science

Random pulse-width modulation

Random 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 Random pulse-width modulation rather than just read about it. In short: Random pulse-width modulation (RPWM) is a modulation technique introduced for mitigating electromagnetic interference (EMI) of power converters by spreading the energy of the noise signal over a wider bandwidth, so that there are no significant peaks of the noise. This is achieved by randomly varying the main parameters of the pulse-width modulation signal.

Key takeaways

Random 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 Random pulse-width modulation to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Random pulse-width modulation from memory before moving on to harder problems.

Reference excerpt

Random pulse-width modulation (RPWM) is a modulation technique introduced for mitigating electromagnetic interference (EMI) of power converters by spreading the energy of the noise signal over a wider bandwidth, so that there are no significant peaks of the noise. This is achieved by randomly varying the main parameters of the pulse-width modulation signal.

Description Electromagnetic interference (EMI) filters have been widely used for filtering out the conducted emissions generated by power converters since their advent. However, when size is of great concern like in aircraft and automobile applications, one of the practical solutions to suppress conducted emissions is to use random pulse-width modulation (RPWM). In conventional pulse-width modulation (PWM) schemes, the harmonics power is concentrated on the deterministic or known frequencies with a significant magnitude, which leads to mechanical vibration, noise, and EMI. However, by applying randomness to the conventional PWM scheme, the harmonic power will spread out so that no harmonic of significant magnitude exists, and peak harmonics at discrete frequency are significantly reduced. In RPWM, one of the switching parameters of the PWM signal, such as switching frequency, pulse position and duty cycle are varied randomly in order to spread the energy of the PWM signal. Hence, depending on the parameter which is made random, RPWM can be classified as random frequency modulation (RFM), random pulse-position modulation (RPPM) and random duty-cycle modulation (RDCM). The properties of RPWM can be investigated further by looking at the power spectral density (PSD). For conventional PWM, the PSD can be directly determined from the Fourier Series expansion of the PWM signal. However, the PSD of the RPWM signals can be described only by a probabilistic level using the theory of stochastic processes such as wide-sense stationary (WSS) random processes.

RFM Among the different RPWM techniques, RFM (random frequency modulation) is the most common method of the three major types, used in many power converter topologies to pass the electromagnetic compatibility (EMC) test. In this type of modulation, the switching frequency of the PWM signal is varied randomly in order to spread the emitted noise of the power converters in which it is applied. RFM is very easy to implement and it offers significant reduction of the noise peaks compared to conventional PWM. However, application is limited to power converters which does not require fixed switching frequency for their normal operation. A greater degree of switching frequency variation can affect the proper functioning of the devices and components inside the power converter circuit.

RPPM RPPM is also commonly deployed in power converters to pass the EMC compliance tests. This modulation technique also offers significant reduction of the conducted emission and, consequentially, the radiated emission of power converters. However, compared to RFM, RPPM is less effective in EMI reduction. This is because the PSD of RPPM contains both the density and harmonic components, and the spectrum cannot be fully spread unlike that of RFM where the spectrum has only the density component. However, in this modulation scheme, both the switching frequency and the pulse width are fixed so that the converter components like inductors and capacitors can function properly.

RDCM In RDCM, the pulse width or the duty cycle of the PWM signal is varied randomly in order to spread the noise spectrum. This kind of modulation is less common compared to the previous ones. This is because RDCM is less effective at spreading the noise. Moreover, randomly varying the duty cycle may cause output voltage fluctuations and ripples. Besides, in some power converter topologies, the duty cycle variation is the primary means of controlling the input-output voltages and currents using closed loop control systems. An example of this could be the drive for a brushed DC motor. Since the power to the motor is already being "chopped" at a specific frequency to vary the voltage and current, introducing randomization into the process could cause detriments to the system's performance.

… excerpt ends here. Continue reading the full article.

Illustrations

Random pulse-width modulation: Main parameters of PWM signal — Main parameters of PWM signal

Worked examples

Example 1 — a first encounter with Random pulse-width modulation

Start with the simplest possible case. Write down what Random 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 Random 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 Random 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 Random pulse-width modulation

In research: Random 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 Random 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: Random 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 Random 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.

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How to study Random pulse-width modulation in 20 minutes

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

Frequently asked questions

What is Random pulse-width modulation in simple terms?

Why does Random 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 Random 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 Random pulse-width modulation.