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外文原文Pulse-width modulationPulse-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.HistoryIn the past, when only partial power was needed (such as for a sewing machine motor), a rheostat (located in the sewing machines 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 otherssome still in usesuch 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. 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 , with period , low value , a high value 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 onthe duty cycle DFig. 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 proportioningMany 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 control4 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 methods 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 theoremThe 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 theorem6 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 (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 deliveryPWM 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 (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 7080% 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 regulationMain article: Switched-mode power supplyPWM 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 amplificationPWM 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 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 ( 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 speakers 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. 中文翻译一、脉冲宽度调制 脉冲宽度调制(PWM),是一种在一定的脉冲持续时间内,基于调制信号来追踪所希望达到的脉冲宽度的调制方式。虽然这种调制技术经常用于对传输信息进行编码,但是它主要的用途是控制电源装置供电到电气设备,特别是对惯性负载的供电,如电动机等。此外,PWM还是光伏太阳能电池充电器中使用的两种主要算法之一。通过快速的转换对电源和负载之间的开关的开断进行控制,将电压的平均值(和电流)供给到负载。与开关较长的打开时相比,关断期间供给到负载的功率较高。PWM的开关频率必须要高于负载的启动频率,也就是说,要使装置在有用功区工作。通常在电炉中,开关会在一分钟内多次切换,在一盏灯光衰减器中会达到120Hz,从几千赫兹(kHz)到几十千赫兹的电机驱动器和顺利进入几十或几百kHz的音频放大器和电脑电源供应器。占空比描述的是持续开启时间与控制周期之比;低占空比时,系统功耗比较低,因为开关大部分时间是关闭的。工作周期用百分比表示,100%是完全工作状态。PWM的主要优点是,开关器件的功率损耗非常低。当开关处于关闭状态时,可以说没有电流通过;当它打开时,整个开关都没有电压降。因为系统中的功率损耗等于电压和电流的乘积,因此,在这两种情况下系统的功率损耗都接近零。同时PWM技术是通过数字来控制,即通过开关性质的变化来控制,我们可以很方便地设置所需的占空比,使达到的效果更好。PWM技术也被用在某些通信系统中,其中它的占空比被用来描述通过通信信道传播信息的比例。二、历史发展在过去,当只有部分功率是有需求的(例如,对于一个缝纫机马达)时候,一个可变电阻器串联连接的电动机(位于缝纫机的脚踏板)由此产生,它是用来调节流过电机的电流的大小,但电阻元件产生的热量也浪费了很多电源功率。这是一个低效率的方案,但是因为总功率同样很低,所以它也被人所接收。 这是控制功率的几种方法之一。还有其他的一些方案仍然在使用,如仍在使用可变自耦变压器的商标为Autrastat的舞台灯光; 和适用于一般的交流功率调节的自耦变压器。这些都是很有效的设计,但成本也比较昂贵。大约一个世纪前,一些变速电动机有相当高的工作效率,但他们中有些比恒转速电机更复杂,有些需要体积较大的外部电气设备,如可变功率电阻堆栈或旋转转换器,病房伦纳德驱动等。然而,除了用于风机,泵和机器人伺服系统的电机驱动模块,人们对于如何能更加简洁和低成本的应用于很多可调节功率的设备,还是有很大的需求,如电炉和灯调光器。PWM的一个早期应用是在辛克莱的X10。在20世纪60年代,一个10瓦的音频放大器应用了这项技术。大约在同一时间,PWM开始在交流电机控制中被使用。 三、原理 图1:一个脉冲波 ,表现出的定义 , 和D。 脉冲宽度调制采用了矩形脉冲波 ,其脉冲宽度被调制为可以形成变化的平均波形的值。如果我们考虑的脉冲波形 ,以周期 ,低电平 ,高电平 和一个占空比 D(见图1),该波形的平均值由下式给出:如果 是脉冲波,则在 时间内,它的值为 ;在 时间内,它的值为。 上面的表达式就变成了:在许多情况下,后面的式子还可以简化,比如在 时, 。 由此,显而易见的是该信号的平均值( )与占空比D有直接的参数关系。 图 2:交互式PWM是一种简单的产生对应于给定信号的PWM脉冲波形的方法:用所述信号(这里为红色正弦波)与锯齿波形(蓝色)进行比较。 当后者小于前者,PWM信号(品红色)处于高电平(1)。 否则,它处于低电平(0)。产生PWM信号的最简单的方法是交互性方法,该方法仅需要一个锯齿或三角形波(使用振荡器容易生成)和一个比较器。当参考信号(图2中的红色正弦波)的值大于所述调制波形(蓝色)时,PWM信号(品红)是在高电平的状态,否则它是在低电平的状态。四、时间比例许多数字电路可以产生PWM信号(例如,许多微控制器具有PWM输出端口)。人们通常使用一个周期性的递增计数器(它直接或间接地连接到时钟电路)来产生PWM信号,并且在每个PWM周期结束之后对计数器进行复位。 当计数器值大于参考值,则PWM输出改变状态从高向低(或者从低到高)。 这种技术被称为时间比例,特别是控制一个固定周期中处于高电平状态的时间比例时,这种技术也被称为时间比例控制法。不断以周期性递增的复位计数器产生的离散的交叉锯齿波。交叉方法的模拟比较器将当前计数器的值与数字参考值做了一个全面的比较。由计数器分辨率的函数可知,占空比仅在离散时间内变化。然而,高分辨率计数器同样可以产生令人相当满意的效果。五、PWM采样定理PWM转换的过程是非线性的,一般假设PWM中的低通滤波器的信号恢复过程是不完善的。 PWM的采样定理表明,PWM转换可以是完美的。该定理指出:任何有限基带信号0.637都可通过脉冲宽度调制单元的振幅(PWM)波形来表示。脉冲波形的数量等于奈奎斯特的采样数量,并且对峰值的约束不依赖于波形是二级还是三级。六、电力输送PWM可被用于不产生由于通过电阻装置的线性功率输送而产生的损耗时,对传输到负载的功率进行控制。其潜在的缺点是,该技术是用占空比来约束脉动,开关频率和负载的性质。具有足够高的开关频率,并在需要使用额外的无源电子滤波器时,脉冲序

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