This is a very general question. In undergrad electrical engineering, students are usually taught about step response to LC (second order) circuits.

This is usually when many parameters are introduced, some of which are

  • rise time
  • peak time
  • percentage overshoot
  • settling time

The definition of these could be found in various sources, such as wikipedia: https://en.wikipedia.org/wiki/Settling_time

and detailed formulas exist for many of these quantities https://ocw.mit.edu/courses/mechanical-engineering/2-004-dynamics-and-control-ii-spring-2008/lecture-notes/lecture_21.pdf


I do not have an extensive circuit design background, I am guessing that these parameters can be used as rule of thumb to calculate system transfer function, or location of poles, etc. I have no idea how they can be used in reality.

Can working electrical engineers in circuit design comment on the practical usefulness of these parameters? Or are these parameters found by some algorithm that is used in design process?

Many thanks!

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    \$\begingroup\$ Depends on the specific application of your work. Being able to approximate or cross-check is very valuable. \$\endgroup\$ Oct 29, 2016 at 0:08
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    \$\begingroup\$ The reality is, while these are important academic exercises, they're pretty useless in real world design engineering in 2016. \$\endgroup\$
    – Matt Young
    Oct 29, 2016 at 3:28
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    \$\begingroup\$ Sometimes there's a gap between academia and reality. If it wasn't so large, astronomers probably would have given it a name and used it as their unit of choice for lengths. ;-) \$\endgroup\$ Oct 29, 2016 at 22:16
  • \$\begingroup\$ If you're asking if is worth teaching a specific point, bear in mind that for any one speficic career, there is a high chance that most of the detail will be irrelevant - what matters is how fast people can learn the specifics of their current role. So some detail is important. What that detail is matters far less. In my current position, stats is the big weak-point (using constrained random testbenches for digital designs). \$\endgroup\$ Oct 31, 2016 at 20:26
  • \$\begingroup\$ You should really ask if there is value in the teaching, not if there is value in the material. They are very different things - I always ask interview questions that I know the candidate won't know the answer to. \$\endgroup\$ Nov 1, 2016 at 13:42

11 Answers 11


Short answer - In 20 years I haven't done so once.

Longer answer:
It depends a lot on the field you're working in.

Do you have to worry about rise times, fall times etc... Yes. Not for every signal, in fact you normally only care about them for a tiny fraction of signals. Knowing which ones matter is an important part of the job.

But for the ones that do matter the formulas in the book are fairly useless, they are great for a first pass approximation but if a rough approximation is good enough it's probably not a signal that's too critical to start with. Any real world circuit is far too complex to analyse in detail by hand, instead you run a simulation rather than using the formula in the book and the simulator already knows the formulas.
So the book formulas are good because then you understand what the simulator is doing behind the scenes and the assumptions and limitations in what it is doing. There is a lot to be said for having an appreciation of what your tools are doing in the background, if nothing else it helps figure out why they break or complain about things when they do. But you don't need to remember or even be able to work through the maths that is going on behind the curtain.

And then ultimately no matter what the simulator tells you after you've build it you check in the real world because as the saying goes in theory theory and practice are the same. In practice they aren't.


These calculations are absolutely used by professional EEs, for some on a daily basis. However, for many this job has been given to simulation software, such as LTSpice, which is also used on a daily basis. Generally the simulation is much faster to complete, so it is much more productive than doing the calculations by hand.

I generally use the formulas only to get a general idea of what to expect (say, within an order of magnitude), and leave the actual number crunching to the simulators.


You refer to these basic formulae at first and then find the real world has a lot of non-linear characteristics like XOR phase detectors in a second PLL loop response when you exceed the phase limit or that all Low Pass filters cause Inter-Symbol-Interference (ISI) unless the filter resonates within the binary symbol then you apply "Raised Cosine" Filters for zero jitter.

