Using Laplace to analyse circuits

[Simon]

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?

[Benta]

Because the unit step in LaPlace notation is 1/s.

[BBBbbb]

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

[Simon]

I see yes that makes sense now I hadn't noticed the step function.

[Simon]

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?

[Benta]

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.

[Kalvin]

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).

[BBBbbb]

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.

[Simon]

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.

[danadak]

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.

[Simon]

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.

[Simon]

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.

[danadak]

Sigma is the exponential decay or rise, of an oscillatory waveform.





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


Regards, Dana.

[Simon]

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.

[Vtile]

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. 

[Vtile]

...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. 

[Simon]

...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.

[rstofer]

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.

[Simon]

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.

[BBBbbb]

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.

[Simon]

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.

[Benta]

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.

[Simon]

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.

[Benta]

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.

[Simon]

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.

[IanB]

Here is a reference that explains something about \$\zeta\$ (damping ratio) and \$\omega_0\$ (natural frequency) in second order systems:

https://ocw.mit.edu/courses/mechanical-engineering/2-003-modeling-dynamics-and-control-i-spring-2005/readings/notesinstalment2.pdf

That particular article is very mathematical (sorry), but once you know the keywords "second order system", "damping ratio" and "natural frequency" you will find more hits when searching.

[Simon]

Thank you, sadly the books I do have by John Bird don't go into any detail on the subject. I effectively reached the end of the book as the subject was broached briefly. I have ordered another book of his called understanding engineering mathematics which hopefully gives a slightly more practical approach to maths than the book I have which is good for getting the hard facts but is not exactly a light reading.

[IanB]

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?

The key concept here is that the Laplace transform method allows you to solve not for a single steady-state answer, but instead to solve for a complete time dependent function for the solution. What you are really doing is solving differential equations, where the solution has two components: a transient response that usually decays with time, and a steady state response which is what is left after the transient response is over. That result after you convert the Laplace solution back to the time domain is a mathematical function that has both transient and steady-state responses included in it.

[IanB]

Thank you, sadly the books I do have by John Bird don't go into any detail on the subject.

You are likely to find coverage of the subject of system responses and first and second order systems in books on control theory. That would be another section of the "bookshelf" to browse for useful books to look at.

[Benta]

You are likely to find coverage of the subject of system responses and first and second order systems in books on control theory.

Good point, those are well documented. 3rd order systems and higher is where you'll need Laplace.

[danadak]

If you go to archive.org and do searches many books, papers, ap notes,
vendor info on just about everything.


Regards, Dana.

[rstofer]

My new best friend, MATLAB, does all this stuff.

https://www.mathworks.com/help/control/ref/damp.html

It knows how to deal with all kinds of math, including Laplace Transforms and Inverse Laplace Transforms.

https://www.mathworks.com/help/symbolic/laplace.html
https://www.mathworks.com/help/symbolic/ilaplace.html

I realize you can't use MATLAB to take a test but sometimes it is nice to know if you are on the right track.

In real life, that arena outside academia, everything is open book and unlimited computing.  It's sad that colleges and universities insist on having students grind through math rather than take the time to learn what it means.

http://www.seas.upenn.edu/~ese216/handouts/Chpt13LaplaceTransformsMATLAB.pdf
http://www.egr.msu.edu/~aviyente/LT_matlab.pdf

I'm trying to ease my grandson into using things like MATLAB.  The other night we were having to do the ever popular 'keep reducing the length of the secant line until it approaches a tangent line' with unending button pushing on a calculator.  He soon came to the conclusion that we should just use MATLAB.  Outstanding!

[IanB]

My new best friend, MATLAB, does all this stuff.

I never really thought about MATLAB doing symbolic math, though I see that it does. I think we have used it at work for helping with symbolic differentiation of complex expressions to avoid human error in the algebra.

Can it pretty-print the algebra in math notation, or is it only text based?

Also, what about the cost? I have the impression MATLAB licenses are pretty expensive outside of academia?

