Efficiency is the ratio of output power to input power in a power converter or other device, with the difference being power loss.
The ratio can be expressed as a percentage, decimal or fraction.
Usually we know the output power and efficiency and need to figure out the total input power and loss.
For example, a circuit design may require 2W of regulated power and our options include a DC-DC converter which is 90% efficient.
Efficiency is always less than 1.00 or 100%.
Contents
Definition
Since every power conversion has some loss the general relationship is:
$$P_{in} = P_{out} + P_{loss}$$
The definition of efficiency is:
$$\eta = \frac{P_{out}}{P_{in}} $$
We can combine the above two forms to get many useful relationships.
Calcuating Loss
$$P_{loss} = P_{in} – P_{out}$$
$$P_{loss} = P_{in}(1 – \eta)$$
$$P_{loss} = P_{out}(\frac{1}{\eta} – 1)$$
Calcuating Input Power
$$P_{in} = P_{out} + P_{loss} $$
$$P_{in} = \frac{P_{out}}{\eta} $$
$$P_{in} = \frac{P_{loss}}{1 – \eta} $$
Calcuating Output Power
$$P_{out} = P_{in} – P_{loss} $$
$$P_{out} = \eta P_{in}$$
$$P_{out} = \frac{\eta}{1 – \eta}$$
Calcuating Efficiency
$$\eta = \frac{P_{out}}{P_{in}} $$
$$\eta = \frac{P_{out}}{P_{out} + P_{loss}} $$
$$\eta = \frac{P_{in} – P_{loss}}{P_{in}} $$