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We are provided a syllabus in our university stating "Unit III - Transient responses of RL,RC,RLC circuits, DC and AC sinusoidal input".

As far as I can see, "transients" are the response a circuit gives when you switch it on abruptly.

I really can't understand transients, I just follow the procedure, form a differential equation, take the Laplace transform find I(s), take inverse Laplace. What does this effectively do. In-class the professor taught us about step and impulse input, and their responses and we got a bunch of waveform corresponding to different cases,

  1. What does the Impulse and step input have to do with transients?
  2. What are AC and DC transients?
  3. How is transient analysis different from AC and DC analysis?
  4. Suppose I'm given a RLC. Assuming zero initial conditions, I switch it on with a DC input, I formulate a differential equation. Take Laplace transform, find I(s) and then take inverse Laplace, to find i(t), what is this i(t), is this the transient response ?
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  • \$\begingroup\$ Both are transients, input transients. \$\endgroup\$
    – Andy aka
    Aug 20, 2019 at 12:47
  • \$\begingroup\$ This gets a lot more intuitive if you look at it on an osciliscope; have you been given the opportunity to do that? \$\endgroup\$
    – pjc50
    Aug 20, 2019 at 12:56
  • \$\begingroup\$ @Andyaka What is transient analysis, suppose I'm given a RLC. Assuming zero initial conditions, I switch it on with a DC input, I formulate a differential equation. Take Laplace transform, find I(s) and then take inverse Laplace, to find i(t), what is this i(t), is this the transient response ? \$\endgroup\$ Aug 20, 2019 at 14:04
  • \$\begingroup\$ @pjc50 No, not yet, what's that i(t) is that transient, god I'm so confused right now ;( \$\endgroup\$ Aug 20, 2019 at 14:05
  • \$\begingroup\$ @AravindhVasu the normal method is (1) obtain the general transfer function and (2) multiply that TF by 1/s (step input). Then (3) do the partial fraction stuff and reverse Laplace to obtain the time response of the output to that step input. With an impulse you multiply by 1 (easy) because that is the laplace of an impulse. \$\endgroup\$
    – Andy aka
    Aug 20, 2019 at 14:34

4 Answers 4

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You're correct in noting that "transient DC" is a contradiction.

I think this is just a somewhat ambiguously-worded syllabus title. They probably mean "responses of {RL, RC, and RLC} circuits to {DC, sinusoidal AC, and transient} inputs".

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  • \$\begingroup\$ Where does the OP mention "transient DC"? I'm seeing "DC transients" which would seem to apply to transients occurring in a DC circuit. \$\endgroup\$
    – Robert M.
    Dec 12, 2023 at 17:39
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It's not really accurate to refer to steady-state responses as transients if nothing is changing. What may be happening here is the instructor is thinking of the different common types of simulations:

  • DC
  • AC
  • Transient

As a simulation type, transient actually just means something like "time-domain." It is the type of simulation which is required to see the transient portions of impulse/step responses. A transient simulation could also be used to analyze responses of DC or steady-state AC signals to get a result similar to those dedicated simulations types, however it will likely have lower accuracy since it is a more general-purpose simulation (especially worse accuracy for AC).

In summary, I think the syllabus means

Time-domain responses of RL,RC,RLC circuits, DC and AC sinusoidal input

or possibly

Time-domain responses of RL,RC,RLC circuits, DC, AC sinusoidal, and transient inputs


As an aside, I actually think this definition of transient (meaning time-domain) is gaining traction. A good argument could be made for adding it to a dictionary. It seems to have this meaning in some areas outside of circuit simulations (Transient climate simulation, Transient modelling).

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  • \$\begingroup\$ I think you are correct. It looks like a poor choice of punctuation in the syllabus. \$\endgroup\$ Aug 28, 2019 at 14:27
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A picture may help:

Current and voltage transients

In this example, a load is connected to a power supply for a while and then disconnected. This causes two transients, at the connection and disconnection.

DC analysis techniques work for the steady state, the flat periods of the graph. For the pointy bits we need transient analysis.

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  • \$\begingroup\$ My question is boiled down to, when we solve the differential equation and obtain a i(t), does this i(t) include both transient and steady state response ? \$\endgroup\$ Aug 20, 2019 at 15:07
  • \$\begingroup\$ Yes, the transient is the behavior you get as soon as there is the change in the system, after a good time, it demonstrates the steady-state response, like, if you solve the differential equation, taking into account the initial state, and obtain i(t), that is your transient. If you look at i(t+100000000) (a lot of time after the input change) this function will be the steady state. \$\endgroup\$
    – jDAQ
    Aug 21, 2019 at 2:04
  • \$\begingroup\$ Can you please provide a link or citation for the image you copied into your answer? We want to make sure that the original creator gets credit for their work. \$\endgroup\$ Aug 28, 2019 at 14:25
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What are AC and DC transients? How is transient analysis different from AC and DC analysis?

