# What are some insights from looking at Bode plots

After studying this in school, the entire concept of a Bode plot still seems to be as a bit of a let down for me given how much emphasis is placed upon it, how often this tool is rumored to be used in the workplace and how little it actually seems to offer. Much ado is placed on how to analytically draw the Bode plot, but very little is said about its interpretation. How does this thing relate back to real life?

Most Bode plots look like this:

I honestly have to say I am not in the least impressed by this plot. All that the Bode plot is telling me is that as frequency go up, at frequency of 1 Hz, there is a peak in system response, then it goes down afterwards (surprise surprise). The phase is a bit more enigmatic, it seems to tell me that the signal experiences a larger delay as frequency goes up.

What are some conclusions that an experienced engineer is able to see from looking at these Bode plots. Are there things that are not obvious that is blocking me from seeing the utility of these bodes plots?

Since I have not done much real life engineering work with Bode plot, can someone please show me an example of a bode plot of a real system that actually provides some more interesting insights?

• As a general answer to your question of the usefulness of what you're learning in school. You might be right, you'll never use Bode plots at work. For this specifically though, they are going to teach you stuff later on, like op-amp design, and you will need to know what a Bode plot is and its implications that you currently find so blasé. In general, an engineering degree isn't going to teach you much at all about your day job. You're there to learn how to learn. – Samuel Mar 16 '15 at 19:54
• I doubt the bode plot was made for entertainment value and wow-factor. But the bode plot is easy to understand and can tell you about DC gain, gain bandwidth, and bandwidth. You can measure Q-factor graphically. You can most of the time see how many zeros and poles there are and where they are, although it's not conclusive because they can mask each other. The bode plot isn't great for stability analysis, but you can find the phase margin and gain margin. – HKOB Mar 16 '15 at 19:55
• Understanding a Bode plot can be very important for using tools to design filters. – Scott Seidman Mar 16 '15 at 21:28

One of the main innovations Bode proposed with Bode Stability plots was how the plot asymptotes behave for stable systems. A knowledge of these rules allows compensation just by manipulating the asymptotes. Much simpler than mathematical techniques like pole placement.

Some main ones spring to mind (but it's not an exhaustive list):

1. When the magnitude crosses from >0dB to <0dB at a lower frequency than the Phase=180degrees then the system is stable.

2. At this crossover frequency your Phase Margin is your "insurance policy" against unmodelled delay. It's only 20 degrees to instability for your system.

3. Falling magnitude and rising phase implies a non-minimum phase system (RHP zeros).

4. A 1-slope (-20dB/dec) at crossover is stable and is equivalent to -90 degrees. (In fact the magnitude is the integral of the phase by Bode's Theorem).

5. A 2nd order system that falls at 2-slope (magnitude) can be adequately compensated by crossing at a 1-slope in the vicinity of the crossover.

• Comment to point (1): ....the the system is stable. My question: Which system? You forgot to mention that this stability criterion is related to the systems LOOP GAIN only! You can consrtuct a BODE plot for all kinds of system - however, if it is used for a stability check it must show the loop gain (magnitude and phase). – LvW Feb 6 '16 at 13:52

The bode plot is a representation of the bigger picture. That bigger picture is the pole zero diagram: -

The top three images (all bode plots) give you different examples of a 2nd order low pass filter. The bottom left picture shows you the bigger picture - it combines the bode plot with the pole zero diagram i.e it's 3D. Bottom right is the view of the 3D image looking down from above - this is the pole zero diagram I mentioned and this contains all the mathematical information for a system or filter.

The bode plot is a simplification of the pole zero diagram but, importantly it shows you directly the response of a filter (or system) in terms of amplitude and frequency (jw).

If some of these concepts are too difficult right now then that's understandable.

• Bode combined with pole zero plot is something I have never seen before – Bajie Mar 16 '15 at 19:58

From your Bode plot (or 'frequency response' is probably a more descriptive term), just by cursory inspection it can be seen that: the system is 2nd order (since the high frequency roll-off is 40dB/decade); underdamped (since it has a resonance peak); probably has natural frequency of 1rad/sec (since the resonance peak is a little lower than 1 rad/sec); Has a DC gain of about 6dB (equivalent to a 'straight' gain of about 2); the resonance peak is about 7 or 8dB above the DC level, hence the damping coefficient is between 0.1 and 0.2, say 0.15, so the system is lightly damped; and the bandwidth is about 1.2rad/sec.

Thus, an estimate of the closed transfer function is:

$$G(s) = \frac{2}{s^2 + 0.3s +1}$$

From this transfer function you can determine the time domain response to any deterministic input signal, such as impulse, step, ramp which, along with the frequency response, gives a lot of insight into the performance of the system in the real world.

• You could also get two poles from the 180 degree phase lag at high frequency, and the shape suggests no zeros, or at least uncancelled zeros (as nothing adds 20 dB/decade of slope anywhere) – Scott Seidman Mar 16 '15 at 21:25