AI Tutor
When radio interference or channel attenuation corrupts a signal, pulse amplitudes get distorted easily. How can an electronic system send precise analog information without relying on voltage amplitude at all?
The answer is to keep pulse amplitudes completely constant and encode the information along the time axis instead.

Pulse Width Modulation (PWM)

In Pulse Width Modulation (PWM), the amplitude and period of the pulse train stay fixed, while the pulse duration Ο„\tau (or high time) varies in direct proportion to the instantaneous amplitude of the modulating signal vm(t)v_m(t).
The duty cycle DD is the fraction of each period TsT_s that the pulse stays high, defined as D=Ο„TsΓ—100%D = \frac{\tau}{T_s} \times 100\%.
Mathematically, the pulse width is Ο„(t)=Ο„0+kpwmvm(t)\tau(t) = \tau_0 + k_{pwm} v_m(t), where Ο„0\tau_0 is the unmodulated resting width and kpwmk_{pwm} is the modulator sensitivity constant in seconds per volt.
In trailing-edge PWM, every pulse begins at the fixed start of a clock period TsT_s, and turns off the moment the sawtooth ramp exceeds the analog message voltage.
Because wide pulses draw continuous current throughout their active state, high-power PWM transmitters consume variable average power. Can we transmit the exact same information using even less energy?

Pulse Position Modulation (PPM)

In Pulse Position Modulation (PPM), both the amplitude and the pulse width remain strictly constant, while the time offset of the pulse relative to a clock reference changes proportionally to vm(t)v_m(t).
The pulse trigger time in sampling period nn is tn=nTs+t0+kppmvm(nTs)t_n = n T_s + t_0 + k_{ppm} v_m(n T_s), where t0t_0 is the nominal baseline delay and kppmk_{ppm} is the position sensitivity in seconds per volt.