Duty Cycle Calculator

With Omni's duty cycle calculator, you can quickly find the value of this important quantity in many fields, from electronics to engineering. Keep reading this short but exhaustive article to learn:

• What is the duty cycle?
• How to calculate the duty cycle from the pulse width.
• What is the relationship between the power and duty cycle?
• Examples of duty cycle in real-world situations.

What are you waiting for? Omni's duty cycle calculator is here for all your needs!

The duty cycle is a measure of the fraction of time a periodic phenomenon (a signal, a mechanical part movement or process, you name it!) is "on", regardless of the effective intensity of the "on" part.

OK, maybe it's time to introduce some jargon; it will make things easier to understand! First, we talked of periodic phenomena: this means that they repeat cyclically in time. The time in which the phenomena repeats is the period.

We define the duty cycle in signals where, in a period, the power is on only for a certain fraction of the time, a pulse if you want. The time the pulse is on is the pulse width. We have all the ingredients to calculate the duty cycle, and we can now introduce the duty cycle formula.

The formula to calculate the duty cycle is:

where:

• $D$ — Duty cycle;
• $PW$ — Pulse width; and
• $T$ — Period.

Notice that we measure both $PW$ and $T$ in time units, which makes the duty cycle dimensionless.

We can also calculate the duty factor, which is nothing but the duty cycle, but expressed as a fraction of the unit rather than as a percentage:

This value is always smaller than one.

You now know how to calculate the duty cycle from the pulse width; what if we told you that there is a formula to calculate the duty cycle from the power of the pulse?

We need two quantities:

• The power of the pulse, $P_\text{p}$; and
• The average power in the period: $\overline{P}$.

The formula is surprisingly similar to the one we met before:

Now that we have explained the calculations for the duty cycle, we can add one last formula that you can use to calculate the energy contained by the pulse. To do so, consider the dimension of energy:

Where can we find these quantities? We use a bit of common sense and choose the right pair of values. The energy of the pulse is:

By equating the two formulas we used to compute the duty cycle, we can find the analog expression:

The duty cycle is a valuable measure of the time a system will be used or available. Whether you know it or not, duty cycles appear in many situations in their "original" form (percentage of the period). You can meet one of them at Omni's 555 timer calculator.

Welders use the duty cycle to understand how long you can use a tool before it overheats, and you can apply the same concept to air compressors: the duty cycle is the time the compressor is on.

In networking, the uptime is a similar concept to the duty cycle: our uptime calculator will be even easier to understand after meeting the duty cycle calculator!

However, we need to go a bit deeper to see one of the most intriguing applications of the duty cycle: calculate the PWM, or pulse width modulation.

Here's a question: how do you obtain a sine curve using just a switch? Answer: with a dextrous use of the duty cycle. If you increase and properly decrease the duty cycle, the average power delivered to the circuit can approximate any arbitrary function.

In the picture below, you can see how varying the duty cycle (the light blue areas correspond to "on" fractions of the period) leads to a variation in the average power (the red line). We start with a small duty cycle (low average power), and we quickly increase the fraction of the time the system is on: $0.0$, $0.1$, $0.2$, $0.3$. The entity of the variations quickly reduces, and our curve flexes.

You can clearly see the sine function appearing from an on-and-off system! Obviously, the shorter the period, the better the approximation.

Take a classic NE555 circuit, and set its oscillation period to $T = 1\ \mathrm{s}$. Now, choose the adequate component to set the high part of the output to $225\ \mathrm{ms} = 0.225\ \mathrm{s}$. The duty cycle we calculate in this example is:

We can also calculate the duty cycle in the PWM examples above, maybe just the first steps. By calculating the sine function at an interval of $0.1$, we find:

The values of the samples are our desired average powers ($\overline{P}$), normalized over the peak power. These values correspond to the duty cycle for each period. If our system has a period of $0.005\ \mathrm{s}$, we can quickly find the times we must keep the signal "on". We apply multiple times the following formula: