# What exactly is transient behavior?

In my circuits lecture we talk about transient behavior and how to express it mathematically. In the lab, someone points out the transient behavior of the circuit while looking at the oscilloscope screen which shows the output signal of the circuit.

All of this is great, but I don't understand conceptually/qualitatively what it is. What does transient behavior look like, for example? Is it that slight upward curve when you zoom in really close on the graph of the voltage across the capacitor as you charge it? Why does transient behavior happen? Do we want it to happen or no?

• Things are not happening instantly in the nature. Transition from state A to state B takes a non-zero time. So everything which is happening between these two state-times is the transient behavior. – Eugene Sh. May 11 '16 at 18:55
• Transient behavior is what happens before steady-state. – Spehro Pefhany May 11 '16 at 19:14
• To add to @SpehroPefhany, a common definition of steady-state is when your observed variable (e.g. voltage across a capacitor) reaches a range of +-2% your final value. For an RC circuit this takes 4 times the RC constant - i.e. this is the time length of transient. – Vicente Cunha May 11 '16 at 19:27
• @VicenteCunha I haven't heard this before... my understanding is that steady state means when the system has reached a condition where the value at time x is the same as the value at time 2x, 4x, 6x, etc. +/- 2% seems rather arbitrary – LShaver May 11 '16 at 20:31
• @LShaver Yes, it is arbitrary but commonly used in control design to calculate a settling time (or end of transient). IIRC Matlab uses this definition in its control design toolboxes. – Vicente Cunha May 11 '16 at 20:41

Steady state behavior is behavior that continues on indefinitely, if you keep the system state and its inputs the same.

For example, if you input a sine wave with amplitude $a$ to a linear system with gain 4, you'll get out a sine wave with amplitude $4 a$ and some phase offset. This behavior will continue as long as you continue to input the sine wave.

Transient behavior is any behavior that dies out over time.

For example if you stepped up the input of your linear system to an amplitude of $2 a$ at time $t=0$, you'd see the output jump in amplitude from $4 a$ to $8 a$, but it would take some time to do that. The behavior during that transition, from when it's behaving like it had a $a$ input for a long time to when it settles down to behave like it had a $2 a$ input for a long time, is the transient behavior.

What does transient behavior look like, for example?

It depends on the circuit and the stimulus that produced it.

Is it that slight upward curve when you zoom in really close on the graph of the voltage across the capacitor as you charge it?

It could be that.

Why does transient behavior happen?

Because the steady state behavior is only a simplified description of the circuit behavior that describes what happens when the inputs remain the same for a long time. Transient behavior gives a more complete picture of the circuit behavior that also includes the possibility of inputs changing over time.

Do we want it to happen or no?

It doesn't matter if we want it or not. It does happen, so as a designer you have to deal with it or design your circuit to produce the behavior you need.

• This seems like the best answer so far but doesn't cover the last bit of the question - "Do we want it to happen or no?" – LShaver May 11 '16 at 20:41
• @LShaver, edited. – The Photon May 11 '16 at 21:17

Transient behavior can be qualitatively defined as any electrical behavior of a system that is not constant in time nor happening periodically in a controlled and desired manner.

Examples include capacitor voltage during charge and discharge.

Do we want it to happen or not? Depends on the context. If, for any reason, you need to charge a capacitor, is desired behavior, of course. Converesely, if you need to reset a peak detector, you'd probably prefer the capacitor to discharge in the smallest amount of time possible.

• And there's no way to completely be free of it, correct? We can only minimize it by choosing appropriate resistances and capacitances? – user104243 May 11 '16 at 20:17
• @user50420 It sounds like your professor should be more careful with the terms. It doesn't make sense wanting to get rid of transients. – pipe May 11 '16 at 21:32
• @user50420: That's correct. Remember also that inductors too are responsible for transients. – Electrical Architect May 11 '16 at 21:32
• @pipe: I think it could make sense if what he means is minimizing them. – Electrical Architect May 11 '16 at 21:33
• @user50420 Correct. Dealing with transient behavior is essentially what control theory is about. Often there is a tradeoff to be made between performance and stability, e.g. you can get the system to respond faster, but it may require allowing it to overshoot the final value. – Alex May 11 '16 at 21:33