Pulse-width modulation, or pulse-duration modulation, is a modulation technique that
controls the width of the pulse, formally the pulse duration, based on modulator signal
information. Although this modulation technique can be used to encode information for transmission,
its main use is to allow the control of the power supplied to electrical devices, especially
to inertial loads such as motors. In addition, PWM is one of the two principal algorithms
used in photovoltaic solar battery chargers, the other being MPPT.
The average value of voltage fed to the load is controlled by turning the switch between
supply and load on and off at a fast pace. The longer the switch is on compared to the
off periods, the higher the power supplied to the load.
The PWM switching frequency has to be much faster than what would affect the load, which
is to say the device that uses the power. Typically switching has to be done several
times a minute in an electric stove, 120 Hz in a lamp dimmer, from few kilohertz to tens
of kHz for a motor drive and well into the tens or hundreds of kHz in audio amplifiers
and computer power supplies. 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. The main advantage of PWM is that power loss
in the switching devices is very low. When a switch is off there is practically no current,
and when it is on, there is almost no voltage drop across the switch. Power loss, being
the product of voltage and current, is thus in both cases close to zero. PWM also works
well with digital controls, which, because of their on/off nature, can easily set the
needed duty cycle. PWM has also been used in certain communication
systems where its duty cycle has been used to convey information over a communications
channel.
History In the past, when only partial power was needed,
a rheostat connected in series with the motor adjusted the amount of current flowing through
the motor, but also wasted power as heat in the resistor element. It was an inefficient
scheme, but tolerable because the total power was low. This was one of several methods of
controlling power. There were others—some still in use—such as variable autotransformers,
including the trademarked 'Autrastat' for theatrical lighting; and the Variac, for general
AC power adjustment. These were quite efficient, but also relatively costly.
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 converter such
as Ward Leonard drive. However, in addition to motor drives for fans,
pumps and robotic servos, there was a great need for compact and low cost means for applying
adjustable power for many devices, such as electric stoves and lamp dimmers.
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.
Principle
Pulse-width modulation uses a rectangular pulse wave whose pulse width is modulated
resulting in the variation of the average value of the waveform. If we consider a pulse
waveform , with period , low value , a high value and a duty cycle D, 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, it is
obvious that the average value of the signal is directly dependent on the duty cycle D.
The simplest way to generate a PWM signal is the intersective method, which requires
only a sawtooth or a triangle waveform and a comparator. When the value of the reference
signal is more than the modulation waveform, the PWM signal is in the high state, otherwise
it is in the low state. Delta
In the use of delta modulation for PWM control, the output signal is integrated, and the result
is compared with limits, which correspond to a Reference signal offset by a constant.
Every time the integral of the output signal reaches one of the limits, the PWM signal
changes state. Figure 3
Delta-sigma
In delta-sigma modulation as a PWM control method, the output signal is subtracted from
a reference signal to form an error signal. This error is integrated, and when the integral
of the error exceeds the limits, the output changes state. Figure 4
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
Direct torque control is a method used to control AC motors. It is closely related with
the delta modulation. Motor torque and magnetic flux are estimated and these are controlled
to stay within their hysteresis bands by turning on new combination of the device's semiconductor
switches each time either of the signal tries to deviate out of the band.
Time proportioning Many digital circuits can generate PWM signals.
They normally use a counter that increments periodically 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. This technique is referred to as time proportioning,
particularly as time-proportioning control – 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 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. Types
Three types of pulse-width modulation are possible:
The pulse center may be fixed in the center of the time window and both edges of the pulse
moved to compress or expand the width. The lead edge can be held at the lead edge
of the window and the tail edge modulated. The tail edge can be fixed and the lead edge
modulated. Spectrum
The resulting spectra are similar, and each contains a dc component, a base sideband containing
the modulating signal and phase modulated carriers at each harmonic of the frequency
of the pulse. The amplitudes of the harmonic groups are restricted by a envelope 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 communications system. By limiting the bandwidth of the PWM
kernel, aliasing effects can be avoided. On the contrary, the delta modulation is a
random process that produces continuous spectrum without distinct harmonics.
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 shows that PWM conversion can be perfect. The theorem states that "Any
bandlimited baseband signal within ±0.637 can be represented by a pulsewidth modulation
waveform with unit amplitude. The number of pulses in the waveform is equal to the number
of Nyquist samples and the peak constraint is independent of whether the waveform is
two-level or three-level." 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 will be sent at regular intervals.
_ _ _ _ _ _ _ _ | | | | | | | | | | | | | | | |
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 the 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. Potential drawbacks to this technique are the pulsations defined
by the duty cycle, switching frequency and properties of the load. With a sufficiently
high switching frequency and, when necessary, using additional passive electronic filters,
the pulse train can be smoothed and average analog waveform recovered.
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, 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 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 but still
more than 70–80% efficiency can be achieved. Variable-speed fan controllers for computers
usually use PWM, as it is far more efficient when compared to a potentiometer or rheostat.
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 in the AC halfcycle the dimmer
begins to provide electrical current to the light source. 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. These rather simple types of dimmers can be
effectively used with inert 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, 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, 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 Simmerstat. This consists of a thermal
oscillator running at approximately two cycles per minute and the mechanism varies the duty
cycle according to the knob setting. The thermal time constant of the heating elements is several
minutes, so that the temperature fluctuations are too small to matter in practice.
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
PWM is sometimes used in sound synthesis, in particular subtractive synthesis, as it
gives a sound effect similar to chorus or slightly detuned oscillators played together.
The ratio between the high and low level is typically modulated with a low frequency oscillator.
In addition, varying the duty cycle of a pulse waveform in a subtractive-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 was distinctive, because even-numbered
harmonics essentially disappear at 50%. Pulse waves, usually 50%, 25%, and 12.5%, make up
the soundtracks of classic video games. A new class of audio amplifiers based on the
PWM principle is becoming popular. Called "Class-D amplifiers", they produce a PWM equivalent
of the analog input signal which is fed to the loudspeaker via a suitable filter network
to block the carrier and recover the original audio. These amplifiers are characterized
by very good efficiency figures and compact size/light weight for large power outputs.
For a few decades, industrial and military PWM amplifiers have been in common use, often
for driving servo motors. Field-gradient coils in MRI machines are driven by relatively high-power
PWM amplifiers. Historically, a crude form of PWM has been
used to play back PCM digital sound on the PC speaker, which is driven by only two voltage
levels, typically 0 V and 5 V. By carefully timing the duration of the pulses, and by
relying on the speaker's physical filtering properties it was possible to obtain an approximate
playback of mono PCM samples, although at a very low quality, and with greatly varying
results between implementations. 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 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 signals are used in micro-inverter design. These switching signals are fed to the FETs
that are used in the device. The device's efficiency depends on the harmonic content
of the PWM signal. There is much research on eliminating unwanted harmonics and improving
the fundamental strength, some of which involves using a modified carrier signal instead of
a classic sawtooth signal in order to decrease power losses and improve efficiency. Another
common application is in robotics where PWM signals are used to control the speed of the
robot by controlling the motors. See also
Delta-sigma modulation Pulse-amplitude modulation
Pulse-code modulation Pulse-density modulation
Pulse-position modulation Radio control
RC servo Sliding mode control - produces smooth behavior
by way of discontinuous switching in systems Space vector modulation
Class-D amplifier References
External links An Introduction to Delta Sigma Converters
Introductory Tutorial on PWM and Quadrature Encoding
Pulse Width Modulation using 555 Timer Pulse Width Modulation in PID control loop
- free simulator