[f5r5e5d]

http://cirlab.dinfo.unifi.it/Sapwin4/ does schematic to Laplace, exports in Matlab .m format, Octave is a free workalike for Matlab that is highly compatable

[Nitrousoxide]

Just going to add my 2 cents here.

From my personal experience I used the textbook "Control Systems Engineering" during a control systems subject, however, they do cover responses in the Laplace and the time domain fairly well (In chapters 2, 3 and 4 respectively). Just another book to add to a (digital) pile.

https://www.amazon.com/Control-Systems-Engineering-Norman-Nise/dp/0470917695

[KE5FX]

My new best friend, MATLAB, does all this stuff.

I never really thought about MATLAB doing symbolic math, though I see that it does. I think we have used it at work for helping with symbolic differentiation of complex expressions to avoid human error in the algebra.

Can it pretty-print the algebra in math notation, or is it only text based?

Also, what about the cost? I have the impression MATLAB licenses are pretty expensive outside of academia?

They now have a "home use" license option.  A couple hundred bucks gets you pretty much everything useful including the EE-related toolboxes at around $50/each. 

There are some unfortunate exclusions, like HDL generation, but it's still a darned good deal.

[mtdoc]

Don’t forget about Scilab which is a free open source Matlab alternative. I believe it does Laplace and has a control systems toolbox as well.

[IconicPCB]

Schaums is the bees knees in many areas.

Once you have mastered S domain... and in particular in computer control systems the dreaded Z domain steps into the picture....

[rstofer]

They now have a "home use" license option.  A couple hundred bucks gets you pretty much everything useful including the EE-related toolboxes at around $50/each. 

There are some unfortunate exclusions, like HDL generation, but it's still a darned good deal.

For those attending a degree issuing institution, the price is even better!  The Student Suite is $99 and contains MATLAB and Simulink.

https://www.mathworks.com/academia/student_version/class_use.html

Add on packages for the Home edition run around $49 so I suspect the Education version might be a little cheaper.

Do be aware that at the end of the year, Mathworks wants you to pay a maintenance fee and, for the packages I have, this runs around $200/yr.  I'm too old to be a student so I just have the Home version.

I don't know about 'pretty print', mostly I use the command line in the IDE or I write a script and the output is just text.  Then there is MuPad which claims to produce typeset output:

https://www.mathworks.com/help/symbolic/typeset-math-and-other-output-modes.html?searchHighlight=typeset%20output&s_tid=doc_srchtitle

https://www.mathworks.com/help/symbolic/getting-started-with-mupad.html

HDL Coder is available for the Student edition but not the Home edition.  They have a truly lame excuse that Home users without support would have a hard time using the package.

https://www.mathworks.com/matlabcentral/answers/332885-why-is-hdl-coder-not-available-for-home-license

[Kalvin]

I went to Youtube for Laplace circuit analysis videos. I happened to run into this nice recap of the Laplace circuit analysis video by rolinychupetin:



Here is a nice video for the second order circuit with some very useful math tricks involved when performing Laplace inverses:



He has other very good videos about circuit analysis, for example tutorial on Modified Nodal Analysis (MNA) which can be used also in Laplace-domain:



Best of all, he doesn't spend half of the video writing things to the whiteboard, but the video rolls on quite smoothly in comfortable pace.

[rstofer]

That Modified Nodal Analysis video (and approach) is terrific.  I need to do a few more problems to make sure I understand the idea of 'evil currents' and 'evil branches' but the author's example shows how to deal with them.

I graduated before the method was invented so I guess I don't feel too left out!

[sibeen]

I'll agree about the MNA video. MNA may have been invented before I graduated, but by less than 10 years so it certainly hadn't made its way anywhere near any text book that I sighted. I'll also be working through a few problems. In the initial video he had 6 unknowns and I immediately thought, "hey, there's a supernode in there, get rid of at least one. " He uses it as an evil current and so may be required, so another view of the video and a run around a few problems may inform me. 

