ArticleslgStudy

science

Pulse-width modulation

Pulse-width modulation is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Pulse-width modulation rather than just read about it. In short: Pulse-width modulation (PWM), also known as pulse-duration modulation (PDM) or pulse-length modulation (PLM), is any method of representing a signal as a rectangular wave with a varying duty cycle (and for some methods also a varying period). PWM is useful for controlling the average power or amplitude delivered by an electrical signal.

Pulse-width modulation — main illustration
Pulse-width modulation — illustration

Key takeaways

  • Pulse-width modulation belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Pulse-width modulation to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Pulse-width modulation from memory before moving on to harder problems.

Reference excerpt

Pulse-width modulation (PWM), also known as pulse-duration modulation (PDM) or pulse-length modulation (PLM), is any method of representing a signal as a rectangular wave with a varying duty cycle (and for some methods also a varying period). 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. 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 Hz (double of the utility frequency) in a lamp dimmer; between a few kilohertz (kHz) and tens of kHz for a motor drive; and well into the tens or hundreds of kHz in audio amplifiers and computer power supplies. Choosing a switching frequency that is too high for the application may cause premature failure of mechanical control components, despite getting smooth control of the load. Selecting a switching frequency that is too low for the application causes oscillations in the load. 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 and power is being transferred to the load, 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.

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 sewing machine motor) require partial or variable power. In the past, control (such as in a sewing machine's foot pedal) was implemented by use of a rheostat connected in series with the motor to adjust the amount of current flowing through the motor. It was an inefficient scheme, as this also wasted power as heat in the resistor element of the rheostat, but tolerable because the total power was low. While the rheostat was one of several methods of controlling power (see autotransformers and Variac for more info), a low-cost and efficient power switching and adjustment method was yet to be found. This mechanism also needed to be able to drive motors for fans, pumps and robotic servomechanisms, and needed to be compact enough to interface with lamp dimmers. PWM emerged as a solution for this complex problem. PWM telecommunications systems were invented just prior to the start of World War II, but at that time time-division multiplexing was already in use and there were only experimental PWM systems. This changed with the introduction of the cavity magnetron in 1940, which could produce pulses of microwave frequency energy but could not vary its frequency or precisely control its amplitude. A PWM encoder was used to trigger a magnetron in the British Army's Wireless Set Number 10, which provided long-distance telephone relay, up to 80 kilometres (50 mi). By 1946, the Philips, N. V. company had designed an optical scanning system for variable area film soundtrack which used PWM while it was scanning the optical audio track transversely with a thin light beam. The electronics then evaluated the threshold between exposed (non-translucent) and unexposed (translucent) parts of the audio track. The proposed system was to reduce noise when playing a film soundtrack. 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. In the mid-1970s, early automotive applications of pulse-width modulation (PWM) were developed in the UK by Associated Engineering Developments Ltd (AED). Engineers Norman Hunt and John Noddings designed systems that used pulse-width modulated electrical signals to control high-speed solenoid valves. By altering the signal's duty cycle, the system could vary hydraulic and pneumatic pressure instead of just turning a solenoid valve fully open or fully closed. This technology was commercialised through AED's subsidiary company, Econocruise Ltd, based in Rugby, Warwickshire. The company used these modulated solenoid valves in pneumatic assemblies to control throttle actuators, supplying cruise control systems for luxury passenger cars and PWM speed limiters for heavy commercial trucks and buses. 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

… excerpt ends here. Continue reading the full article.

Illustrations

Pulse-width modulation: Varying the pulse width of a signal is a method of representing an analog signal as a rectangular wave with a varying duty cycle.
Varying the pulse width of a signal is a method of representing an analog signal as a rectangular wave with a varying duty cycle.
Pulse-width modulation illustration
Pulse-width modulation illustration
Pulse-width modulation: Fig. 1: a periodic pulse wave, showing 
  
    
      
        
          y
          
            min
          
        
      
    
    {\displaystyle y_{\text{min}}}
  
, 
  
    
      
        
          y
          
            max
          
        
      
    
    {\displaystyle y_{\text{max}}}
  
 and constant duty cycle D.
Fig. 1: a periodic pulse wave, showing y min {\displaystyle y_{\text{min}}} , y max {\displaystyle y_{\text{max}}} and constant duty cycle D.
Pulse-width modulation illustration

Worked examples

Example 1 — a first encounter with Pulse-width modulation

Start with the simplest possible case. Write down what Pulse-width modulation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Pulse-width modulation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Pulse-width modulation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Pulse-width modulation

In research
Pulse-width modulation appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Pulse-width modulation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Pulse-width modulation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Signal processing, so understanding it makes those chapters shorter.
In everyday life
Look for Pulse-width modulation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Pulse-width modulation in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Pulse-width modulation means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Pulse-width modulation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Pulse-width modulation in simple terms?

Pulse-width modulation (PWM), also known as pulse-duration modulation (PDM) or pulse-length modulation (PLM), is any method of representing a signal as a rectangular wave with a varying duty cycle (and for some methods also a varying period). PWM is useful for controlling the average power or ampli…

Why does Pulse-width modulation matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Pulse-width modulation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Pulse-width modulation.

Tags

  • Signal processing

Keep exploring