PAM, PWM, & PPM Online Simulators

Modulation Type:

Message Frequency (Hz):

Carrier Frequency (Hz):

Modulation Simulator

Mathematical Representation

MATLAB Logic

% Logic will update based on selection

Mathematical Foundations

Pulse modulation transforms a continuous-time message signal m(t) into a sequence of pulses. The three types demonstrated in this lab are defined by which pulse parameter is varied.

1. Pulse Amplitude Modulation (PAM)

In PAM, the amplitude of each pulse is made proportional to the instantaneous amplitude of the message signal at the sampling instant. This is essentially a multiplication of the message signal and a periodic pulse train carrier.

      s_pam(t) = m(t) × Σ p(t - nTs)
      where:
      m(t) = Message Signal
      Ts   = Sampling Period
      p(t) = Pulse shape (Rectangle)
    

2. Pulse Width Modulation (PWM)

In PWM, the duty cycle (width) of the carrier pulse is varied. The simulator implements this by comparing the message signal with a sawtooth or triangular waveform. When the message signal is higher than the carrier, the output is "High".

      Width (W_n) ∝ [1 + k_w · m(nTs)]
      Duty Cycle (%) = (Pulse Width / Period) × 100
    

3. Pulse Position Modulation (PPM)

In PPM, the amplitude and width of the pulses are constant, but the position (timing) of each pulse relative to a reference clock is varied. In practical circuits, PPM is often generated by creating a pulse at the falling edge of a PWM signal.

      t_n = nTs + t_shift
      t_shift ∝ m(nTs)
      (Pulse arrival time depends on message amplitude)
    

Sampling Theorem Note: To reconstruct the signal without distortion (aliasing), the carrier frequency (fc) must be at least twice the message frequency (fm).
Condition: fc > 2fm

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