# Angle harmonic distortion in FM modulation

As you know the output form of FM modulator is something like this: $$s(t)=A_{C}\cos(2\pi F_{c}t+\beta \sin(2\pi F_{m}t))$$ where $\beta$ is the phase deviation. I want to know why in this book the write has mentioned that narrow-Band FM modulation has angle harmonic distortion?

Because the phase changes is related to $\theta(t)=2\pi F_{c}t+\beta \sin(2\pi F_{m}t)$ and it isn't related to $\beta$(even large or small enough)(Any harmonic distortion? No). However, In complex base-band form we can write $\theta(t)=2\pi F_{c}t+\arctan(\textrm{Quadrature-component}/\textrm{In-phase component})$ and it shows the harmonic distortion.
1. why do we use complex base-band form for FM phase rather than $\theta(t)=2\pi F_{c}t+\beta \sin(2\pi F_{m}t)$? and what does complex base-band form exactly do?
2. why can't we accept $\theta(t)=2\pi F_{c}t+\beta \sin(2\pi F_{m}t)$ as phase deviation?