For which value of s does a DC waveform result?

A DC waveform is characterized by having a constant value over time. In the context of Laplace or frequency domain analysis, the variable 's' represents the complex frequency, which can be expressed as ( s = \sigma + j\omega ). Here, ( \sigma ) is the real part associated with growth or decay, and ( \omega ) is the imaginary part linked to oscillatory components.

When considering DC signals, they exhibit no oscillation (or frequency) hence ( \omega = 0). This implies that for a pure DC representation, ( s ) must not have any imaginary component, and therefore the real part can be set to zero as well, leading to ( s = 0 ).

Evaluating the other options:

• The value of ( s = \sigma ) would imply there is still a growth or decay condition, which deviates from the pure DC nature.
• The expression ( s = j\omega ) suggests pure oscillation with no real part, again not representing DC.
• The value ( s = \sigma + j\omega ) incorporates both growth/decay and oscillation, which also does not align with the properties of a DC waveform.

Thus,