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hambasics:sections:wavemodulationmath [2021/01/03 08:05] – created - external edit 127.0.0.1hambasics:sections:wavemodulationmath [2026/04/01 20:59] (current) – va7fi
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-~~NOTOC~~ 
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 ====== 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.
  
-For both AM and FM examples, we'll Let:+For both AM and FM examples, we'll let:
   * \$c(t) = \cos(2 \pi f_c t)\$ be the <fc #4682b4>radio carrier</fc> with frequency \$f_c\$   * \$c(t) = \cos(2 \pi f_c t)\$ be the <fc #4682b4>radio carrier</fc> with frequency \$f_c\$
   * \$s(t) = \cos(2 \pi f_s t)\$ be the <fc #ff0000>baseband audio signal</fc> with frequency \$f_s\$   * \$s(t) = \cos(2 \pi f_s t)\$ be the <fc #ff0000>baseband audio signal</fc> with frequency \$f_s\$
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 FIXME: animation in wrong place FIXME: animation in wrong place
-{{ggb>/howto/hambasics/sections/am.ggb 800,405}}+{{ggb>/hambasics/sections/am.ggb 800,405}}
  
 Some things to try: Some things to try:
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 <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) \$$
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 </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 \$$
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 FIXME: animation in wrong place FIXME: animation in wrong place
-{{ggb>/howto/hambasics/sections/fm.ggb 800,350}}+{{ggb>/hambasics/sections/fm.ggb 800,350}}
  
  
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