Let's start from what are transients rather! First of all recall that capacitor and inductor are devices which are capable of storing energy into electrostatic or electromagnetic fields respectively (they are not meant to permanently store energy like batteries, in fact in ususal operations they'll store and relaease energy frequently). So this change in their energy doesn't happens suddenly but rather it takes finite time. Moreover as stored energy varies the value of current/voltage in various circuit elements may become time-varying. Suppose if you're charging an initially uncharged capacitor from a DC battery through resistance, the voltage across capacitor will be time-varying in that it'd rise exponentially from 0 to (almost) battery voltage. In this time-frame, the current will also change, however circuit parameters will soon attend a "steady-state" where values of them will not change significantly (like cap voltage will be almost full supply voltage and won't change significantly, mathematically speaking 'steady-state' is reached when value remains in 2% band around final value and is attained in time equal to 4*time-constant).

During the transition from one steady-state to another steady-state, circuit undergoes what we call as transient. Transients are also brought when you switch circuit containing caps or inductors. We mathematically say that 'total response' of circuit is then transient response + stead-state response'. In what is called steady-state analysis, we learn how to find its second part and as you might've guessed, in transient analysis you'll learn to find the former part. You'll also see that type of transient response varies significantly when source is AC as compared to when it's DC hence study of transient response is divided into two parts, AC transients and DC transients.

What does the Impulse and step input have to do with transients?

The importance of these functions, especially impulse input is more in developing foundation of frequency domain techniques. For more general treatment of any system including electrical system(source being any signal, not limited to just AC or DC), we use frequency-domain techniques for analysis. The impulse and step response are of great importance in them (step response being more useful in control system applications due nature of problems encountered there). So why is impulse so important? Because you can represent any signal as sum of shifted and scaled impulses & hence, by properties of linear system (homogeneity and superposition), if you know response to input signal (called impulse response), you can calculate system's response to any signal! This gives rise to what is called as convolution sum and convolution integral techniques, later gets converted into simple multiplication of two functions (instead of intergration) into Laplace transform, making Laplace powerful tool. Also, the Laplace inverse of impulse response of system gives you transfer function. THEN, you can use Laplace transform to calculate total response, which will by definition include transient response. In a nutshell, these signals and responses will become significant in development of introductory subject matter of Signals & Systems and Control systems.

Suppose I'm given a RLC. Assuming zero initial conditions, I switch it on with a DC input, I formulate a differential equation. Take Laplace transform, find I(s) and then take inverse Laplace, to find i(t), what is this i(t), is this the transient response ?

It is the total response. Sometimes people may call total response as transient response (correctly or incorrectly I won't judge, but it is quite common practice) as total response is different from steady-state response in way it includes transient response, but strictly speaking it is total response = steady-state response + transient response. (Just remember that steady-state response is not function of time WHILE REMEMBERING that in AC, by steady-state we mean that RMS value is not function of time i.e. RMS value of a signal or parameter is very near to its final RMS value, this doesn't means signal is not alternating, it still alternates, however in the way that it's RMS value doesn't makes 'too-large' oscillations around final RMS value. To shed some more light, very informally speaking if output of a linear time-invariant system attains some steady-state value for e.g. if voltage across capacitor attains some steady final value, we say that system is stable but if we, out of evil thoughts, design a system in which voltage across capacitor keeps on increasing rather than getting settled down to a particular value, it is said to be unstable system - well atleast till cap doesn't turns whole system into smoke...)

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  • \$\begingroup\$ "Loosely I can say that impulse response is source-free response of a circuit" What do you mean, by source-free response? Do you mean that, once you calculate the "change" it has caused to the system after 0+, it's just a source free system with initial conditions? \$\endgroup\$ Aug 28, 2019 at 12:08
  • \$\begingroup\$ @AravindhVasu I couldn't understand what you are trying to ask or say..however I've edited my answer to explain why are impulse and step important, and have done some other corrections. \$\endgroup\$
    – Deep
    Aug 28, 2019 at 12:49
  • \$\begingroup\$ Oh and source-free response is complementary function of solution of differential equation. We however don't talk about it much in networks and stick to steady-state+transient=total thing. \$\endgroup\$
    – Deep
    Aug 28, 2019 at 12:53

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