Digital Circuits

Timer Circuits

18 questions By Tony R. Kuphaldt

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Question 16 of 18

An important measurement of pulse waveforms is duty cycle. Give a precise. mathematical definition for this term.

Also, write an equation solving for pulse width given duty cycle (D) and frequency (f).

Reveal answer

“Duty cycle” is a measure of a pulse waveform’s on time versus its total time (period):

D = t_on
t_total

I’ll let you figure out how to write an equation solving for pulse width (t_on) in terms of duty cycle and frequency.

Notes:
Duty cycle is a very important concept, as analog information may be conveyed through the variable duty cycle of an otherwise digital pulse waveform. Discuss this application with your students, if time permits.
Question 17 of 18

Research the “pinout” for a 555 timer integrated circuit, in an 8-pin DIP package. Then, label the pins as shown on this figure:

Reveal answer

Notes:
This question is a simple exercise in researching a component datasheet.
Question 18 of 18

Write equations for the charging and discharging times of the capacitor, given the values of R₁, R₂, and C in a circuit of this design:

Base your equations on the general rules of RC time constant circuits. Don’t just copy the completed equations from some reference book! Assume that the 555’s discharge transistor is a perfect switch when turned on (0 volts drop). Note that the supply voltage is irrelevant to these calculations, so long as it remains constant during the charging cycle.

Reveal answer

t_charge = − ln0.5 (R₁ R₂) C

t_discharge = − ln0.5 R₂ C

Follow-up questions: write an equation for the circuit’s frequency, given values of R₁, R₂, and C. Then, write another equation for the circuit’s duty cycle.

Notes:
Have your students show you how they mathematically derived their answer based on their knowledge of how capacitors charge and discharge. Many textbooks and datasheets provide this same equation, but it is important for students to be able to derive it themselves from what they already know of capacitors and RC time constants. Why is this important? Because in ten years they won’t remember these specialized equations, but they will probably still remember the general time constant equation from all the time they spent learning it in their basic DC electricity courses (and applying it on the job). My motto is, “never remember what you can figure out.”

The challenge questions are worthwhile to do in class, even if few students were able to derive them on their own. If nothing else, such an exercise reviews the meaning of “frequency” and its relationship with period, as well as the definition of “duty cycle.”