Bode Plots: Frequency Response Analysis Quiz Quiz

This quiz assesses your understanding of Bode plots, including magnitude and phase analysis, frequency response characteristics, and interpretation methods. Strengthen your grasp of system behavior using expertly crafted frequency response scenarios and practical examples.

1. Interpreting Bode Magnitude Plots

   If a Bode magnitude plot for a first-order low-pass filter shows a slope of -20 dB/decade after its corner frequency, what does this slope indicate about the system's frequency response?

   1. The gain doubles every decade.
   2. The output decreases by a factor of 10 for every tenfold increase in frequency.
   3. The system becomes unstable at high frequencies.
   4. The phase increases linearly with frequency.

   Explanation: A slope of -20 dB/decade means the output magnitude drops by 20 dB for every tenfold increase in frequency, which equates to the output decreasing by a factor of 10. The phase response is not described directly by the magnitude slope, so the second option is incorrect. The gain does not double; instead, it decreases with frequency, making the third option wrong. Unstable systems are not inferred solely from this slope, so the last option is also incorrect.

2. Phase Shift in Frequency Response

   For a simple RC low-pass filter, what is the theoretical phase shift at the cutoff (corner) frequency according to the Bode phase plot?

   1. +45 degrees
   2. -45 degrees
   3. 0 degrees
   4. -90 degrees

   Explanation: At the corner frequency, the phase shift of an RC low-pass filter is -45 degrees, meaning the output lags the input by forty-five degrees. -90 degrees is the phase well above the cutoff frequency, not at the exact corner. 0 degrees only occurs at very low frequencies, and +45 degrees does not apply in this context, as passive RC filters cannot exhibit positive phase shifts.

3. Identifying Bandwidth from Bode Plot

   On a Bode magnitude plot for an amplifier, how is the -3 dB point most appropriately interpreted regarding system bandwidth?

   1. The frequency at which resonance occurs.
   2. The frequency where output falls to 70.7% of its maximum value, defining the bandwidth.
   3. The point where the phase shift is exactly 180 degrees.
   4. The location of maximum gain.

   Explanation: The -3 dB point signifies the frequency where the output magnitude is reduced to about 70.7% of its low-frequency value, defining the system's bandwidth. A phase shift of 180 degrees may be significant in oscillators but is not how bandwidth is defined. Resonance occurs at peak response, not at -3 dB. Maximum gain is at low frequencies, not at the -3 dB cutoff.

4. Bode Plot Characteristics of a Second-Order System

   Given a second-order underdamped system with a noticeable peak in its Bode magnitude plot, what does this peak indicate?

   1. The presence of resonance and potential overshoot in time response.
   2. That the system is critically damped and does not oscillate.
   3. A purely resistive load with no frequency dependence.
   4. A low-pass filter with no bandwidth limitation.

   Explanation: A peak in the Bode magnitude plot of an underdamped second-order system indicates resonance and suggests that the time response will show overshoot. Critically damped systems do not exhibit resonance peaks, so the second option is incorrect. Low-pass filters can have bandwidth limitations, so the third statement is not accurate. A purely resistive load would not display such a peak, rejecting the final option.

5. Effect of Adding a Pole on Bode Plot Slope

   What happens to the slope of the Bode magnitude plot when a new pole is added at a higher frequency than existing poles?

   1. The magnitude plot flattens out above the new pole frequency.
   2. The phase shift is unaffected by the added pole.
   3. The slope increases by 20 dB/decade before the new pole.
   4. The slope decreases by 20 dB/decade after the new pole.

   Explanation: Each added pole causes the magnitude slope to decrease by 20 dB/decade after its corner frequency. The slope does not increase before the pole, so the second option is incorrect. The plot does not flatten above the pole; instead, it continues to drop, countering the third option. Finally, a pole also shifts the phase, disproving the last statement.