Pulse-width modulation
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Passband modulation |
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Analog modulation |
Digital modulation |
Hierarchical modulation |
Spread spectrum |
See also |
Pulse-width modulation (PWM), also known as pulse-duration modulation (PDM) or pulse-length modulation (PLM),
PWM is useful for controlling the average power or amplitude delivered by an electrical signal. The average value of voltage (and current) fed to the load is controlled by switching the supply between 0 and 100% at a rate faster than it takes the load to change significantly. The longer the switch is on, the higher the total power supplied to the load. Along with maximum power point tracking (MPPT), it is one of the primary methods of controlling the output of solar panels to that which can be utilized by a battery.[2] PWM is particularly suited for running inertial loads such as motors, which are not as easily affected by this discrete switching. The goal of PWM is to control a load; however, the PWM switching frequency must be selected carefully in order to smoothly do so.
The PWM switching frequency can vary greatly depending on load and application. For example, switching only has to be done several times a minute in an electric stove; 100 or 120
In electronics, many modern microcontrollers (MCUs) integrate PWM controllers exposed to external pins as peripheral devices under firmware control. These are commonly used for direct current (DC) motor control in robotics, switched-mode power supply regulation, and other applications.
Duty cycle
The term duty cycle describes the proportion of 'on' time to the regular interval or 'period' of time; a low duty cycle corresponds to low power, because the power is off for most of the time. Duty cycle is expressed in percent, 100% being fully on. When a digital signal is on half of the time and off the other half of the time, the digital signal has a duty cycle of 50% and resembles a "square" wave. When a digital signal spends more time in the on state than the off state, it has a duty cycle of >50%. When a digital signal spends more time in the off state than the on state, it has a duty cycle of <50%. Here is a pictorial that illustrates these three scenarios:
History
The Corliss steam engine was patented in 1849. It used pulse-width modulation to control the intake valve of a steam engine cylinder. A centrifugal governor was used to provide automatic feedback,
Some machines (such as a
The Philips, N. V. company designed an optical scanning system (published in 1946) for variable area film soundtrack which produced the PWM. It was intended for reducing noise when playing back a film soundtrack. The proposed system had a threshold between "white" and "black" parts of soundtrack.[3]
One early application of PWM was in the Sinclair X10, a 10 W audio amplifier available in kit form in the 1960s. At around the same time PWM started to be used in AC motor control.[4]
Of note, for about a century, some variable-speed electric motors have had decent efficiency, but they were somewhat more complex than constant-speed motors, and sometimes required bulky external electrical apparatus, such as a bank of variable power resistors or rotating converters such as the Ward Leonard drive.
Principle
Periodic pulse wave
If we consider a periodic pulse wave with period , low value , a high value and a constant duty cycle D (Figure 1), the average value of the waveform is given by:
As is a pulse wave, its value is for and for . The above expression then becomes:
This latter expression can be fairly simplified in many cases where as . From this, the average value of the signal () is directly dependent on the duty cycle D.
However, by varying (i.e. modulating) the duty cycle (and possibly also the period), the following more advanced pulse-width modulated waves allow variation of the average value of the waveform.
Intersective method PWM
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 or a 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:
- Leading 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
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
On the contrary, delta modulation and delta-sigma modulation are random processes[clarification needed] 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.
Delta modulation
Delta modulation produces a PWM signal (magenta in above figure) which changes state whenever its integral (blue) hits the limits (green) surrounding the input (red).
Asynchronous delta-sigma PWM
Asynchronous (i.e. unclocked) delta-sigma modulation produces a PWM output (blue in bottom plot) which is subtracted from the input signal (green in top plot) to form an error signal (blue in top plot). This error is integrated (magenta in middle plot). When the integral of the error exceeds the limits (the upper and lower grey lines in middle plot), the PWM output changes state. By integrating the difference of the error with the input signal, delta-sigma modulation shapes noise of the resulting spectrum to be more in higher frequencies above the input signal's band.
Space vector modulation
Space vector modulation is a PWM control algorithm for multi-phase AC generation, in which the reference signal is sampled regularly; after each sample, non-zero active switching vectors adjacent to the reference vector and one or more of the zero switching vectors are selected for the appropriate fraction of the sampling period in order to synthesize the reference signal as the average of the used vectors.
Direct torque control (DTC)
Direct torque control is a method used to control AC motors. It is closely related with the delta modulation (see above). Motor torque and magnetic flux are estimated and these are controlled to stay within their hysteresis bands by turning on a new combination of the device's semiconductor switches each time either signal tries to deviate out of its band.
