# Clarification on video about frequency deviation in phase modulation bandwidth

I am watching this video and at 7:12 he calculates the frequency deviation $$\Delta f = f_{c}f_{m}A_{m}$$ where the $$c$$ underscript is for "carrier" and the $$m$$ underscript is for "message".

But if you analyze it dimensionally the units dont match $$\Delta f$$ should be in Hz but $$f_{c}$$ and $$f_{m}$$ are in Hz and $$A_{m}$$ is dimensionless so on the one side we have Hz while on the other side we have Hz^{2}.What is going on?

• that video isn't great. He acts very "oh yes these formulas are all very important", "the numbers are very large" (what makes a number large? They're not really.) but he doesn't really explain them. Basically, you need to understand the things before you watch this video, otherwise all you get is formulas that you are supposed to learn by heart, which will help you nowhere, because nobody needs you to know them by heart, but to understand them. Commented Sep 14, 2023 at 12:27
• Anyway, I can't find your formula $\Delta f = f_{c}f_{m}A_{m}$ at all at 7:12. Are you sure about that timestamp? I'll also say that defining a frequency deviation for a phase modulator might not be very useful. What the video says is that $\Delta f = k_P V_m f_m$, but that's simply a different formula than you claim here. Commented Sep 14, 2023 at 12:28
• Ah!You are correct.$K_{p}$ is the modulation sensitivity of the local oscillator which produces the carrier signal and it is measured in $Hz/V$ but we still have 2 Hz's in the nominator so what is going on? Commented Sep 14, 2023 at 12:42
• "He acts very "oh yes these formulas are all very important", "the numbers are very large" (what makes a number large? They're not really.) but he doesn't really explain them. Basically, you need to understand the things before you watch this video, otherwise all you get is formulas that you are supposed to learn by heart, which will help you nowhere, because nobody needs you to know them by heart, but to understand them. "Angle modulation in the time domain gives $sin(sin(f(t))$.How can you Fourier transform this?Also I am trying to learn the basics. Commented Sep 14, 2023 at 12:43
• $K_p$, as a sensitivity, should be 1/V here, not Hz/V. Commented Sep 14, 2023 at 12:44