The Most Important Lesson to learn ,is to understand the problems for any environmental stress, influence from EMI, SNR and WRITE GOOD Design Specs without any implementation restrictions. i.e. "non-implementation specific. Understand this better, by reading good specs like any commercial component and make your project well specified to know ALL requirements for inputs and outputs like Z,V,I,of t and f and ALL TOLERANCES, then you have something to validate, test and have good acceptance criteria and margin for error and test to failure to know the consequences, the weakest link and the fault detection, correction aspects of your design.

They don't teach this is in school. But you can learn quick by attention to details.

Then you learn how to make the system more linear by constraints or limited range or dual bandwidth or a better PID loop to minimize or prevent overshoot by changing feedback modes from acceleration mode to velocity to position.

Some key critical skill useful in Analog/Digital Electronics is to perform a Sensitivity analysis, Worst case tolerances, Design of Experiments (DoE), Margin Testing ( e.g. change Supply error, %Clock error and vibration simultaneously) and Design/Process Verification Test Plans or DVT/PVT.

I have used the dozens of different tools for Simulation from high end to free tools like VSpice, Mag-designer, Filter designers, Bode Analyzers, Network Analyzers, Modal Analyzers and ... 96 channel Logic Analyzers. Sometimes everything works when you put all the probes on.... But lately for show N tell I like all the dozens of Physics Java tools including circuit analyzers with this primitive Type II PLL example.

For a linear 2nd Order System, I prefer my own tested benchmarks;

  • \$Ts_{2\%} = \frac{Q * T_o}{2} \$ , for resonant \$f_o=\frac{1}{T_o}\$ and ac gain \$= Q=\$ impedance ratio

  • Step Response Overshoot=200% for high Q & 70% for critically damped.
    • then you learn shock mount elastomers( e.g. Lord mounts) have a Q=5 at \$f_o\$ ( and that is good !)
  • You learn after Test Verification with Spectrum Analyzers and DSO's to develop your equations for different Impedance and Force relationships
  • e.g. for a given drop height, , and stop height, ( in most materials)
    • peak mechanical shock level \$ g= \frac{drop. height}{stop. height}\$
      • verified with accelerometers , followed by damped oscillation
      • also important is velocity vs shock in g to create a inverse power curve call Fragility Boundary for different time intervals of mechanical impulses.

Anecdotal Experience

When I started in 1975, I usually did all my calculations on Impedance Nomograph chart unless I needed 1% accuracy. This graph works well for series or shunt filters of many kinds. Then you learn the useful range of L and C values for useful impedance ranges. e.g. Supply ripple filters to data/signal filters. But for serious RF filters they will be >5th order bandstop-bandpass with complex specs using common characteristics like Bessel, Cauer, Gaussian etc.

enter image description here

With reactance / impedance ratios I get Q and from Resonant frequency I get bandwidth which gives me 1st order response time.

Or from RC value I get corner frequency.

Or for Tuned filter with L and F, I can choose Q and C in either resonant or anti resonant (180 or 0 deg )

You can find this and similar charts by web searching " RLC NOMOGRAPH"

This answer was Not intended to teach you how to use it's dozens of applications, rather assumes you have a solid understanding of Q, ESR, ESL, Zo stripline and all variations of applications of RLC and just want to get a quick "Sliderule speed vs calculator answer".

We used Slide Rules for square rootsand multiplying in 1975 and had an exam question to statistically define its accuracy on each scale; log, x, division, etc.

  • In retrospect, it depends on your passions, luck, opportunities and skills. what you remember usually, is that you once knew how to prove Gauss's Law. or Runga Cutta methods or Eigenvalue equations or non-linear integrals. These are all Tools that many may never use again, until you have a problem that needs it , then you may find an easier way, but you understand that someone has already done this before and you learn from them how to solve in new ways.

  • University is not just about problem solving tools and equations that you may never use, but knowing how to understand what you see and hear by fundamentals like the behaviour of insulators by its Fourier Spectrum of non-linear behaviour or how Ohm's Law applies to Life in so many absurd yet introspective ways.