[Wimberleytech]

Similar story...I learned the old way for my undergraduate.  Then I went into industry later to return to academia for my Ph.D.  My particular course of study led me to methods of doing circuit analysis using computer and that is where I was introduced to MNA.  This is a great video on MNA, but learned it in an even more regimented way.  You have to be more methodical if you are going to write a SPICE simulator--which is what I had to do.  The circuit parser just plugs each element into a nodal admittance matrix and then you send that to a sparse matrix solver...voila!  All of the work is in the parser!!

>>I found this on the internets...this is the way I learned it. 
https://www.swarthmore.edu/NatSci/echeeve1/Ref/mna/MNA2.html

[IanB]

Interesting. I watched that video on MNA and as I write simulators for a living it contained no surprises. I'm curious that it is something that might need to be "invented".  Isn't it just the logical application of basic circuit principles in a systematic way?

(I remember as an undergraduate my fellow students writing spice-like simulators using using similar principles round about 1980.)

[Wimberleytech]

Isn't it just the logical application of basic circuit principles in a systematic way?

Yes, I agree.  What has changed is ubiquitous computing power.  With computers, solving large matrices is trivial.    Now that we have huge computing power, systematic methodologies were developed that fed naturally into a computer solution.

[rstofer]

It's slightly different in that it solves for both voltage and current simultaneously.  Nodal analysis give node voltages, mesh analysis gives  branch currents and this modified nodal analysis seems to do both.  There are more equations and more unknowns in that there are KCL equations for every node, EVL equations for every 'evil current' and CTL equations for every controlling variable.  In the old days (slide rules), this wouldn't be considered an advantage.  It's easy to solve a 2x2, even a 3x3, but once you get to 4x4 things get out of hand.  Creating 6 equations in 6 unknowns is only useful when using a computer or high end calculator.

[rstofer]

For giggles, I fed the equations into MATLAB see attached screen shot

[rstofer]

While I was on a roll, I decided to port the equations to wxMaxima.  For folks looking for a terrific math tool that happens to be free, wxMaxima is worth the time to evaluate.

Attached is a PDF of the code and the output.  Note that the equations look an awful lot like the ones I used with MATLAB.  In fact, I copied and pasted and just changed a wee bit for syntactic reasons.

Everything below 'res : ' is just used to produce a sorted output list.  That very same code is used in all of my files - now that I figured out how to do it.

So, why do I get into this stuff?  Well, in a year or so, my grandson is going to take his very first circuit analysis course and I need a head start.

BTW, don't expect a flat learning curve with either of these tools.  It takes time.  Mostly it takes copy and paste!

[Hextejas]

   I take my hat off to you folks that have the patience to learn this "stuff".
I'm not sure how or if it would be used to  try and figure out why my ham radio stopped working.
Wowsers!

[rstofer]

  I take my hat off to you folks that have the patience to learn this "stuff".
I'm not sure how or if it would be used to  try and figure out why my ham radio stopped working.
Wowsers!

It probably won't help a bit!

However, you can bet that Laplace Transforms were used to design some of the more sophisticated filters.

Here is a Wiki on the Butterworth Filter that makes my head spin:

https://en.wikipedia.org/wiki/Butterworth_filter

To think there was a time, back 45 years ago, where I actually understood this stuff.  Today it would be a stretch!  The good news today is that MATLAB will solve all the Laplace and Inverse Laplace transforms.

[Kalvin]

Thanks, rstofer! I modified your script and solution to the freely available GNU Octave with Symbolic package. The GNU Octave is missing some MATLAB packages and functions, so I had to modify the original script a little.

[sibeen]

Just for giggle the same calculation done using Mathcad

[rstofer]

Just for giggle the same calculation done using Mathcad

Could you explain the first line of your script?  Are you giving Mathcad hints?

[rstofer]

sibeen and Kalvin

Thanks for posting alternate solutions.  I like the way Mathcad prints but Octave is also impressive, a lot like Maxima (I use wxMaxima to get the GUI);
I hope other people are getting something out of this.  I know I am!

Students are lucky, all of these tools make the math part of electronics a lot easier.  Using a slide rule wasn't nearly as cool as it looked!

[sibeen]

Could you explain the first line of your script?  Are you giving Mathcad hints?

