PWM: Duty Cycle and Average Output

Electronics and Embedded Systems · CHAPTER 3 / 5

Level: introductory undergraduate · Study session: 15–20 minutes including practice.

Learning outcome: Relate pulse timing to an ideal average voltage.

Before you begin: Complete earlier chapters in this discipline; revise algebra and units as needed.

1. Understand the idea

Pulse-width modulation switches between two levels while varying the fraction of time spent high. The duty cycle controls the average of an ideal waveform. A motor or filtered circuit responds according to its electrical and mechanical dynamics; a microcontroller pin cannot directly power a large load.

2. Write the model

D = ton/T; f = 1/T; Vavg = D·Vhigh

Define the symbols from the worked case before substituting values. Keep units consistent, record the assumptions and round only after the calculation.

3. Follow a worked example

At a 5 V high level and 25% duty, the ideal average is 1.25 V. With period 1 ms, frequency is 1 kHz and high time is 0.25 ms.

4. Explore the model

Figure: calculated teaching cases; straight segments connect sampled points, not experimental observations. Read exact values below.

Illustrative scenario sweep — synthetic educational data
Duty (%)	Average at 5 V (V)	High time for 1 ms period (ms)
25	1.25	0.25
50	2.5	0.5
75	3.75	0.75

Change duty while keeping period fixed. Average changes, but switching frequency remains 1 kHz.

5. Reproduce it yourself

Copy the input cases into Excel or a notebook and name each quantity and unit.
Recalculate each result from the stated equation or rule. For qualitative cases, explain the state or partition decision instead.
Change one input, predict the direction of change, then calculate again.
Write one sentence explaining where the model stops being valid.

6. Check your understanding

What is the average for 80% duty at 5 V?

Reveal the answer and check your work

4 V for the ideal two-level waveform.

Compare your result, units and reasoning. If they differ, return to the equation and test the worked case first.

7. Common mistake

Averaged PWM is not automatically a clean DC voltage.

Further study and academic note

Explore the discipline reference and further learning resources. This is an original IIMEEE introductory teaching note with synthetic examples; it is not a peer-reviewed research result or a professional design specification. Figures were constructed from the listed teaching cases. Resource links support further study and do not imply endorsement.