# VCO and FM modulation

#### justtrying

Joined Mar 9, 2011
439
I am trying to bring the two concepts together and am a bit stuck...

So far I understand that VCO achieves FM by modulating a carrier wave according to the amplitude of the incoming signal (I do understand how the PLL locks and tracks the frequency and that the bandwidth of the VCO depends on external components and Vdd) What I do not understand and cannot find info for is how exactly modulation is achieved. Is amplitude compared to some sort of internal reference?

The other question is this - the diagram for FM that I have in my notes shows that as amplitude of Vin increases, frequency of Vout decreases and visa versa. However, all other references state that the relationship between the two is direct?!

Thanks.

#### t_n_k

Joined Mar 6, 2009
5,455
The VCO output would typically have a relationship of the form

Fout=Fc+k*Vmod

Where Fc is the nominal carrier frequency.

k is a constant determined by the modulation requirements such as modulation index.

Vmod=Vp*cos(ωm*t)

The maximum frequency deviation from the carrier frequency is ±k*|Vp|.

Where Vp is the peak modulation signal amplitude and ωm is the modulation frequency.