Author Topic: Using Laplace to analyse circuits  (Read 13308 times)

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Offline SimonTopic starter

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Using Laplace to analyse circuits
« on: February 18, 2018, 11:54:38 am »
I'm at the section of my HNC where I'm being taught (badly) to use Laplace transforms in the analysis of circuits to cut down on the working out. Attached is an image from a separate book I'm using to backup my course material that is otherwise confusing where it gives a simple example of working out the voltage across a capacitor in an RC circuit. Having just explained that voltage in the S domain is V(s) the equations in this example have V over s. Why is this so?
 

Offline Benta

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Re: Using Laplace to analyse circuits
« Reply #1 on: February 18, 2018, 12:37:23 pm »
Because the unit step in LaPlace notation is 1/s.

 

Offline BBBbbb

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Re: Using Laplace to analyse circuits
« Reply #2 on: February 18, 2018, 12:42:43 pm »
Not sure what your exact question is, but it's a basic example where you're given a circuit and asked to analyze what happens when the switch is flipped to ON. (focusing on the transient)
So your input voltage goes from 0 to V (some DC value), which is basically a step function, represented in Lapalace domain as V*1/s
 

Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #3 on: February 18, 2018, 12:53:15 pm »
I see yes that makes sense now I hadn't noticed the step function.
 

Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #4 on: February 18, 2018, 01:09:38 pm »
I little confused. As using Laplace takes the time and frequency out of the equation what is the difference between the voltage across the capacitor at a steady-state and during the step function. The net result of the step function is that the voltage is applied what is the difference between the result when the step function happens and in the steady-state later on? Or is it that by using Laplace I'm not having to calculate with time but once transformed back the results will take into account the timing?
 

Offline Benta

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Re: Using Laplace to analyse circuits
« Reply #5 on: February 18, 2018, 01:22:00 pm »
Laplace is a transformation from the time domain into the complex frequency domain. To get the final response, you'll have to transform back into the time domain at the end.

For a simple step response of an RC circuit it's no big deal, but when you operate with Nth order circuits it is basically the only way to do it.

In the time domain you have to work with differential equations which a major pain, if not plain impossible (depending on circuit complexity).
In the Laplace domain, you work with algebraic equations.
 

Offline Kalvin

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Re: Using Laplace to analyse circuits
« Reply #6 on: February 18, 2018, 01:27:28 pm »
Laplace-transformation is a transformation from time-domain to s-domain. When you convert the circuit to s-domain, you can analyze the circuit using simple algebraic manipulation using familiar Kirchhoffs rules etc. without complicated differential equations. After you have analyzed the circuit in s-domain, you can convert the result back to time-domain applying inverse Laplace-transform. If you look carefully, you may find out that s is so called complex frequency variable ie. s = jw, which will give you a hint that Laplace-transformation is actually a time-to-frequency transformation and the inverse Laplace transformation is frequency-to-time transformation. This can easily be seen as the impedance of the inductor is sL and the impedance of the capacitor is 1/(sC).
 

Offline BBBbbb

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Re: Using Laplace to analyse circuits
« Reply #7 on: February 18, 2018, 02:09:48 pm »
I little confused. As using Laplace takes the time and frequency out of the equation what is the difference between the voltage across the capacitor at a steady-state and during the step function. The net result of the step function is that the voltage is applied what is the difference between the result when the step function happens and in the steady-state later on? Or is it that by using Laplace I'm not having to calculate with time but once transformed back the results will take into account the timing?

First of all Laplace on an RC is probably an overkill, complicates the calculus, but if you keep in mind Laplace equivalents you might find it easier to understand (e.g. 1/s is practically an integral, s is a derivative, both over time, for frequency domain you'd just go s=jw - as previously mentioned).

So basically when you do a reverse Laplace you'll get a time dependent expression (exponential in this case)
Steady state is therefore not of interest but the transient that happens as a result from instantaneous switching on the voltage. Transient will last some time depending on the RC constant. In the time dependent formula that you get reversing from Laplace you'd get SS by putting t=+infinity

Laplace really comes into play on complicated systems in analysis of bandwidth, stability and control design. In case of an RC circuit a classical mathematical approach would have been the easiest, but it's just an example.
« Last Edit: February 18, 2018, 02:13:34 pm by BBBbbb »
 

Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #8 on: February 18, 2018, 02:14:28 pm »
Yes it is just an example. It often makes a lot of sense to use something already well-known and simple and recalculate it with the new method before moving onto more, complicated things. This is the problem with the actual material supplied by the University it often makes large jumps as one of my work colleagues also complained. I have been getting around this by using a book as the course material feels more like the notes a lecturer might be using to scribble on the blackboard whilst taking questions from students or at least judging the mood and elaborating.
 

Offline danadak

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Re: Using Laplace to analyse circuits
« Reply #9 on: February 18, 2018, 03:04:52 pm »
Not to mix up the discussion but LaPlace coupled with signal flow graphs
makes life so easy, and yields a visual understanding of circuit behavior.

