Basics of AC

DC and AC difference

In direct Current (DC), the voltage and current may vary, but they do not change sign, the charges always flow in the same direction. With alternating current (AC), the charges also change direction as a function of time.

Periodic signals

The most common periodic AC signals are sine wave, square wave, triangle wave and sawtooth. Amplitude, period, frequency, slope, phase angle, offset and RMS voltage are all parameters which describe them.

Simple sine wave

In homes, sockets supply alternating current. The AC voltage produced by the generators of the electricity supplier is a sine wave with a voltage of 230V and a frequency of 50Hz. These values vary by continent.

A: Amplitude/Peak voltage $ (V_{p}) $

B: Peak-to-peak voltage $ (V_{p-p}) $

C: Period $ (T) $

Frequency:

$ f[Hz] = \dfrac{1}{T} $

Angular frequency:

$ \omega \left[\dfrac{rad}{s}\right] = 2\pi ⋅ f = \dfrac{2\pi}{T} $

Voltage function:

$ V(t) = V_{p} ⋅ sin(\omega ⋅ t) $

Introduction of Phase angle and Offset

Any signal can be shifted horizontally and vertically. Vertical shift is called offset, while the horizontal shift is called phase shift. A signal can be delayed relative to another. A difference of exactly 180° is an inverted signal.

A: Amplitude/Peak voltage $ (V_{p}) $

B: Peak-to-peak voltage $ (V_{p-p}) $

C: Period $ (T) $

D: Time delay $ (\Delta t) $

E: Offset voltage $ (V_{DC}) $

Offset voltage:

$ V_{DC} = \dfrac{1}{T} ⋅ \displaystyle\int_{0}^{T} V(t) \, \,dt $

Phase angle:

$ \dfrac{\varphi}{360°} = - \dfrac{\Delta t}{T} $

Voltage function:

$ V(t) = V_{p} ⋅ sin(\omega ⋅ t + \varphi) + V_{DC} $

What is RMS voltage?

The abbreviation is Root Mean Square. It is the effective voltage, which shows how much DC voltage a given AC voltage signal corresponds to. In Europe, the peak voltage value is not the commonly known 230V, because it is actually the RMS voltage. The peak value is obviously higher, around 325V.

Calculation by integration:

$ V_{RMS} = \sqrt{ \dfrac{1}{T} ⋅ \displaystyle\int_{0}^{T} V^2(t) \, \,dt } $

Perfect sine wave:

$ V_{RMS} = \dfrac{V_{p}}{\sqrt{2}} $