  • Univ is all about learning how to teach yourself new technology and find solutions that may seem impossible, yet from the past, you know a solution may exist and you must discover how to make it work by collaboration.

FWIW some 40yrs later , I married the Mother-in- law of the son (who is also a U of T EE prof) of my Prof at Winnipeg U of M in Controls Systems 401 , who taught me how to analyze Bode Plots , overshoot, cumulative Integrated error squared analysis and Root Locus. Now when I see professional truck drivers I compare this computation in my head if I am bored driving on the highway and compare with slack consumer car drivers and imagine how robotic automated driving cars algorithms work today with PID loops and compensation for risk avoidance analysis and overshoot from excessive gain due software algorithms on high speed video and other such mind-numbing topics...

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    \$\begingroup\$ That chart says "copyright 6/9/03." Unless you had a working time machine in 1975, you couldn't have used that chart! ;) \$\endgroup\$
    – jonk
    Oct 29, 2016 at 7:21
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    \$\begingroup\$ @jonk This is my chart. There are many like it, but this one is mine. My chart is my best friend. It is my life. I must master it as I must master my life. \$\endgroup\$
    – nitro2k01
    Oct 29, 2016 at 19:57
  • \$\begingroup\$ @nitro2k01 Okay. I was just teasing Tony, though. ;) \$\endgroup\$
    – jonk
    Oct 29, 2016 at 20:20
  • \$\begingroup\$ jonk this is just a web version that someone created with more decades , mine was on paper . I approve this message ©®™ ( you shud know betta) \$\endgroup\$ Oct 29, 2016 at 20:24
  • \$\begingroup\$ Watching truckers on the highway, and passenger cars towing smallish trailers, I tend to wonder about trailer sway. It's a closed loop system, with vehicle and trailer mass/inertia and tyre elasticity in play (defining the resonant frequency) - the one thing I keep wondering about: why does the resonant Q or regulation gain get higher at higher speeds? Possibly because, at a higher speed, one quarter-period of the sway translates into more wheel revolutions, resulting in more energy being available for the reactive sideways action? ;-) Food for thought \$\endgroup\$
    – frr
    Nov 1, 2016 at 20:31

Engineers design things because there is a customer that wants or needs something. The time parameters you are asking about and others effect how satisfied the customer will. I would say engineers calculate these parameters from the transfer function because they know how they be perceived by the customer.

One example I can give is video amplifiers in the days of CRTs. These usually have feedback so the parameters you mentioned will all be present. Now picture a scene where there is a sharp transition from black to white. If there is a large overshoot an long settling time the customer will see a series of dark and light lines. This is typically objectionable to the viewer. But some overshoot is actually desirable to the customer because it makes the edges look sharper. The engineering is looking for a prescribed overshoot to please the customer.

So the parameters you are asking about come from the transfer function. The transfer function comes form the components the engineer selects and how she puts them together. An engineer designing an amp like this would come with a circuit configuration based on past experience or other examples for similar products. Typically in design process very simple models and quick hand analysis can be done to get to something that has promise. Then a more detailed analysis will be done using more detailed models. The transfer function of the detailed model will give the parameters you are asking about. If they meet the need of the customer, then you are done.


While the specific detailed formulas are not useful, knowing the types of relationships between different parameters is certainly useful. If you somehow increase the rise time of a circuit, what is likely to happen to percentage overshoot and settling time? As more time is spent with such circuits, students/engineers will have a better and better idea what to expect.

But it's hard to design circuits without already having a gut feel for how each parameter affects the others. New designers often run far more combinations of simulations to approach a viable solution because they don't know which way to tweak the parameters.

Circuit analysis (even with multiple unknown variables) is usually easier than blank-sheet circuit design. Just looking at circuits on a page and reading about how they work will not get beginning students the familiarity they need to internalize the relationships between parameters; they need to work with the circuits. Using detailed formulas is a way for students to work on circuits and focus on the relationship between a couple specific parameters at a time.