Online there are signal flow graph calculators, that will generate the transfer
function using simple GUI description of circuit and what Z is in each branch.

https://ieee.li/pdf/viewgraphs/analyzing_feedback_systems_with_ignal-flowGraphs.pdf



These tend to be advanced topics, but if you plan on a career in the field very useful.
They share properties of general directed graph theory. The displayed graph is done
in Voltage node, there is a technique to transform it (simply) to a current graph, which
can impact ones circuit design approaches. Lots of fun.


Regards, Dana.




« Last Edit: February 18, 2018, 03:09:33 pm by danadak »
Love Cypress PSOC, ATTiny, Bit Slice, OpAmps, Oscilloscopes, and Analog Gurus like Pease, Miller, Widlar, Dobkin, obsessed with being an engineer
 
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Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #10 on: February 18, 2018, 03:12:34 pm »
Well I have been right through my course material now and I'm still stumped when it comes to one of the questions. I can't even understand what they are asking. Is this related to how damp a circuit is at a particular frequency? I have not seen the notation anywhere in the course module or even in my book by John Bird. As always this course is a flipping shambles. Attached is an image of the question I be grateful someone could explain what they are actually asking.
 

Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #11 on: February 18, 2018, 03:16:44 pm »


These tend to be advanced topics, but if you plan on a career in the field very useful.
They share properties of general directed graph theory. The displayed graph is done
in Voltage node, there is a technique to transform it (simply) to a current graph, which
can impact ones circuit design approaches. Lots of fun.


Regards, Dana.





at the moment my plan is to understand enough to get shot of this flipping course and get the wonderful piece of paper that will shut my boss up. And hopefully get me a pay rise. After that is achieved if you can call that an achievement because I don't anymore it would be nice to learn how to use the scenes properly for useful things because I doing this course for the love of the information otherwise I would not be doing it at all but the course is doing a damn bad job of explaining anything to me. Meanwhile the maths bridging module that I had to do before I started this course has been made even easier to answer as I see from the new assignments my colleague has been given whereby he only has to put the answer to a question in and not show his working out when the whole point of the module he is studying is to understand how to do the maths which was the whole point of both of us doing this module before we even start the HNC. I have completely and utterly lost any respect for qualifications taken today. Over 10 years ago maybe they actually meant something today were just buying a commodity from a university which is basically a company giving you a piece of paper so that you can get a job or have a pay rise the whole thing is a sham and a scam. To be honest the education system of India is no worse than the current UK system.
 

Offline danadak

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Re: Using Laplace to analyse circuits
« Reply #12 on: February 18, 2018, 03:54:58 pm »
Sigma is the exponential decay or rise, of an oscillatory waveform.





http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html


Regards, Dana.
Love Cypress PSOC, ATTiny, Bit Slice, OpAmps, Oscilloscopes, and Analog Gurus like Pease, Miller, Widlar, Dobkin, obsessed with being an engineer
 

Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #13 on: February 18, 2018, 03:59:46 pm »
Thank you Dana, it would seem that I'm not the only person who has discovered that the course material does not actually cover the theory required to answer these questions. Over here: https://www.physicsforums.com/threads/sketch-waveform-to-represent-the-transient-response.764761/ other people although some years ago are also trying to answer the same questions and are in my same boat of having to basically go out and find the information from scratch. I am deeply pissed off with this course because they are doing nothing but waste my time. I'm being made to read over complicated rubbish that does not actually mean very much when they could just tell me to buy a book by John Bird and asked me to study each particular subject chapter and then just give me a sensible assignment that I can actually do. Instead I waste my time wading through the course material trying to understand it realising it's a pile of trash and then picking up a book and reading the same stuff all over again and actually learning it. And then discovering that even though I have learnt it the assignment is asking me about something completely different. I know there is a concept such as self research but these people are just wasting my time.
 

Offline Vtile

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Re: Using Laplace to analyse circuits
« Reply #14 on: February 18, 2018, 04:27:30 pm »
Not to mix up the discussion but LaPlace coupled with signal flow graphs
makes life so easy, and yields a visual understanding of circuit behavior.

Online there are signal flow graph calculators, that will generate the transfer
function using simple GUI description of circuit and what Z is in each branch.

https://ieee.li/pdf/viewgraphs/analyzing_feedback_systems_with_ignal-flowGraphs.pdf



These tend to be advanced topics, but if you plan on a career in the field very useful.
They share properties of general directed graph theory. The displayed graph is done
in Voltage node, there is a technique to transform it (simply) to a current graph, which
can impact ones circuit design approaches. Lots of fun.


