Bode Plots: Magnitude, Phase, and Feedback Stability

All flashcards

What is a Bode plot?

A pair of graphs showing a system's frequency-response magnitude and phase versus logarithmic frequency.

How is the frequency response obtained from a transfer function $H(s)$?

Evaluate the transfer function at $s=j\omega$ to obtain $H(j\omega)$, then examine its magnitude and phase.

What happens to the steady-state frequency of a sinusoid passing through an LTI system?

It remains the same; the system may change the sinusoid's amplitude and phase.

What is the phase of a normalized first-order low-pass filter at its cutoff frequency?

It is $-45^\circ$.

How are magnitude and phase contributions from transfer-function factors combined?

Add their magnitude contributions in decibels and their phase contributions in degrees.

Quiz questions

1. How is the magnitude of a frequency response commonly plotted in decibels?Answer: $20\log_{10}|H(j\omega)|$
2. After its break frequency, how does a first-order pole change the asymptotic magnitude slope?Answer: It decreases the slope by $20$ dB per decade.
3. At which frequency is phase margin evaluated?Answer: At the gain-crossover frequency, where loop-gain magnitude is unity.
4. For a normalized first-order low-pass filter, what is the magnitude in decibels at its cutoff frequency?Answer: Approximately $-3$ dB.
5. What loop-gain condition corresponds to the critical negative-feedback condition associated with instability?Answer: Loop gain has magnitude one and phase $-180^\circ$.