# What is steady state analysis?

#### leodavinci90

Joined Oct 22, 2014
57
Can someone explain in a few sentences what the title means ? Also provide Example of a steady state ac voltage and current waveforms and circuit.

#### WBahn

Joined Mar 31, 2012
25,065
Can someone explain in a few sentences what the title means ? Also provide Example of a steady state ac voltage and current waveforms and circuit.
Sounds like a homework question. So why don't you take your best shot at providing an answer and we'll help you correct it or flesh it out.

#### crutschow

Joined Mar 14, 2008
24,057
The term is pretty well self explanatory.

#### WBahn

Joined Mar 31, 2012
25,065
The term is pretty well self explanatory.
Yes and no. When first introduced to most students it is within the context of first- and second-order DC circuits having a transient response and a steady state response and the distinction is often phrased along the lines that steady state is when none of the voltages or currents are changing. This is frequency emphasized mathematically by saying that in steady state the time derivatives of all signals are zero.

This causes confusion when the notion of AC steady state is introduced because the currents and voltages never stop changing, so it seems that the whole notion of an alternating signal being in steady state is self-contradictory. And certainly the time derivatives of the signals no longer need to be zero, even though this was just recently given out as the definition of steady state. Worse for students new to this, particularly since they almost certainly have yet to be introduced to the frequency domain, a clean mathematical definition is a bit elusive and so it often comes down to handwaving and the use of buzz words such as envelopes, periodic waveforms, and such. Even if the textbook or the instructor emphasizes that what constitutes DC steady state and AC steady state, while conceptually related, are quite a bit different in the fine print (from the time-domain perspective that students are immersed in at that point), that is going to be theory mumbo-jumbo that goes in one ear and out the other and many will latch only onto applying the "nothing is changing" notion and apply it too strictly.

#### MrAl

Joined Jun 17, 2014
6,945
Hi,

I agree with WBahn. We have to differentiate between AC steady state and DC steady state, and both may happen in the same circuit.

However, if someone doesnt know how this works already then they probably have to be told. Some things can not be discovered or they are so difficult to be rediscovered that they must be actually taught from the standpoint of no previous knowledge. That means that unless they want to look it up on the web or in some book or ask some teacher then they will never know. Simulations MAY show this behavior, but then it depends on the observation skills of the experimenter if they can figure out that during many simulations some things stop changing and other things dont stop changing (sometimes). So it can be quite a challenge if they dont know it already unless they look it up. They must have come here either because they did not find info yet or they did not know enough to look it up on the web, or maybe this is the only site they know of right now that deals with this area.

#### leodavinci90

Joined Oct 22, 2014
57
Hi, thanks for your replies. I only asked this because I am have a Power Electronics module and in the first lecture's slides there is a waveform of current and voltage in phase. And the title of the graph was "Steady State AC Voltage & Current Waveforms for a purely resistive load". I know when current lags voltage or when current leads voltage. My only question was: what does steady state means? I have done transient state analysis for capacitor. Don't know what this means. That's all.

#### shteii01

Joined Feb 19, 2010
4,647
Let me present a slightly different engineering perspective.

One way to approach response of a circuit is to divide it into Transient Response and Steady State Response.

A good example of transient response is the sound that an audio speaker makes when you turn it on. It might be some hum that quickly goes away or just a sudden short burst of sound. This sound represents the circuit response to sudden presence of electricity because you closed the switch and connected the circuit to the source of electricity. However, the transient response is... transient. We do not design products for their transient response. We design products for their steady state response.

Steady state response is the normal operation of a product and since product is some kind of circuit, it is normal operation of the circuit, it is what the designer wants the circuit to do which means it is predictable and reproducible.

#### WBahn

Joined Mar 31, 2012
25,065
Hi, thanks for your replies. I only asked this because I am have a Power Electronics module and in the first lecture's slides there is a waveform of current and voltage in phase. And the title of the graph was "Steady State AC Voltage & Current Waveforms for a purely resistive load". I know when current lags voltage or when current leads voltage. My only question was: what does steady state means? I have done transient state analysis for capacitor. Don't know what this means. That's all.
For AC steady state it means that the response has settled into a stable set of sinewaves. Whether voltage lags current or vice versa is irrelevant. In general when the input to the system changes you will have a response that is transient and goes away and a response that, barring any further changes in the input, stays the same. By "stays the same" (for both input and output) we mean a periodic signal that repeats itself over and over and over -- generally a sine wave, but not necessarily.