A quirk of mathcad. You need to define a variable for mathcad to begin to recognise it.  I could have set the variable definitions to be all be minus 100 (-100) and it wouldn't have made any difference.

[rstofer]

Could you explain the first line of your script?  Are you giving Mathcad hints?

A quirk of mathcad. You need to define a variable for mathcad to begin to recognise it.  I could have set the variable definitions to be all be minus 100 (-100) and it wouldn't have made any difference.

Sort of like the syms statement in MATLAB.  I have to define the symbols before I can use them.
Good to know!

[rstofer]

A long time back, analog computers were used to simulate mechanical systems and, specifically, solve differential equations.  I have been playing with a very small analog computer for the last couple of years.

MATLAB, my new best friend, also has Simulink which allows me to create a virtual analog computer.  See attached and notice the cool use of knobs to set the various parameters.

The equation for Damped Harmonic Motion is: my'' + Dy' + Sy = 0 and we'll assume consistent units.  Sum of the forces = 0

m is the mass
y'' is the acceleration
D is the damping coefficient
y' is the velocity
S it the spring rate
y is the displacement

FWIW, this is also the equation for an R-L-C circuit.

With Simulink, you can drop integrators, adders and mutlipliers on a sheet and wire them up.  We have Lord Kelvin to thank for the approach to solving the equation.  Assume we have y'' then integrate once to get y' and integrate again to get y.  Now, manipulate those variables to form y'' = (-1/m)*(Dy'+Sy) and stuff this back into the first integrator where we assumed we had y'' which we just created!  Toss in the initial values and sit back and watch!

So, what's the point?  Sometimes a picture is worth 1000 words and although MATLAB can solve the equation and plot the results mathematically, sometimes it is fun to do it 'old school'.

Just another reason to consider MATLAB...

http://chalkdustmagazine.com/features/analogue-computing-fun-differential-equations/

[Simon]

Problem I have with programs like Matlab is that I'm already so engrossed in my studies I don't have time to study something else as well. I think my university forgets that I'm actually working whilst trying to study and that the material they present is but a small portion of what I eventually end up having to study. The first video on Laplace transforms was quite interesting and has shed some more light on the subject for me.

[rstofer]

Problem I have with programs like Matlab is that I'm already so engrossed in my studies I don't have time to study something else as well. I think my university forgets that I'm actually working whilst trying to study and that the material they present is but a small portion of what I eventually end up having to study. The first video on Laplace transforms was quite interesting and has shed some more light on the subject for me.

I understand completely!  There is only so much time available and it needs to be properly allocated.

One reason I understand is that I worked full time days (often 60 hour weeks) for the entire four years of undergrad at night.  That wasn't enough pain so I did the same thing in grad school.  I don't recall when I slept.  I may have missed that...

No matter what, my grandson is going to concentrate on classes.  Working can wait!

[Simon]

What I am finding really depressing is that once I use alternative material I realize that the course material is jumping all over the place in an attempt to shorten the theory and get more theory in. the result is a mess and I have long since abandoned the idea of looking back on my time studying safe in the knowledge it was time well spent and rather an exercise in jumping through hoops to get a piece of paper valued by everyone but me. qualifications are becoming garbage. hopefully people wake up to this soon.

[rstofer]

What I am finding really depressing is that once I use alternative material I realize that the course material is jumping all over the place in an attempt to shorten the theory and get more theory in. the result is a mess and I have long since abandoned the idea of looking back on my time studying safe in the knowledge it was time well spent and rather an exercise in jumping through hoops to get a piece of paper valued by everyone but me. qualifications are becoming garbage. hopefully people wake up to this soon.

What's hard about electrical engineering?  Or any other engineering, for that matter?  Math!

The great filter is the ability to do the math.  The models are simple, the concepts are not overly complex but the math separates the techs from the engineers.  I don't want to start a techs versus engineers conversation, I'll just note that engineers, on average, make more money and if it wasn't for money, there would be no reason to put up with college.

Keep your eye on the prize!  It's not the paper, it's the money that comes for having the paper.

