Alternating current circuits (AC). Theory and practice with simulations

Fundamental parameters of an AC signal

An alternating current signal is described by a series of parameters that determine its shape and behavior over time. Among these, amplitude, period, frequency, and phase are particularly important, as they allow us to characterize how voltage or current varies over the course of each cycle. Understanding these parameters is essential for correctly interpreting any sinusoidal signal and for analyzing how the various components of a circuit will respond when operating with alternating current.

Amplitude

The amplitude of an alternating current signal indicates the maximum value reached by the voltage or current during each cycle. It is measured from the average value—which in a sinusoidal wave is zero—to the positive or negative peak. This parameter determines the “height” of the wave and is directly related to the energy the signal can carry. In practice, amplitude defines the peak and peak-to-peak values, which are useful for describing the instantaneous magnitude of the signal before introducing the concept of rms value.

Period and Frequency

The period is the time it takes for a signal to complete one full cycle of oscillation and is measured in seconds. Frequency indicates how many cycles occur in one second and is measured in hertz (Hz). These two parameters are linked by a simple inverse mathematical relationship:

f = 1 / T

T = 1 / f

This means that a signal with a short period has a high frequency, while a signal with a long period corresponds to a low frequency. This relationship is fundamental for analyzing how AC signals evolve and how they interact with the various elements of a circuit.

Phase

Phase indicates at what point in its cycle an alternating current signal is at a given instant. Two signals with the same frequency can be “in phase” or exhibit a phase shift relative to each other. This phase shift is expressed as an angle, typically in degrees, and allows us to compare the lead or lag of one signal relative to another. When two waves have the same value at every instant, we say they are in phase; if one reaches its peaks before the other, it is leading; and if it reaches them later, it is lagging. Phase is an essential parameter for analyzing how multiple signals interact within an AC circuit.

Time Domain Representation of Sinusoidal Signals

The time domain representation shows how the voltage or current of a sinusoidal signal varies over time. In this type of representation, the horizontal axis corresponds to time and the vertical axis to the instantaneous value of the electrical quantity. This view allows us to clearly identify the peaks, troughs, zero crossings, and the periodic repetition of the wave. It is the most intuitive way to understand how an AC signal evolves and serves as the foundation for introducing concepts such as instantaneous values, rms values, and waveform analysis.

Waveform and instantaneous values

The waveform shows how the voltage or current of a sinusoidal signal varies over time. Each point on the graph represents an instantaneous value—that is, the value of the electrical quantity at a specific instant. These values change continuously, following the characteristic profile of the sinusoidal wave: they rise to a maximum, fall to a minimum, and cross zero again in each cycle. Analyzing the waveform allows us to identify the moments when the signal reaches its peak values, when it changes sign, and how the pattern repeats over time.

Effective values and average value

In a sinusoidal signal, the instantaneous value changes continuously, so it is useful to define quantities that represent its overall behavior. The average value indicates the average of the signal over a complete cycle. In a pure sinusoidal wave, this value is zero, since the positive and negative parts cancel each other out.

The root mean square (RMS) value is different: it represents the equivalent direct current value that would produce the same energy effect. For a sinusoidal signal, the RMS value is obtained from the peak value using the following relationship:

Veff = Vpeak / √2

Ieff = Ipeak / √2

These values allow AC signals to be compared with DC signals and are commonly used in electrical installations and measuring equipment.