#### WBahn

Joined Mar 31, 2012
25,065
Let me present a slightly different engineering perspective.

One way to approach response of a circuit is to divide it into Transient Response and Steady State Response.

A good example of transient response is the sound that an audio speaker makes when you turn it on. It might be some hum that quickly goes away or just a sudden short burst of sound. This sound represents the circuit response to sudden presence of electricity because you closed the switch and connected the circuit to the source of electricity. However, the transient response is... transient. We do not design products for their transient response. We design products for their steady state response.

Steady state response is the normal operation of a product and since product is some kind of circuit, it is normal operation of the circuit, it is what the designer wants the circuit to do which means it is predictable and reproducible.
I think this is going too far. The designer might well design for the transient response, such as an echo effect, and in doing so they do not turn the echo into some kind of steady state response.

#### shteii01

Joined Feb 19, 2010
4,647
I think this is going too far. The designer might well design for the transient response, such as an echo effect, and in doing so they do not turn the echo into some kind of steady state response.
Is it predictable?
Is it reproducible?

#### WBahn

Joined Mar 31, 2012
25,065
Is it predictable?
Is it reproducible?
It doesn't matter whether it is or not, it is part of the transient response of the circuit, not the steady state response.

If I show you the voltage-vs-time plot of a signal this is clearly the step response of an under-damped second-order circuit, could you (at least roughly) draw a line that separates the transient response from the steady state response (or even a pair of lines such that the region between them is too ambiguous to classify)? Or would your immediate first thought be that you have to know which part of the waveform the designed was trying to craft before you could even begin to answer the question?

Or, for another example, lots of circuits are designed specifically to produce predictable and reproducible one-shot pulses. Would you consider that single pulse to be the steady-state response of that circuit?

Mathematically there is a very clear definition of the two. The transient response is the natural response of the system and the steady state response is the forced response (of the differential equation that describes the system response). There is nothing there that takes the designer's intent into consideration.

#### MrAl

Joined Jun 17, 2014
6,945
Hi, thanks for your replies. I only asked this because I am have a Power Electronics module and in the first lecture's slides there is a waveform of current and voltage in phase. And the title of the graph was "Steady State AC Voltage & Current Waveforms for a purely resistive load". I know when current lags voltage or when current leads voltage. My only question was: what does steady state means? I have done transient state analysis for capacitor. Don't know what this means. That's all.
Hi,

In that case you've already had much of the math i would presume, so it's really quite easy to understand and the model is usually just a second order system (as are many learning based systems).
An example second order system can be depicted by a time equation such as:
v(t)=e^(-at)*(A*cos(w1*t)+B*sin(w1*t))+C*cos(w2*t)+D*sin(w2*t)+K

and if you look at this you'll see that as time goes on the first term eventually goes away because the e^(-at) factor makes that part zero eventually, so all that remains are the following three terms, and if C and D are zero then the only thing that remains is K the DC voltage.
So we get an exponentially decreasing sinusoidal wave, possibly a constant sinusoidal, and possibly a DC voltage. The steady state response is everything that is left after that first term decays to near zero and that may end up being zero for some circuits and drive signals.
So the results can be one of:
1. Zero,
2. DC only,
3. AC only,
4. AC+DC both.

and in some cases the AC or DC may actually increase indefinitely in an unstable circuit if the exponent a is negative already (making the exponent positive).

#### leodavinci90

Joined Oct 22, 2014
57

#### MrAl

Joined Jun 17, 2014
6,945
MrAl said: Oh no he didn't
Hi,

Thanks!
Hello there,

Normally you would put your text AFTER the quote.
Note that i had said something very different in my post #12, that was actually your reply above

so it should look more like this:
MrAl said:
Hi,
<snip>
Thanks!

Last edited:

#### crutschow

Joined Mar 14, 2008
24,057
I believe everyone has made clear the difference between transient and steady-state conditions, but here's a simulation for a simple RLC resonant circuit to show that.
As can be seen, the AC current through the circuit exponentially builds up from the start of the AC signal application at 0ms (the start-up transient) and settles to the steady-state value after about 7ms.