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## August 22, 2001

### Duty Cycle and DC Gain

**Question:** What is the Duty Cycle and DC Gain of a switching-mode power supply?

**Original Question:** How do I define "**duty cycle**" and what does it actually means. Please don't give me the formula.

**Answer:** The duty ratio D is the ratio of the on-time (ton) to the period (T). The on-time(ton) is the time that the energy transfer inductor is taking energy from the source and is usually controlled by the on-time of a power transistor switch. The off-time (toff) is the time that the energy transfer inductor is idle or delivering energy to the load which is usually controlled by the off-time of a power transistor switch. The sum of the on-time and off-time is the period (T), which is also the reciprocal of the switching frequency (f). The dimensions of ton, toff, and T is seconds. D is a dimensionless ratio that can have values between zero and one. Frequency (f) has the dimensions Hertz (preferred) or cycles-per-second.

In terms of a formula you did not request:

D = ton/T = ton/(ton+toff) = ton*f

D is often used to describe the DC Gain of a switching-mode power supply.

DC Gain in switching-mode power supplies is defined as the (output voltage)/(input voltage) and is often described in terms of the duty cycle D and 1-D. D' is sometimes used for 1-D. For example, the DC Gain of a buck-boost converter would be expressed as D/(1-D) or D/D'. It is a dimensionless parameter and can have the values of zero to infinity. It is often non-linear.

This information is mostly embedded in an expert system on my website, which identifies the seven single-inductor two-state converters and gives their characteristics.

Posted by Jerrold Foutz at August 22, 2001 12:20 PM