Back to questionChoose “Save as PDF” in the print window.

SarkariResultOutBMS · 2024

Previous Year Question

In a bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order system having two zeros in left half of s-plane?
  1. −80 dB/decade
  2. −40 dB/decade
  3. 80 dB/decade
  4. 40 dB/decade

Correct answer: B

Explanation

Each first-order pole contributes −20 dB/decade and each first-order zero contributes +20 dB/decade after its corner frequency. With 4 poles and 2 zeros, the high-frequency slope is 20(2−4)=−40 dB/decade.

Formula

High-frequency slope = 20(Nz − Np) dB/decade
Np = 4, Nz = 2
Slope = 20(2 − 4) = −40 dB/decade

Step-by-step solution

High-Frequency Bode Magnitude Slope explanatory diagram

Correct Answer

B — −40 dB/decade

The system has two more poles than zeros, so its final Bode magnitude asymptote falls at 40 dB/decade.

What This Question Is Really Testing

At frequencies well above all finite corner frequencies, every pole and zero has contributed its full asymptotic slope. A first-order pole contributes −20 dB/decade; a first-order zero contributes +20 dB/decade.

Concept Foundation

The high-frequency slope can be obtained from the pole-zero count:

Final slope = 20(Nz − Np) dB/decade

Step 1 — Count the Poles

A 4th-order denominator has four poles in the pole count.

Pole contribution = 4(−20) = −80 dB/decade

Step 2 — Count the Zeros

The system has two zeros.

Zero contribution = 2(+20) = +40 dB/decade

Step 3 — Add the Contributions

Net slope = −80 + 40
Net slope = −40 dB/decade

Therefore option B is correct.

Why This Method Works

In the Bode magnitude, a numerator factor grows with frequency and contributes positive slope; a denominator factor reduces the magnitude and contributes negative slope. The net slope therefore depends on the relative degree.

Independent Verification / Cross-Check

Relative degree = Np − Nz = 4 − 2 = 2
Final slope = −20(2) = −40 dB/decade

The relative-degree method independently gives the same result.

Concept Extension

  • LHP versus RHP location affects phase behavior.
  • For magnitude asymptotic slope, a first-order zero still contributes +20 dB/decade.

Exam Strategy

At high frequency, use the one-line check −20 × (poles − zeros) dB/decade.

Other options

A counts the four poles but ignores the two zeros. C and D have the wrong positive sign because poles outnumber zeros by two.

Common mistake

Using only the 4th-order denominator and writing −80 dB/decade without adding the +40 dB/decade contribution of the two zeros.

Exam tip

Use relative degree for the final slope: −20(Np−Nz) dB/decade.

Quick method

4 poles − 2 zeros = 2 excess poles → −40 dB/decade.