Instructions for Amplitude Modulation (AM)
- Step 1: Click on 'Generate Message' button to generate input message signal
- Step 2: Then click on 'Generate Carrier' button to generate carrier signal. The carrier frequency has to be more than the message frequency and You can change frequencies using sliders
- Step 3: Click on 'Generate Amplitude Modulated Signal' button to generate Amplitude Modulated Signal
- Step 4: Click the 'Show Frequency Spectrums' button to view the AM spectra.
- Here, the modulation index is defined as the ratio of the message signal amplitude to the carrier signal amplitude. You can adjust both values.
Message Signal Amplitude
Carrier Signal Amplitude
Amplitude Demodulation
- Demoulation Process: A LPF's cutoff frequency is set near the message frequency to pass desired signals and attenuate higher frequencies.
Message Frequency (Hz)
Carrier Frequency (Hz)
Cut-off Frequency (Hz)
How the Message Signal is Recovered (AM)
In this simulation, the message signal is recovered using Synchronous Detection followed by a Low-Pass Filter (LPF).
1. The AM Signal Equation
$$s(t) = [A_c + m(t)] \cos(2\pi f_c t)$$
Where $A_c$ is the carrier amplitude and $m(t) = A_m \sin(2\pi f_m t)$ is the message.
2. Product Detection
The received signal is multiplied by a local carrier $\cos(2\pi f_c t)$:
$$v(t) = s(t) \cdot \cos(2\pi f_c t) = [A_c + m(t)] \cos^2(2\pi f_c t)$$
Using the identity $\cos^2(\theta) = \frac{1 + \cos(2\theta)}{2}$:
$$v(t) = \frac{A_c + m(t)}{2} + \frac{[A_c + m(t)] \cos(4\pi f_c t)}{2}$$
3. Low-Pass Filtering & DC Removal
The LPF removes the high-frequency term at $2f_c$. The resulting baseband signal is:
$$y(t) = \frac{A_c}{2} + \frac{m(t)}{2}$$
After blocking the DC component ($\frac{A_c}{2}$), the recovered signal is $\frac{1}{2}m(t)$, which is exactly the original message signal shape.