What is the value of s for a DC waveform?

What is the value of s for a DC waveform?

• A. s = jω
• B. s = σ
• C. s = σ + jω
• D. s = 0

Answer: (D)

In the context of analyzing signals, especially in Laplace transforms, the variable \( s \) is used to represent a complex frequency, which typically has a real part and an imaginary part. For DC (direct current) waveforms, there are specific traits that help us determine the value of \( s \). A DC waveform does not change over time, which means its frequency components are zero. In the Laplace transform context, this is often represented as \( s = \sigma + j\omega \), where \( \sigma \) is the real part and \( \omega \) represents the angular frequency (imaginary part). For a pure DC signal, the angular frequency \( \omega \) is equal to zero, leading to the conclusion that the imaginary component vanishes. Therefore, the appropriate representation simplifies to \( s = \sigma \), where \( \sigma \) can also be interpreted as zero for an ideal DC voltage without any growth or decay. In practice, setting both \( \sigma \) and \( \omega \) to zero identifies the value of \( s \) specifically for a DC waveform: \( s = 0 \). This indicates that a DC signal can be analyzed using just its constant value without factoring

In the context of analyzing signals, especially in Laplace transforms, the variable ( s ) is used to represent a complex frequency, which typically has a real part and an imaginary part. For DC (direct current) waveforms, there are specific traits that help us determine the value of ( s ).

A DC waveform does not change over time, which means its frequency components are zero. In the Laplace transform context, this is often represented as ( s = \sigma + j\omega ), where ( \sigma ) is the real part and ( \omega ) represents the angular frequency (imaginary part).

For a pure DC signal, the angular frequency ( \omega ) is equal to zero, leading to the conclusion that the imaginary component vanishes. Therefore, the appropriate representation simplifies to ( s = \sigma ), where ( \sigma ) can also be interpreted as zero for an ideal DC voltage without any growth or decay.

In practice, setting both ( \sigma ) and ( \omega ) to zero identifies the value of ( s ) specifically for a DC waveform: ( s = 0 ). This indicates that a DC signal can be analyzed using just its constant value without factoring