Asymptotes are used when:

• A. Zeros exceed poles
• B. Poles exceed zeros
• C. Poles equal zeros
• D. Gain is zero

Answer: (B)

In control systems and signal processing, asymptotes are often discussed in the context of analyzing the behavior of transfer functions, particularly as frequency approaches infinity or zero. The correct answer emphasizes that when the number of poles in a system exceeds the number of zeros, this typically indicates a certain behavior regarding the system's stability and response.

When the poles exceed the zeros, the system is likely dominated by its poles, which can lead to a response that decreases to zero over time (for stable systems), or it may show a certain trend in its asymptotic behavior in the frequency domain. This is especially important when constructing Bode plots or analyzing the root locus of a system. The nature of the asymptotes—whether they approach a specific value or exhibit certain characteristics—depends on the order of the poles and zeros.

In contrast, the other situations do not yield the same implications for the system's behavior. When zeros exceed poles, the system may actually exhibit a rising response, and the presence of equal numbers of poles and zeros can lead to more complex behaviors but does not primarily dictate asymptotic behavior in the same way. A gain of zero, while it may signify certain characteristics of a system, does not inherently involve asymptotes.