PWM sampling theorem
The process of PWM conversion is non-linear and it is generally supposed that low pass filter signal recovery is imperfect for PWM. The PWM sampling theorem[8] shows that PWM conversion can be perfect:
Any
bandlimited baseband signal whose amplitude is within ±0.637 can be represented by a PWM waveform of unit amplitude (±1). The number of pulses in the waveform is equal to the number of Nyquist samplesand the peak constraint is independent of whether the waveform is two-level or three-level.
For comparison, the Nyquist–Shannon sampling theorem can be summarized as:
If you have a signal that is bandlimited to a bandwidth of f0 then you can collect all the information there is in that signal by sampling it at discrete times, as long as your sample rate is greater than 2f0.[9]
Applications
Servos
PWM is used to control servomechanisms; see servo control.
Telecommunications
In telecommunications, PWM is a form of signal modulation where the widths of the pulses correspond to specific data values encoded at one end and decoded at the other.
Pulses of various lengths (the information itself) will be sent at regular intervals (the carrier frequency of the modulation).
_ _ _ _ _ _ _ _ | | | | | | | | | | | | | | | | Clock | | | | | | | | | | | | | | | | __| |____| |____| |____| |____| |____| |____| |____| |____ _ __ ____ ____ _ PWM signal | | | | | | | | | | | | | | | | | | | | _________| |____| |___| |________| |_| |___________ Data 0 1 2 4 0 4 1 0
The inclusion of a clock signal is not necessary, as the leading edge of the data signal can be used as the clock if a small offset is added to each data value in order to avoid a data value with a zero length pulse.
_ __ ___ _____ _ _____ __ _ | | | | | | | | | | | | | | | | PWM signal | | | | | | | | | | | | | | | | __| |____| |___| |__| |_| |____| |_| |___| |_____ Data 0 1 2 4 0 4 1 0
Power delivery
PWM can be used to control the amount of power delivered to a load without incurring the losses that would result from linear power delivery by resistive means. Drawbacks to this technique are that the power drawn by the load is not constant but rather discontinuous (see Buck converter), and energy delivered to the load is not continuous either. However, the load may be inductive, and with a sufficiently high frequency and when necessary using additional passive electronic filters, the pulse train can be smoothed and average analog waveform recovered. Power flow into the load can be continuous. Power flow from the supply is not constant and will require energy storage on the supply side in most cases. (In the case of an electrical circuit, a capacitor to absorb energy stored in (often parasitic) supply side inductance.)
High frequency PWM power control systems are easily realisable with semiconductor switches. As explained above, almost no power is dissipated by the switch in either on or off state. However, during the transitions between on and off states, both voltage and current are nonzero and thus power is dissipated in the switches. By quickly changing the state between fully on and fully off (typically less than 100 nanoseconds), the power dissipation in the switches can be quite low compared to the power being delivered to the load.
Modern semiconductor switches such as MOSFETs or insulated-gate bipolar transistors (IGBTs) are well suited components for high-efficiency controllers. Frequency converters used to control AC motors may have efficiencies exceeding 98%. Switching power supplies have lower efficiency due to low output voltage levels (often even less than 2 V for microprocessors are needed) but still more than 70–80% efficiency can be achieved.
Variable-speed
Light dimmers for home use employ a specific type of PWM control. Home-use light dimmers typically include electronic circuitry which suppresses current flow during defined portions of each cycle of the AC line voltage. Adjusting the brightness of light emitted by a light source is then merely a matter of setting at what voltage (or phase) in the AC half-cycle the dimmer begins to provide electric current to the light source (e.g. by using an electronic switch such as a triac). In this case the PWM duty cycle is the ratio of the conduction time to the duration of the half AC cycle defined by the frequency of the AC line voltage (50 Hz or 60 Hz depending on the country).
These rather simple types of dimmers can be effectively used with inert (or relatively slow reacting) light sources such as incandescent lamps, for example, for which the additional modulation in supplied electrical energy which is caused by the dimmer causes only negligible additional fluctuations in the emitted light. Some other types of light sources such as light-emitting diodes (LEDs), however, turn on and off extremely rapidly and would perceivably flicker if supplied with low frequency drive voltages. Perceivable flicker effects from such rapid response light sources can be reduced by increasing the PWM frequency. If the light fluctuations are sufficiently rapid (faster than the flicker fusion threshold), the human visual system can no longer resolve them and the eye perceives the time average intensity without flicker.