Another spotlight: as an engineer, you should be able to make your own tools.

You can use tools others prepared for you if they are okay for the job but you will eventually run into the situation when they aren't, and then you need a deep understanding about what you do and why. There's no reason to be ashamed when you fall out of your daily routine and at first feel as you know nothing about your work — because you totally forgot about your lectures and those stupid Laplace and Z transformations.

But you have to be able to catch up. In a hurry. Because people a nagging you why you aren't done yet. And that's why you need to learn this stuff once … and for all. Because then, you know you will grok it. Again.


Personally, I have not used those parameters at all but it could be because I am not working with "control systems". I was introduced to those terms and equations back in control systems classes but that was the last I have heard of them.

So to answer your question, I would say it depends a lot on the field you are working on. Someone that uses automatic control with sensor applications will most likely use those terms for stability purpose. Also, if you are designing PI, PD, and PID controllers you will need to know those terms in much more details.


"All models are wrong. Some models are useful" - G Box.

Everything we do is related to "modelling reality".
You mention on the one hand system transfer function and location of poles and on the other hand formulae which need input of known parameters to produce useful results.
In reality NEITHER end is reality - distributed parameters tend to get lumped for calculation, non linearities tend to get approximated as linear functions, aspects which are "known" to be likely to be unimportant (and which often but not always are) get approximated or ignored or replaced by a constant. The whole collection is a 'tool kit' which is to be used in conjunction with our brain and experience and other newer powerful tools such as simulations which attempt (and often manage) to more closely approximate the unrealities of reality.

My point in writing what may seem to be a self-obvious and rambling collection of thoughts (and may be :-) ) is to note that as experience grows you use everything available to different extents as it is found to be useful and the more you "know" the less you use some parts BUT they are always useful as tools waiting for the moments when experience or bad results tell you that what you usually use is not going to be good enough.

This is in part a rambling way [tm] of addressing your title "Beached Whale" - don't let it all overwhelm you. Learn, grow, rejoice in the perversity of reality and the fact that some tools work well enough most of the time but that some less commonly encountered quirk of creation is always waiting to make your day interesting.

Use all the tools when/as needed.


Depends on your particular job, your scope, and how far you are willing to go in a troubleshooting effort (your passion, to quote Mr. Tony Stewart :-) One facet of my tech support job is troubleshooting fieldbus/data communications. I could just check the wiring against the textbook / vendor docs and shrug my shoulders if it doesn't work. Or I can attach an oscilloscope and try to understand what it is that I'm looking at. If that's your approach, it is very useful to understand the workings of "lumped components" and wavelength effects on a transmission line. Such knowledge (with a bit of experiment / calibration) allows me to guesstimate, how much of the glitching/overshooting that I can see on the scope is down to the limited bandwidth of my probes, how much is actually present on the line, to what extent it's detrimental to the data transfer, and what can possibly be done about it :-)


Well, I believe all the answers above me should already open your mind, but I cant resist to answer as well since I am also a graduated from Electrical Engineering

I don't know about the others, but since my job is focused on production instead of research, every time we got those parameters causing problem (such as unstable system in analog circuit, or bad filter), we replace it after doing trial-error or research from another documentation instead of calculating the transfer system. Maybe its because the only things that matters is the final results, and nobody seems to care about the transfer system.

I repeat myself again, it is what happened to me, and I don't know about the other, no offense.


These parameters are used in High Voltage engg. for designing Impulse Voltage generators--up to 20 MV . Impulse voltages are used to test the strength of Insulators . Also to simulate Lightning Surges and study the effect of Lightning on various systems.
Low voltage Impulse generators , are also used for generating Digital Signals.

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    \$\begingroup\$ You don't answer the right question. This is not: "In which situation can these formulas be useful?", but it is "Are those formulas actually used in daily engineering?" \$\endgroup\$
    – dim
    Nov 1, 2016 at 20:05

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