Intro

• first form of modulation used in radio transmission
• MF band (medium frequency, 300 kHz - 3 MHz)
• Basic Form:
  • DSB-LC (Double Side Band)
  • DSB-SC
• offers narrow bandwidth transmission
  • $B=2\times f_{max}$ (DSB-LC)
• Very inefficient in use of transmit power
• Message signal is
  $k_{a}m(t)$

DSB-LC

Modulate

With the modulated signal

$$\begin{array}{rl}{v}_{AM}(t)& =A_c\cos \left({\omega }_{c}t\right)\times [1+k_{a}m(t)]\\ & =A_c\cos \left({\omega }_{c}t\right)+k_a{A}_{c}m(t)\cos \left({\omega }_{c}t\right)\end{array}$$
Considering

$k_{a}m(t)=k_a\cos \left({\omega }_{m}t\right)$

$$\begin{array}{rl}& v_{AM}(t)=A_c\cos \left({\omega }_{c}t\right)+\frac{1}{2}{k}_a{A}_c\cos ({\omega }_{c}t+{\omega }_{m}t)+\frac{1}{2}{k}_a{A}_c\cos ({\omega }_{c}t-{\omega }_{m}t)\end{array}$$

• Two copies of m(t) appear on either side of
  $f_c$
• Power of each term:
  • Carrier:
    $\frac{1}{2}{A}_c^2$
  • Upper sideband:
    $\frac{{\left(\frac{1}{2}{k}_a{A}_c\right)}^2}{2}$
  • Lower sideband:
    $\frac{{\left(\frac{1}{2}{k}_a{A}_c\right)}^2}{2}$
• if
  $k_a=1$(maximum value), ratio of message power to carrier power = 0.5

Typical mean value for

$k_a=0.3$

$$\frac{P_{msg}}{P_c}=\frac{1}{2}{k}_a^2=0.045$$
Less than 5% of transmitted power is in the message

Demodulate

• Apply large AM signal to a diode
  $v_{AM}(t)=A_c\cos \left({\omega }_{c}t\right)\times [1+k_{a}m(t)]$
• Sole action of carrier is to switch the demoduulator diode in the AM receiver

1. Generates switching function s(t) at carrier frequency
   • $s(t)=\frac{1}{2}+\frac{2}{\pi }(\cos \left({\omega }_{c}t\right)-\frac{1}{3}\cos \left(3{\omega }_{c}t\right)+\cdots )$
2. Multiply s(t) by AM signal
   • $x(t)=v_{AM}(t)\times (\frac{1}{2}+\frac{2}{\pi }\cos \left({\omega }_{c}t\right)-\frac{2}{3\pi }\cos \left(3{\omega }_{c}t\right)+\cdots )$
3. for convenience, set k_a = 1
4. $\frac{2}{\pi }{A}_c{(\cos \left({\omega }_{c}t\right))}^2=\frac{2}{\pi }{A}_c(1+\frac{1}{2}\cos \left(2{\omega }_{c}t\right))=\frac{2}{\pi }{A}_c+\frac{1}{\pi }{A}_c\cos (A_c\cos \left(2{\omega }_{c}t\right))$
5. Place a low pass filter at the output of the diode to get the following lower-frequency terms.
   • $y(t)=\frac{2}{\pi }{A}_c+\frac{1}{\pi }{A}_{c}m(t)$
6. Output contains a DC term and the message signal

• Wanted signal has amplitude proportional to received carrier voltage A_c
• Control gain of AM receiver to make output signal of demodulator constant
  • requires Automatic Gain Control (AGC)

Diode Detector

• Since mesage abides as the amplitude of the received signal, detecting amplitude change = obtaining message!

Adventage

• verfy simple circuit
• Very low cost

Disadventage

• Poor linearity - distorion
• Poor selectivity
• Affected by selective fading