Regards, Dana.
Dang... Thats nice (new to me) method. It somewhat resembles the odd resistance/conductance hybrid graph model I created last summer.  :D
 

Offline Vtile

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Re: Using Laplace to analyse circuits
« Reply #15 on: February 18, 2018, 05:04:40 pm »
...I know there is a concept such as self research but these people are just wasting my time.
There is also a such concept as a teacher.  ::)
 

Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #16 on: February 18, 2018, 05:09:54 pm »
...I know there is a concept such as self research but these people are just wasting my time.
There is also a such concept as a teacher.  ::)

All this is supposed to be a distance learning course which is why it's even more infuriating. The material is like double dutch a lot of the time and quite frankly it looks like they have worked out they can make some extra money by throwing the lecturers notes onto a PDF producing an assignment for us to fill out and charging us £470 per module. They are also now working out ways to make it even easier to answer the questions. So as far as I'm concerned they are just selling qualifications. If you really give a shit you'll spend a lot of time trying to fathom it out. If you don't care and just one certificate you work out how to get round it all but if I'm doing this I'm doing it properly.
 

Offline rstofer

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Re: Using Laplace to analyse circuits
« Reply #17 on: February 18, 2018, 06:22:52 pm »
There are videos re: Laplace Transforms at Khan Academy along with an entire EE program.

https://www.khanacademy.org/search?referer=%2Fscience%2Felectrical-engineering&page_search_query=laplace+transform

Under the EE program they have an EXTENSIVE series of videos on circuit analysis:

https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic

Don't know if these will help, I haven't worked through them yet.
 

Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #18 on: February 18, 2018, 06:54:42 pm »
Well I'm at the point now where I need to look at the dampening factor of a circuit. I have found a section in my module where it may have been discussed I stopped reading the module long before I got to it and had to divert to a proper book. I will now have to read through all of the gibberish to work out where I can pick up from.

I did have a look at the Khan Academy videos about Laplace transforms. They help a little as having somebody talk it through can be very helpful.
 

Offline BBBbbb

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Re: Using Laplace to analyse circuits
« Reply #19 on: February 18, 2018, 07:15:53 pm »
Seems to me they did a bad job at presenting the underlying mathematics of the Laplace transform, mostly relationship with the time and frequency domain. Which is quite a shame because a bit more emphasis on the mathematics here could help you a lot in further learning and grasping of domain transformation concepts.
 
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Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #20 on: February 18, 2018, 07:20:37 pm »
I think a lot of the problem is that they try to teach both the underlying maths and the Laplace transforms and differential equations all in one module. I have already done two modules of maths and therefore I expected to be equipped to deal with any concepts that required maths. The analytical methods for engineers did not teach Laplace transforms or differential equations. So in four PDFs they have tried to explain differential equations and then to ignore that and use Laplace transforms to solve them whilst also try to explain the damping factor and how to use Laplace transformed versions of component equations to represent circuits and solve circuits. The problem is on the one hand they are dillydallying around in circles explaining why it works rather than how to use it and then they make great leaps of faith in the fact that you understand stuff they have not explained. My colleague who is doing the bridging module which comes before this course and before the initial module of this course in mathematics has found exactly the same as me. They explain stuff they explain the basics and then they suddenly jump over a canyon.
 

Offline Benta

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Re: Using Laplace to analyse circuits
« Reply #21 on: February 18, 2018, 08:59:24 pm »
Simon, an extremely useful and valuable book for electronics students and engineers is this one (I still use my copy from the 80s, it's become somewhat tattered over the years):

"Mathematical Handbook of Formulas and Tables",
Murray R. Spiegel,
Schaum's Outline Series.

It contains all formulas that you'll ever need. But more importantly, it's got tables of the inverse Laplace transforms.

As you've gathered from the replies above, finding the equations for a circuit using Laplace notation is not difficult. Finding a transfer function from those is also not difficult. And doing a frequency analysis (amplitude, phase etc.) is also not difficult.
But getting back in the time domain can be really hard, eg, for impulse response, ringing, rise time, overshoot etc., because this is where you need the inverse Laplace.

If you don't have it, I encourage you to get it. Cheers.

 

Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #22 on: February 18, 2018, 09:02:45 pm »
I will have a look. The tables are readily available in maths books. I have two books by John Bird one is on mathematics and one on electrical theory. They complemented each other quite well. Everything is explained reasonably clearly I just wish somebody would tell me one earth I'm supposed to be studying.
 

Offline Benta

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Re: Using Laplace to analyse circuits
« Reply #23 on: February 18, 2018, 09:11:31 pm »
Quote
The tables are readily available in maths books.

I know, but you always have to hunt for them and they're often not complete. The book I recommended is not a text book, but a no-frills collection of formulas and tables. I you have no need, then leave it. I don't have shares in the publisher.
 

Offline SimonTopic starter

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Re: Using Laplace to analyse circuits
« Reply #24 on: February 18, 2018, 09:19:39 pm »
I do have a similar sounding book called practical Electronics calculations and formulae by FA Wilson I don't know if this will carry similar information I have never really read it given my previous lack of mathematical understanding.
 


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