[Vtile]

...I know the frustration. On the otherhand you are searching the solutions and even if you at the moment get all the pieces together you will fill the pieces later.  Have you read the Shoums outline Math and Electical books edit. with PC: Schaum's Outline of .. https://www.amazon.com/Schaums-Advanced-Mathematics-Engineers-Scientists/dp/0071635408 <- these series, they have lots of example solutions in every chapter. (don't touch the "lite" versions, as they seems to have those in some subjects)

One reason we need Laplace is because our phasor calculus is working only with steady state AC circuits. If the spiral vector analysis   would be more matured up we could use one method for all three .. DC, AC and transients.

[sibeen]

spiral vector analysis

OK, that's a rabbit hole that I'm definitely not going down. Had a very, very brief look - nup, definitely not.

[Simon]

What I am finding really depressing is that once I use alternative material I realize that the course material is jumping all over the place in an attempt to shorten the theory and get more theory in. the result is a mess and I have long since abandoned the idea of looking back on my time studying safe in the knowledge it was time well spent and rather an exercise in jumping through hoops to get a piece of paper valued by everyone but me. qualifications are becoming garbage. hopefully people wake up to this soon.

What's hard about electrical engineering?  Or any other engineering, for that matter?  Math!

The great filter is the ability to do the math.  The models are simple, the concepts are not overly complex but the math separates the techs from the engineers.  I don't want to start a techs versus engineers conversation, I'll just note that engineers, on average, make more money and if it wasn't for money, there would be no reason to put up with college.

Keep your eye on the prize!  It's not the paper, it's the money that comes for having the paper.

Yes it has become about the price, and therefore anything now goes. not the way I wanted to do it but I will have to revisit the topics later anyway, sadly I have been made to despise the very topics I was hoping to really get into.

[Vtile]

spiral vector analysis

OK, that's a rabbit hole that I'm definitely not going down. Had a very, very brief look - nup, definitely not.

Yes, that is why I said it is sadly not more matured up. 

[rstofer]

What I am finding really depressing is that once I use alternative material I realize that the course material is jumping all over the place in an attempt to shorten the theory and get more theory in. the result is a mess and I have long since abandoned the idea of looking back on my time studying safe in the knowledge it was time well spent and rather an exercise in jumping through hoops to get a piece of paper valued by everyone but me. qualifications are becoming garbage. hopefully people wake up to this soon.

What's hard about electrical engineering?  Or any other engineering, for that matter?  Math!

The great filter is the ability to do the math.  The models are simple, the concepts are not overly complex but the math separates the techs from the engineers.  I don't want to start a techs versus engineers conversation, I'll just note that engineers, on average, make more money and if it wasn't for money, there would be no reason to put up with college.

Keep your eye on the prize!  It's not the paper, it's the money that comes for having the paper.

Yes it has become about the price, and therefore anything now goes. not the way I wanted to do it but I will have to revisit the topics later anyway, sadly I have been made to despise the very topics I was hoping to really get into.

You thought you were going to enjoy college?  You should have taken English Lit - that's where the girls are.  Very few are slugging it out in EE school (I ran across a few and they were super smart).  I always wanted to have the time to sit on the lawn and watch the other students walk by.  Alas, I had to work...

Fully 80% of the courses I had to take meant nothing other than a grade.  My only interest was digital design and that is because the math for analog circuits is so heavy.  Digital is simple!

Grad school was better.  Basically, I got to pick and choose the courses I wanted and there were only 2 math courses and an engineering seminar that were mandatory.  Yup!  I took digital courses, again!

Turns out I still use the book from the Numerical Analysis course.  Every once in awhile something comes up that is discussed in the book and code is usually provided.  You just never know what you're going to need later.

You just have to put your head down and drive on through it.  Later you can look back and laugh.  What an enormous waste of time!  Except for the money...  It's all about the money!

[Simon]

as its a distance learning course it comes with no added social activities I wanted to learn something but instead I am wasting my time making it look like I learned something, its just a farce.

