# Solving for frequency deviation, $\Delta f$ (FM modulation)

I'm sorry if I posted this in the wrong section. I solved the question and got $50\textrm{kHz}$, but the solution says it is $100\textrm{kHz}$ without any proof.

Im asking for someone to tell me which is correct. • Welcome to DSP.SE! Which particular question are you trying to answer. There are many on that page. – Peter K. Jun 8 '16 at 15:09
• I am trying to answer exercise 3, part 1. (The one with the line figure and VCO) – Frapto Jun 8 '16 at 15:10

## 1 Answer

If you use the standard definition of frequency deviation as the

"maximum instantaneous difference between an FM modulated frequency and the nominal carrier frequency"

then for the given example you indeed have $\Delta f=50\;\text{kHz}$, because the nominal carrier frequency is $f_c=10\;\text{MHz}$, the maximum frequency is $f_c+\Delta f=10.05\;\text{MHz}$, and the minimum frequency is $f_c-\Delta f=9.95\;\text{MHz}$.

• That is how I solved it, found equation of the line and found min and max frequencies from it. Your answer makes it clear, thank you :) – Frapto Jun 8 '16 at 15:49