Two signals that are equal in amplitude but different in phase refer to sinusoidal waveforms that have the same magnitude but are shifted in time. The phase shift represents a delay or advance in the waveform with respect to time.
In simple terms, the phase of a signal determines its position in the waveform cycle. A phase shift represents a displacement of the waveform along the time axis. Here's a comparison of two signals that are equal in amplitude but differ in phase:
Amplitude: The amplitude refers to the magnitude or intensity of the signal. When two signals have the same amplitude, it means that their maximum and minimum values are identical. So, visually, they will have the same "height" on a graph.
Phase: The phase of a signal indicates the position of the waveform relative to a reference point or another signal. It is usually measured in degrees or radians. A phase shift means that the waveform is shifted to the left or right along the time axis.
When comparing two signals with the same amplitude but different phase, the main difference lies in the timing of their peaks and troughs. For example, if one signal is shifted by 90 degrees (π/2 radians) with respect to the other, the peaks of one signal will align with the troughs of the other, and vice versa.
Mathematically, a phase shift can be represented as a time delay in the sinusoidal function. If we denote a sinusoidal signal as A * sin(ωt + φ), where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase, a phase shift can be introduced by altering the value of φ.
In summary, two signals that have equal amplitudes but different phases will appear similar in magnitude but will exhibit a time displacement or phase shift in their waveform cycle.