Bode Plots and Frequency Response Problem-Solving Quiz Quiz

Strengthen your understanding of Bode plots and frequency response concepts with this quiz focused on interpretation, magnitude and phase calculation, and practical problem-solving. Designed for learners aiming to enhance their grasp of system behavior in the frequency domain.

1. Identifying Corner Frequency

   Given a transfer function H(s) = 10 / (s + 10), what is the corner frequency in radians per second for plotting its Bode plot?

   1. 10
   2. 100
   3. 0.1
   4. 1

   Explanation: The corner frequency is defined as the value of s where the denominator term equals the numerator frequency component, which in this case is 10 radians per second. The options 1 and 0.1 are incorrect because they do not match the constant in the denominator. Option 100 would be too high for this configuration. Thus, 10 is the correct corner frequency.

2. Bode Plot Slope Calculation

   For the transfer function H(s) = 1 / (s^2 + 2s + 1), what is the expected slope of the magnitude Bode plot after the corner frequency at high frequencies?

   1. -10 dB/decade
   2. -40 dB/decade
   3. -20 dB/decade
   4. +20 dB/decade

   Explanation: The function has two poles at s = -1, creating a second-order system which yields a slope of -40 dB/decade after the corner frequency. The choice -20 dB/decade is for a single-pole system. -10 dB/decade and +20 dB/decade do not apply for standard pole-zero arrangements in such transfer functions. The correct answer reflects the cumulative effect of two poles.

3. Interpreting Phase Shift

   At what phase angle will a simple first-order lag system H(s) = 1 / (s + a) approximately be when the input frequency is equal to its corner frequency?

   1. -45 degrees
   2. -90 degrees
   3. 0 degrees
   4. -180 degrees

   Explanation: For a first-order lag system, the phase shift at the corner frequency is approximately -45 degrees. The -90 degrees option is the asymptotic value approached at frequencies much higher than the corner frequency. 0 degrees occurs at very low frequencies, and -180 degrees is not reached for a single-pole system. Thus, -45 degrees is the correct phase angle at the corner.

4. Magnitude Calculation Example

   If the magnitude of a system at 1 rad/s is 20 dB and the slope is -20 dB/decade, what will the magnitude be at 10 rad/s?

   1. -20 dB
   2. 20 dB
   3. 10 dB
   4. 0 dB

   Explanation: A slope of -20 dB/decade means the magnitude decreases by 20 dB when the frequency increases by a factor of 10 (a decade). Therefore, at 10 rad/s, the magnitude will drop from 20 dB to 0 dB. 10 dB and -20 dB are not correct for this setting, and 20 dB would ignore the effect of the negative slope. Zero decibels is the correct answer given these conditions.

5. Effect of Zeros on Bode Plots

   How does the presence of a zero at s = -5 affect the magnitude Bode plot of a transfer function for frequencies much higher than 5 rad/s?

   1. It has no effect on the slope
   2. It decreases the slope by -20 dB/decade
   3. It increases the slope by +20 dB/decade
   4. It decreases the slope by -40 dB/decade

   Explanation: A zero contributes a +20 dB/decade increase in magnitude on the Bode plot for frequencies above its location, so the correct answer is an increase in slope by +20 dB/decade. A decrease by -20 or -40 dB/decade refers to the effect of one or two poles, not zeros. Stating it has no effect is incorrect, as a zero changes the slope. Only the +20 dB/decade increase matches the effect of a single zero.