Design Project: Pulse-Width Modulation (PWM) signal generator

Question 1:

What shape of voltage waveform would you expect to measure (using an oscilloscope) across capacitor C₁? How does this waveform interact with the DC reference voltage at the wiper of R_pot2 to produce a pulse-width modulated square wave output?

Reveal Answer

The waveform will be a ßawtooth" shape. When compared against the DC reference voltage at R_pot2's wiper by the LM339 comparator IC, the result is a square wave of varying duty cycle.

Notes:
Many students will initially be puzzled by the operating principle of this circuit. The best way I have found to answer their questions, I have found, is with a multi-trace oscilloscope (preferably one that can show three traces simultaneously). Connect one channel to the top of C₁, the next channel to R_pot2's wiper, and the third to the comparator's output terminal. A picture, as they say, is worth a thousand words.

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Question 2:

Which direction would you have to move the wiper on potentiometer R_pot2 to increase the duty cycle of the output waveform? Explain your answer.

Reveal Answer

Moving the wiper up (as drawn in the schematic) produces greater duty cycles.

Notes:
Notice that I did not even hint at why this is. Ask your students to fully explain their answers!

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Question 3:

The design recommendation for this circuit is to make resistors R₂ and R₃ both equal to the resistance of the potentiometer R_pot2. This way, the full mechanical range of the potentiometer will be useful for adjusting duty cycle: fully turning it one way will just produce a 0% duty cycle, while fully turning it the other way will just produce a 100% duty cycle.
Explain why those resistor values need to be equal to achieve this optimum usage of pot range. Hint: it has something to do with the internal workings of the 555 timer IC.

Reveal Answer

The sawtooth signal seen at capacitor C₁ (with reference to ground) oscillates between ¹/₃ and ²/₃ supply voltage.

Notes:
This question forces students to explore what the 555 is really doing, and to recognize the comparator's function in generating PWM square waves.

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Question 4:

It is important to not make resistor R₁ too small in value. Explain why, and what might happen if it were.

Reveal Answer

In the 555's discharge cycle, resistor R₁ will drop (almost) the full power supply voltage when R_pot1 is set for minimum resistance. Not only could this overheat R₁, but it could also damage the discharge transistor within the 555 timer.

Notes:
In order to really understand why insufficient resistance at R₁ would be a bad thing, students must understand the astable operating cycle of the 555 timer. This question provides a very practical context in which to explore and/or review it!

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Question 5:

For those of you who are used to working with regular opamps, the presence of resistor R₄ may be a mystery. It is necessary because of a special limitation of the type LM339 comparator IC. Research and explain what this limitation is.

Reveal Answer

The LM339 comparator is only able to sink current at its output. Therefore, R₄ acts as a pullup resistor.
Follow-up question: is this (overall) circuit capable of sourcing current to a load? Explain why or why not.

Notes:
This characteristic of the LM339 caused problems for me the first few times I tried to use it in my designs. Despite this limitation, though, the LM339 is very aptly suited for this application with its fast response and very wide power supply voltage limits.

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Question 6:

The following modification may be made to the circuit to provide it with additional output current capability:

Here, six CMOS inverters (IC part number 4049) are ganged together in parallel to supply significantly more sourcing and sinking current capability than the LM339-with-pullup-resistor could on its own. Since CMOS logic gates are inherently on-or-off devices, they have no trouble handling the square wave output of the LM339.
Two questions here: first, why all the resistors at the outputs of the inverter gates? Why not just connect all the inverter outputs directly in parallel? Secondly, what value of resistor would you suggest at the output of each gate (R₅ through R₁₀)?

Reveal Answer

The resistors prevent the (unlikely) occurrence of a short-circuit between two or more inverter gates, if one gate happens to fail high or low, or if some gates are significantly slower than others (and thus will "fight" with the faster gates during each transition).
Challenge question: adding inverter gates to the output of this circuit has an interesting effect on the duty cycle control. The potentiometer will now act backward from the way it was before (decreasing duty cycle when it formerly increased duty cycle, and visa-versa). Explain why.

Notes:
This question may or may not be suitable for your students, depending on whether or not they have studied logic gates yet. If they have not yet studied digital circuits, it may be wise to skip this question!
Note that I did not answer the question of resistor sizes. Discuss this with your students, and let them determine how these resistors should be sized. Let them have access to datasheets for the 4049 inverter IC, and ask them what parameter(s) would be the most important in this decision.
If no one notices, point out how the power supply wires are drawn for the six-gate (hex) inverter. This is a common way to show power wiring for multiple gates (or opamps, or any other sort of IC where complex elements are duplicated).

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