Sun Coast Amateur
Radio Club Society

User Tools

Site Tools

You are here: home » hambasics » sections » wavemodulationmath
hambasics:sections:wavemodulationmath

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
hambasics:sections:wavemodulationmath [2026/04/01 20:49] – [More Details: AM / FM] va7fihambasics:sections:wavemodulationmath [2026/04/01 20:59] (current) – va7fi
Line 1: Line 1:
-~~NOTOC~~ 
- 
 ====== More Details: AM / FM ====== ====== More Details: AM / FM ======
 Here are a few more details about the AM, SSB, and FM modulation schemes introduced on the [[wavemodulation |Wave Modulation]] page. Here are a few more details about the AM, SSB, and FM modulation schemes introduced on the [[wavemodulation |Wave Modulation]] page.
Line 78: Line 76:
  
 <WRAP round alert box center 80%> <WRAP round alert box center 80%>
-Now, it might be tempting to simply substitute this sum in the wave like so:+It might be tempting to simply substitute this sum in the wave like so:
  
 \$$ \cos(2\pi f_c t) \quad \rightarrow \quad \cos\Big(\big(2\pi f_c + 2\pi k s(t)\big) t\Big) \$$ \$$ \cos(2\pi f_c t) \quad \rightarrow \quad \cos\Big(\big(2\pi f_c + 2\pi k s(t)\big) t\Big) \$$
Line 85: Line 83:
 </WRAP> </WRAP>
  
-To solve this properly, we need some calculus and deduce the angle from our new frequency:+To solve this properly, we need some calculus to deduce the angle from our new frequency:
  
 \$$ \frac{d}{dt}\theta(t) = 2\pi f_c + 2\pi k s(t) \qquad  \Rightarrow \qquad \theta(t) = 2\pi f_c t + 2\pi k \int_0^{t}s(\tau) d\tau \$$ \$$ \frac{d}{dt}\theta(t) = 2\pi f_c + 2\pi k s(t) \qquad  \Rightarrow \qquad \theta(t) = 2\pi f_c t + 2\pi k \int_0^{t}s(\tau) d\tau \$$
hambasics/sections/wavemodulationmath.1775101761.txt.gz · Last modified: by va7fi