Joined Apr 14, 2005
7,014
The rate of change encodes the frequency component of the modulating signal, the amount of deviation from the carrier frequency encodes the magnitude of the modulating signal.
Actually, the second half of the sentence says it all. The deviation from carrier frequency is simply proportional to the instantaneous value of the modulating signal. The first half of the sentence follows from that.

#### recca02

Joined Apr 2, 2007
1,212
i m happy to know that my guess was somewhat along those lines.
thanks ,i was curious abt the answer too.

#### Dave

Joined Nov 17, 2003
6,969
Actually, the second half of the sentence says it all. The deviation from carrier frequency is simply proportional to the instantaneous value of the modulating signal. The first half of the sentence follows from that.
As an exact representation, you can state that FM is produced when the instantaneous frequency is varied linearly with the message signal. This statement can be expressed in the following form:

fi(t) = fc + k*m(t)

fi(t) is the instantaneous freq at t
fc is the carrier freq
m(t) is the message signal

And the instantaneous frequency is defined in terms of the coresponding phase angle as:

fi(t) = (1/2π)(d/dt)φ(t)

Where φ(t) is the phase angle, then:

φ(t) = 2π∫fi(λ)dλ

Over the period t = 2π

Therefore using substitution, the phase angle is:

φ(t) = 2πfc + 2πk∫m(λ)dλ

We know x(t) = A*Cos(φ(t))

Therefore the FM signal is defined as:

xfm(t) = Ac*Cos(2πfc + 2πk∫m(λ)dλ)

Although this is pretty hefty, it is the fundamental expression of frequency modulation mathematically expressing what RonH has stated above.

Dave

#### gootee

Joined Apr 24, 2007
447
You should ask about what happens on the other end; the demodulation. That's the coolest part!

#### mentaaal

Joined Oct 17, 2005
451
well i am still tryin got get my head around how the output frequency deviation from the carrier reflects the input signals instantaneous voltage (as in the amplitude of the wave? ) and then how the instanteous rate of change of this deviation reflects the input signals frequency. I think thats a very hard concept to visualise in my head!

but yeah i would also love to know what happens on the other end. I had never really thought about it i just guessed the process would happen in reverse?

#### recca02

Joined Apr 2, 2007
1,212