Duty cycle

Also called: duty ratio, duty factor

The fraction of each period that a repeating signal spends high, often given as a percentage. A 50 % duty cycle is a symmetric square wave.

The duty cycle of a repeating digital signal is

duty cycle = time high ÷ period.

A clock is usually close to 50 %: high for half of each period, low for the other half. A short pulse once per period has a small duty cycle.

For counter outputs there's a neat shortcut. Every state lasts exactly one clock period, so

duty cycle = (number of states where the output is 1) ÷ (total number of states).

Each bit of a full binary counter is 1 in exactly half the states: 50 %.
The terminal count of a mod-N counter is 1 in one state: 1/N.
The top bit of a mod n counter whose N isn't a power of 2 is usually lopsided. In a mod-6 counter, Q2 is 1 only in states 4 and 5: 2/6 = 1/3.
Every output of a johnson counter is high for exactly half its states, so it gives a clean 50 %.

The duty cycle doesn't change the frequency: a mod-6 counter's Q2 still repeats every 6 clocks. It changes the shape of the wave, which matters when the signal drives something like a buzzer, a display multiplexer, or PWM brightness control.

Worked examples

Example

The top bit of a BCD counter

A BCD counter runs 0 to 9. What is the duty cycle of Q3?

1.
Q3 = 1 only in 1000 (8) and 1001 (9).
2.
That's 2 of the 10 states.
3.
Duty cycle = 2/10 = 20 %. Its frequency is f/10, but it is not a square wave.

Example

Reading the diagram

The diagram shows Q2 of a mod-6 counter (states 0 to 5) over 12 clock edges.

1.
Q2 is high in states 4 and 5, then low for states 0 to 3.
2.
High for 2 clock periods out of every 6.
3.
Duty cycle 2/6 = 1/3 ≈ 33 %.

Common mistakes

Mixing up duty cycle and frequency. Two signals can repeat at the same rate with very different duty cycles.
Assuming a mod-N counter's top bit is a 50 % square wave. That's only true when N is a power of 2.
Dividing by the number of flip-flops instead of the number of states.

Practice Duty cycle

Interactive questions with instant feedback and a worked solution for every wrong answer.

Counters lesson full course

Timing and Sequential Logic lesson full course

Practice exams

Learn it step by step

Duty cycle is taught in Counters.

Counters →

All terms