Editing Pulse-width modulation (section)

=== Intersective method PWM ===
[[File:Pwm.svg|frameless|400x400px]]

The intersective method is a simple way to generate a PWM output signal (magenta in above figure) with fixed period and varying duty cycle is by using a [[comparator]] to switch the PWM output state when the input waveform (red) intersects with a [[Sawtooth wave|sawtooth]] or a [[Triangle wave|triangle]] waveform (blue).

Depending on the type of sawtooth or triangle waveform (green in below figure), intersective PWM signals (blue in the below figure) can be aligned in three manners:

[[File:Three_PWM_types.svg|frameless|400x400px]]

* Leading [[Signal edge|edge]] modulation (top plot) uses a reverse sawtooth wave to generate the PWM. The PWM's leading edge is held at the leading edge of the window and the trailing edge is modulated.
* Trailing edge modulation (middle plot) uses a normal sawtooth wave to generate the PWM. The PWM's trailing edge is fixed and the leading edge is modulated.
* Centered pulses (bottom) uses a triangle waveform to generate the PWM. The pulse center is fixed in the center of the time window and both edges of the pulse are moved to compress or expand the width.

==== Time proportioning ====
Many digital circuits can generate PWM signals (e.g., many [[microcontrollers]] have PWM outputs). They normally use a [[counter (digital)|counter]] that increments periodically (it is connected directly or indirectly to the [[clock signal|clock]] of the circuit) and is reset at the end of every period of the PWM. When the counter value is more than the reference value, the PWM output changes state from high to low (or low to high).<ref>{{cite web |last=Barr |first=Michael |date=1 September 2001 |title=Introduction to Pulse Width Modulation (PWM) |url=https://barrgroup.com/Embedded-Systems/How-To/PWM-Pulse-Width-Modulation |website=Barr Group}}</ref> This technique is referred to as '''time proportioning,''' particularly as '''time-proportioning control'''<ref>''Fundamentals of HVAC Control Systems,'' by Robert McDowall, [https://books.google.com/books?id=UMk1EUp-W-UC&pg=PA21&dq=%22time+proportioning%22 p. 21]</ref> – which ''proportion'' of a fixed cycle time is spent in the high state.

The incremented and periodically reset counter is the discrete version of the intersecting method's sawtooth. The analog comparator of the intersecting method becomes a simple integer comparison between the current counter value and the digital (possibly digitized) reference value. The duty cycle can only be varied in discrete steps, as a function of the counter resolution. However, a high-resolution counter can provide quite satisfactory performance.

==== Spectrum ====
The resulting [[spectrum|spectra]] (of the three alignments) are similar. Each contains a [[DC component]], a base sideband containing the modulating signal, and phase modulated [[Carrier signal|carriers]] at each [[harmonic]] of the frequency of the pulse. The amplitudes of the harmonic groups are restricted by a <math>\sin x / x</math> envelope ([[sinc function]]) and extend to infinity. The infinite bandwidth is caused by the nonlinear operation of the pulse-width modulator. In consequence, a digital PWM suffers from [[aliasing]] distortion that significantly reduce its applicability for modern [[communication system]]s. By limiting the bandwidth of the PWM kernel, aliasing effects can be avoided.<ref>{{cite journal |last=Hausmair |first=Katharina |author2=Shuli Chi |author3=Peter Singerl |author4=Christian Vogel |date=February 2013 |title=Aliasing-Free Digital Pulse-Width Modulation for Burst-Mode RF Transmitters |journal=IEEE Transactions on Circuits and Systems I: Regular Papers |volume=60 |issue=2 |pages=415–427 |citeseerx=10.1.1.454.9157 |doi=10.1109/TCSI.2012.2215776 |s2cid=21795841}}</ref>

On the contrary, [[delta modulation]] and [[delta-sigma modulation]] are random processes{{Clarification needed|reason=What exactly is meant by "random" here?|date=February 2024}} that produces a continuous spectrum without distinct harmonics. While intersective PWM uses a fixed period but a varying duty cycle, the period of delta and delta-sigma modulated PWMs varies in addition to their duty cycle.