[mtdoc]

Don’t confuse studying to be an engineer (or any technical field) with what you will do when you are actually working in the field.  As someome with several degrees and who has worked in more than one professional technical field, including as a university instructor,  i can say for certain that the hurdles you must jump over to get the requisite degree, whether it be math courses, chemistry, physics, or whaever - while serving some educational utility, often have very little application to what you do in practice (or none at all!).

How many EEs have ever needed to use Laplace in their professional work? Likely < 1%. Same goes for many other advanced technical topics in engineering or other fields.

Sometimes you just need to trudge through it to get the degree.

[Simon]

Yes it is exactly as you say. It is all a circus and a farce. The material I am studying from is quite confusing and I'm pretty sure it was written by somebody who thinks the student has experience and knowledge from other modules within the University that a student in my position would not have. I don't see the material as very well joined up. There are no indexes no contents it is just a rambling mess of rubbish. But when I do look outside of the material to books and the Internet suddenly I find that the subject is much vaster and that they are also whilst explaining it badly trying to present a wide-ranging topic in a concise manner.

If the object of the game simply to get the certificate then that is easy because I can and have bought the answers to the questions. Education has become that not of a farce in this country that they can't even be bothered to slightly change the questions each year. There is abundant evidence online people asking for help with these questions dating back 10 or 15 years. So when I look at this I wonder is everybody else buying the answers? Am I going to get a lower grade for being honest? If it's simply about getting the piece of paper I can do that. But I would prefer to understand the subject and honestly answer the assignment. I would in the future like to learn more about control systems which is why I am somewhat interested in this subject although it may appear my maths skills are not good enough to even bother.

Yes in real life I will probably not use an awful  lot of the skills I am learning. If what I am learning could be called skills. I run my own company I don't need a degree to run a company and as a company nobody asks me what my qualifications are. If I got an order tomorrow for 1 to 2000 of a product for the next five years I would be walking out of my day job in four weeks time as per my contract. And it is just a matter of potluck that that could happen nothing to do with my qualifications or lack of. I have in the past carried out work for a project manager who had a HNC in electronics the very qualification I am trying to obtain and of his own admission understood nothing of electronics and blew his project up at the demonstration yet he still got qualified. So yeah you're right it is a massive waste of time and a silly system that society expects us to go through in order to pretend we know what we are doing. Working for my current employer I have come across people with degrees to whom I have had to explain how to do things to or I have had to fix their basic mistakes in circuit board layout and lack of bypass capacitors it does indeed get that bad. You can have a degree in electronics and not realise that you can't have a trace that is over 6 inches long leading to a switching MOSFET with no bypass capacitor across the MOSFET. Doing this qualification really is a backup for getting another job or getting some sort of recognition (money) from my current employer. For me and for my company it is clearly meaning very little and I agreed to undergo it on the assumption that I personally would gain from my employer. Thankfully they are paying not to me.

[rstofer]

But when I do look outside of the material to books and the Internet suddenly I find that the subject is much vaster and that they are also whilst explaining it badly trying to present a wide-ranging topic in a concise manner.

Saturday the grandson was over and I was showing him that MATLAB Damped Harmonic Motion project I posted earlier.  I showed him how a change in the parameters would change the damping or the frequency and so on.  Then I pointed out that this was the exact same equation for an R-L-C circuit and, indeed, the solution to most 2d order differential equations took the same form.  The math was the same regardless of the field.

Then we moved on to shaker tables and building dynamics.  Very interesting stuff.

Indeed these underlying math does cover a vast array of topics.  It's all the same equations, just a different application.

If you are interested in control systems, I have to recommend the 'katkimshow' videos.  Here is one and it isn't the first but there isn't a simple playlist to work from (that I have found).

[rstofer]

But when I do look outside of the material to books and the Internet suddenly I find that the subject is much vaster and that they are also whilst explaining it badly trying to present a wide-ranging topic in a concise manner.

Saturday the grandson was over and I was showing him that MATLAB Damped Harmonic Motion project I posted earlier.  I showed him how a change in the parameters would change the damping or the frequency and so on.  Then I pointed out that this was the exact same equation for an R-L-C circuit and, indeed, the solution to most 2d order differential equations took the same form.  The math was the same regardless of the field.

