大连交通大学2014届本科生毕业论文外文翻译
外文原文
Pulse-width modulation
Pulse-width modulation (PWM)is a modulation technique that conforms 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,[1]
The average value of voltage (and current) 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 is.
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 switchings have to be done several times a minute in an electric stove, 120 Hz in a lamp dimmer, from few kilohertz (kHz) 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 (such as for a sewing machine motor), a rheostat (located in the sewing machine's foot pedal) 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 thetrademarked '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.
1
大连交通大学2014届本科生毕业论文外文翻译
Fig. 1: a pulse wave, showing the definitions of , and D.
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 low value
, a high value
, with period
,
and a duty cycle D (see 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, it is obvious that the average value of the signal () is directly dependent on
the duty cycle D
2
大连交通大学2014届本科生毕业论文外文翻译
Fig. 2: A simple method to generate the PWM pulse train corresponding to a given signal is the intersective PWM: the signal (here the red sinewave) is compared with a sawtooth waveform (blue). When the latter is less than the former, the PWM signal (magenta) is in high state (1). Otherwise it is in the low state (0).
The simplest way to generate a PWM signal is the intersective method, which requires only a sawtooth or atriangle waveform (easily generated using a simple oscillator) and a comparator. When the value of the reference signal (the red sine wave in figure 2) is more than the modulation waveform (blue), the PWM signal (magenta) is in the high state, otherwise it is in the low state. Time proportioning
Many digital circuits can generate PWM signals (e.g., many microcontrollers have PWM outputs). They normally use a counter that increments periodically (it is connected directly or indirectly to the 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).[3] This technique is referred to as time proportioning, particularly as time-proportioning control[4] – 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.
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[6] shows that PWM conversion can be perfect. The theorem states that \bandlimited baseband signal within ±0.637 can be represented by a pulsewidth modulation (PWM) 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.\Power delivery
PWM can be used to control the amount of power delivered to a load without incurring the losses that
3
大连交通大学2014届本科生毕业论文外文翻译
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 (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 fan controllers for computers usually use PWM, as it is far more efficient when compared to a potentiometer or rheostat. (Neither of the latter is practical to operate electronically; they would require a small drive motor.)
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 halfcycle the dimmer begins to provide electrical 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). Voltage regulation
Main article: Switched-mode power supply
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 (music) synthesis, in particular subtractive synthesis, as it gives a sound effect similar to chorus or slightly detuned oscillators played together. (In fact, PWM is equivalent to the difference of two sawtooth waves with one of them inverted.[1]) 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 (true square wave) 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 \amplifiers\a suitable filter network to block the carrier and recover the original audio. These amplifiers are
4
大连交通大学2014届本科生毕业论文外文翻译
characterized by very good efficiency figures (≥ 90%) 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 drivingservo 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 (limited frequency response, self-inductance, etc.) 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 (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.
5