---
title: "Short note: Bode plot"
subject: "Signals and Systems"
chapter: 5
key: "semester_4/signals_and_systems:short-note-bode-plot"
source: https://www.bctengineer.com/q/semester_4/signals_and_systems/short-note-bode-plot
site: BCT Engineering
---

# Short note: Bode plot

Signals and Systems · Chapter 5: Continuous-Time Systems

- Asked in: 2076 Baisakh, 3 marks
- Video: [Control System Lectures - Bode Plots, Introduction](https://www.youtube.com/watch?v=_eh1conN6YM) — Brian Douglas
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/signals_and_systems/short-note-bode-plot
- Whole chapter: https://www.bctengineer.com/md/semester_4/signals_and_systems/chapter-5

## Question

Write a short note on Bode plot.

## Short answer

Bode plot shows magnitude in dB and phase versus log frequency, using straight-line asymptotes. Poles at origin give -20 dB/decade and -90 degrees; simple pole adds -20 dB/decade after corner and -45 degrees at corner. Used for bandwidth and stability margins.

## Answer

A **Bode plot** is a pair of graphs of a system's frequency response $H(j\omega)$ against $\log_{10}\omega$:
- **Magnitude plot:** $20\log_{10}|H(j\omega)|$ in dB,
- **Phase plot:** $\angle H(j\omega)$ in degrees.

Because a product of factors becomes a sum of dB values, the plot is drawn by adding simple **straight-line (asymptotic) approximations** of each factor.

**Rules for sketching:**
- A constant $K$ adds $20\log K$ dB.
- Each pole at the origin adds $-20$ dB/decade and $-90^\circ$; each zero at the origin $+20$ dB/dec and $+90^\circ$.
- A simple pole $1/(1 + j\omega/a)$: 0 dB up to the corner frequency $a$, then $-20$ dB/dec; phase goes from $0^\circ$ to $-90^\circ$ ($-45^\circ$ at $a$). At the corner frequency, the true curve is 3 dB below the asymptote.

**Example:** $H(j\omega) = \dfrac{1}{1 + j\omega RC}$ (RC LPF): flat 0 dB up to $\omega = 1/RC$, then $-20$ dB/dec.

**Uses:** read bandwidth and filter type, and find gain and phase margins for stability of control systems.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. A Bode plot shows:
   A. |H| versus linear frequency
   B. Real versus imaginary parts
   C. 20log|H| in dB and phase versus log frequency
   D. Pole-zero positions
   Answer: C. Magnitude (dB) and phase on a log-ω axis. (Key point: Axes)

2. A simple pole beyond its corner frequency gives a slope of:
   A. +20 dB/decade
   B. -40 dB/decade
   C. 0 dB/decade
   D. -20 dB/decade
   Answer: D. A simple pole drops 20 dB per decade. (Key point: Pole slope)

3. The phase of 1/(1+jω/a) at ω = a is:
   A. -45°
   B. -90°
   C. 0°
   D. -180°
   Answer: A. Phase goes from 0° to -90°, passing -45° at the corner. (Key point: Phase at corner)

4. Why use dB on a Bode plot?
   A. It makes the phase linear
   B. Products of factors become sums, so straight-line asymptotes can be added
   C. It removes the poles
   D. It converts to time domain
   Answer: B. Log turns products into sums. (Key point: Why dB)

## Related in Signals and Systems

- [Bode plot with example](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Abode-plot) — Signals and Systems, chapter 5, asked 2×
- [DT transfer function; drawing a Bode plot](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Adt-transfer-function-bode) — Signals and Systems, chapter 6

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