# Important Variables and Notation

Graphic definitions of the peak voltage, peak-to-peak voltage, and RMS voltage for a sine wave.

In a power electronic system, several electrical quantities are of special interest. Efficiency has already been identified in previous posts. Maximum values of currents and voltages will be needed to determine the necessary device ratings. Energy flow is the underlying objective, and power and energy levels in each part of the system are very important. We are most interested in energy flow over reasonable lengths of time. The power electronic circuit must work to alter the flow of energy from source to load. The average energy flow rate, or average power, is therefore of particular interest.

Some important quanties are listed below:

• Average power at a specified location. This represents useful energy flow over time.
• Peak values of voltages and currents. These determine device ratings.
• Average values of voltages and currents. These represent the DC values in a circuit.
• RMS voltages and currents. These represent power in resistors, and often determine the losses in a converter.
• Waveforms. Power electronic circuits often have clear graphical properties. Study of waveforms is often the most direct way to evaluate a circuit’s operation.
• Device power. Switches are not quite ideal, and some residual power will be lost in them.

All these quantities are crucial to a basic understanding of power electronics and the circuits studied in it.

The peak voltage is simply the difference between maximum and average values of the waveform.

The peak-to-peak voltage is the difference between the maximum and minimum values of the waveform. For a wave with no DC offset, the peak-to-peak voltage is double the peak voltage.

Notation for average value of some periodic function v(t) will be given as

$\langle v\rangle = \frac{1}{T} \int_0^T{v(t)}dt$

While the RMS value for the same function is expressed

$V_{RMS} = \sqrt{\frac{1}{T} \int_0^T{v(t)}dt}$