In electric cookers, continuously variable power is applied to the heating elements such as the hob or the grill using a device known as a
Voltage regulation
PWM is also used in efficient voltage regulators. By switching voltage to the load with the appropriate duty cycle, the output will approximate a voltage at the desired level. The switching noise is usually filtered with an inductor and a capacitor.
One method measures the output voltage. When it is lower than the desired voltage, it turns on the switch. When the output voltage is above the desired voltage, it turns off the switch.
Audio effects and amplification
Varying the duty cycle of a pulse waveform in a synthesis instrument creates useful timbral variations. Some synthesizers have a duty-cycle trimmer for their square-wave outputs, and that trimmer can be set by ear; the 50% point (true square wave) was distinctive, because even-numbered harmonics essentially disappear at 50%. Pulse waves, usually 50%, 25%, and 12.5%, make up the
Historically, a crude form of PWM has been used to play back
In more recent times, the Direct Stream Digital sound encoding method was introduced, which uses a generalized form of pulse-width modulation called pulse-density modulation, at a high enough sampling rate (typically in the order of MHz) to cover the whole acoustic frequencies range with sufficient fidelity. This method is used in the SACD format, and reproduction of the encoded audio signal is essentially similar to the method used in class-D amplifiers.
Electrical
SPWM (sine–triangle pulse-width modulation) signals are used in micro-inverter design (used in solar and wind power applications). These switching signals are fed to the
Soft-blinking LED indicator
PWM techniques would typically be used to make some indicator (like a LED) "soft blink". The light will slowly go from dark to full intensity, and slowly dimmed to dark again. Then it repeats. The period would be several soft-blinks per second up to several seconds for one blink. An indicator of this type would not disturb as much as a "hard-blinking" on/off indicator. The indicator lamp on the Apple iBook G4, PowerBook 6,7 (2005) was of this type. This kind of indicator is also called "pulsing glow", as opposed to calling it "flashing".
See also
- Analog signal to discrete time interval converter
- Class-D amplifier
- Computer fan control
- Continuously variable slope delta modulation
- Delta-sigma modulation
- H-bridge
- Pulse-amplitude modulation
- Pulse-code modulation
- Pulse-density modulation
- Pulse-position modulation
- Radio control
- Random pulse-width modulation
- RC servo
- Sliding mode control - produces smooth behavior by way of discontinuous switching in systems
- Space vector modulation
- Sound chip
References
- .
- ^ "Sizing a Grid-Tied PV System ...with Battery Backup". Home Power Magazine.
- ISSN 0097-5834– via IEEE.
- ^ Schönung, A.; Stemmler, H. (August 1964). "Geregelter Drehstrom-Umkehrantrieb mit gesteuertem Umrichter nach dem Unterschwingungsverfahren". BBC Mitteilungen. 51 (8/9): 555–577.
- ^ Barr, Michael (1 September 2001). "Introduction to Pulse Width Modulation (PWM)". Barr Group.
- ^ Fundamentals of HVAC Control Systems, by Robert McDowall, p. 21
- S2CID 21795841.
- ^ J. Huang, K. Padmanabhan, and O. M. Collins, “The sampling theorem with constant amplitude variable width pulses”, IEEE transactions on Circuits and Systems, vol. 58, pp. 1178 - 1190, June 2011.
- ^ Wescott, Tim (August 14, 2018). "Sampling: What Nyquist Didn't Say, and What to Do About It" (PDF). Wescott Design Services.
The Nyquist-Shannon sampling theorem is useful, but often misused when engineers establish sampling rates or design anti-aliasing filters.
- ^ "Synthesizing Strings: PWM & String Sounds". www.soundonsound.com.
- ^ Hirak Patangia, Sri Nikhil Gupta Gourisetti, "A Harmonically Superior Modulator with Wide Baseband and Real-Time Tunability", IEEE International Symposium on Electronic Design (ISED), India, Dec.11.
- ^ Hirak Patangia, Sri Nikhil Gupta Gourisetti, “Real Time Harmonic Elimination Using a Modified Carrier”, CONIELECOMP, Mexico, Feb 2012.
- ^ Hirak Patangia, Sri Nikhil Gupta Gourisetti, “A Novel Strategy for Selective Harmonic Elimination Based on a Sine-Sine PWM Model”, MWSCAS, U.S.A, Aug 2012.