--- title: "Bode plot with example" subject: "Signals and Systems" chapter: 5 key: "semester_4/signals_and_systems:bode-plot" source: https://www.bctengineer.com/q/semester_4/signals_and_systems/bode-plot site: BCT Engineering --- # Bode plot with example Signals and Systems · Chapter 5: Continuous-Time Systems - Asked in: 2079 Chaitra, 4 marks; 2071 Magh, 4 marks (asked 2 times) - 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/bode-plot - Whole chapter: https://www.bctengineer.com/md/semester_4/signals_and_systems/chapter-5 ## Question Describe bode plot with example. ## Short answer A Bode plot graphs magnitude (dB) and phase (deg) vs log frequency. For H(jω)=10/(1+jω/10), magnitude is 20 dB up to ω=10 rad/s, then falls at -20 dB/dec; phase goes from 0° to -90°, with -45° at ω=10. ## 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. #### Basic factors | Factor | Magnitude (asymptote) | Phase | |---|---|---| | Constant $K$ | $20\log K$ flat | $0^\circ$ | | Zero at origin $j\omega$ | $+20$ dB/dec, 0 dB at $\omega=1$ | $+90^\circ$ | | Pole at origin $1/j\omega$ | $-20$ dB/dec | $-90^\circ$ | | Simple pole $\frac{1}{1 + j\omega/a}$ | 0 dB up to $a$, then $-20$ dB/dec | $0^\circ \to -90^\circ$, $-45^\circ$ at $a$ | | Simple zero $1 + j\omega/a$ | 0 dB up to $a$, then $+20$ dB/dec | $0^\circ \to +90^\circ$ | The frequency $a$ is the **corner (break) frequency**; the true curve is 3 dB from the asymptote there. #### Example $$ H(j\omega) = \frac{10}{1 + j\omega/10} $$ - $K = 10 \Rightarrow 20\log 10 = 20$ dB. - Pole at $\omega = 10$ rad/s. Magnitude: 20 dB flat up to 10 rad/s, then falls at $-20$ dB/dec: 0 dB at 100 rad/s, $-20$ dB at 1000 rad/s. Actual value at $\omega = 10$: $20 - 3 = 17$ dB. Phase: $-\tan^{-1}(\omega/10)$: about $0^\circ$ at 1, $-45^\circ$ at 10, about $-90^\circ$ at 100 rad/s. ```text dB 20 |--------. | \ -20 dB/dec 0 +----------\--------------> w (log) 1 10 100 1000 deg 0 |----. -45 | `--. -90 | `-------------> w (log) 1 10 100 ``` #### Uses - Shows bandwidth, cutoff frequency and filter type at a glance. - Gives gain margin and phase margin for stability of feedback systems. - Quick to sketch by hand, covering a wide frequency range. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A Bode plot shows: A. |H| against linear ω B. h(t) against t C. 20log|H| in dB and phase against log ω D. Real vs imaginary part of H only Answer: C. Two graphs: magnitude in dB and phase vs log frequency. (Key point: Bode axes) 2. A simple pole at a gives magnitude slope after a of: A. -20 dB/decade B. +20 dB/decade C. -40 dB/decade D. 0 dB/decade Answer: A. 0 dB up to a, then -20 dB/dec. (Key point: Simple pole) 3. H = 10/(1 + jω/10): low-frequency magnitude is: A. 10 dB B. 20 dB C. 0 dB D. -20 dB Answer: B. 20 log 10 = 20 dB flat until 10 rad/s. (Key point: Example gain) 4. At ω = 10 the actual magnitude and phase are: A. 20 dB and 0° B. 17 dB and -90° C. 23 dB and -45° D. 17 dB and -45° Answer: D. At the corner the true curve is 3 dB below the asymptote and phase is -45°. (Key point: At corner) ## Related in Signals and Systems - [Short note: Bode plot](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Ashort-note-bode-plot) — Signals and Systems, chapter 5 - [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 ## Related in other subjects - [Bode plot: 10(S+10)/(S(S²+5S+4)(S+40))](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Abode-10s10-s-s2-5s-4) — Electrical Circuit Theory, chapter 5, asked 4× - [Bode plot: 64(S+2)/(S(S²+0.5S)(S²+3.2S+64))](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Abode-64s2-s-s2-05s-s2) — Electrical Circuit Theory, chapter 5, asked 4× - [Bode plot: 200(S+1)/(S(S+5)(S²+2S+100))](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Abode-200s1-s-s5-s2-2s) — Electrical Circuit Theory, chapter 5, asked 4× - [Bode plot: 20(S+1)/((S²+4S+2)(S²+5S))](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Abode-20s1-s2-4s-2-s2) — Electrical Circuit Theory, chapter 5, asked 4×