Then we moved on to shaker tables and building dynamics.  Very interesting stuff.

Indeed the underlying math does cover a vast array of topics.  It's all the same equations, just a different application.

If you are interested in control systems, I have to recommend the 'katkimshow' videos.  Here is one and it isn't the first but there isn't a simple playlist to work from (that I have found).

[vodka]

What I am finding really depressing is that once I use alternative material I realize that the course material is jumping all over the place in an attempt to shorten the theory and get more theory in. the result is a mess and I have long since abandoned the idea of looking back on my time studying safe in the knowledge it was time well spent and rather an exercise in jumping through hoops to get a piece of paper valued by everyone but me. qualifications are becoming garbage. hopefully people wake up to this soon.

What's hard about electrical engineering?  Or any other engineering, for that matter?  Math!
The great filter is the ability to do the math. 

It is truth, but the trap is that the maths aren't taught  or aren't taught fine. On my case, i didn't know differential equation neither laplace transform when i went into university, because at the Spanish Education System(before university) didn't  teach. At the first quarter, i was an Maths subject , there they taught me  limits, complex number etc; less differential equation and laplace transform.
Now , when i began the second quarter they taught us in 10 days the differential equations and laplace transform(3 weeks) and the 11th day exam; the brutality result only passed 15/150. 

I happened the same that are passing Simon , i ate the full duck with plumes and peak. If i would had more information , i would had tried to learn myself the laplace transforms before getting in at university

[IanB]

It is truth, but the trap is that the maths aren't taught  or aren't taught fine. On my case, i didn't know differential equation neither laplace transform when i went into university, because at the Spanish Education System(before university) didn't  teach. At the first quarter, i was an Maths subject , there they taught me  limits, complex number etc; less differential equation and laplace transform.
Now , when i began the second quarter they taught us in 10 days the differential equations and laplace transform(3 weeks) and the 11th day exam; the brutality result only passed 15/150. 

I happened the same that are passing Simon , i ate the full duck with plumes and peak. If i would had more information , i would had tried to learn myself the laplace transforms before getting in at university

Same with me. Differential equations and Laplace transforms are too advanced for high school education. Even taking Further Mathematics 'A' Level many years ago I only got a basic introduction to differential equations.

So in the first year of my engineering degree we got a crash course in all of that that you mentioned during a single term.

[rstofer]

Your system is MUCH different than ours.  The expectation on entry to a STEM program is pre-calculus in High School.  Some may have had differential calculus but not all.

Then the progression for the first two years (up to the AS degree):
Calc 1 - Differential
Calc 2 - Integral
Calc 3 - Linear Algebra and Numerical Analysis - a lot of matrix math.
Differential Equations - the end for the lower level stuff

Those courses are all 1 semester each and cover the entire lower level 2 year program.

Then we get into the things like Laplace Transforms, Fourier Analysis, Field Theory and so on, all as part of the
upper level (BS) program.  Every STEM major does the first 4 classes and then it splits.  Laplace and so on will be in the EE program and I have no idea what happens in the other majors.
 
So, in some ways it's a slow path - two years to get through differential equations.  BUT, the subjects are taught in depth - as though you intend to major in math.  Perhaps a little too much depth and not enough utility.

[IconicPCB]

I completed  my degree in '77.

In order to get into the degree course i had to have reasonable results in year 6 high school.

I did not attend high school , instead i went through the secondary technical schools program which culminated in year 5 .
Technical schools in the state of Victoria were geared towards creating trades and technicians albeit with Maths 1 and 2 ( pure and applied maths an sciences courses).

At the end of Year 5 i attended year 6 at a tertiary institution, way back when... an Institute of technology ( now a part of a university )
Year 6 was designed  to ensure we were university ready.

I then commenced my degree course  initially based on two years of common subjects to all engineering students with some subject indicating specialisation.

Two years of Maths.. a year of chemistry and physics thermodynamics, machines ( mechanical machines) design .. etc.

It was only in the final two years that the specific engineering field was broached.

In retrospect it is hard to say what was a waste of time and what was useful.
I thiink that certain knowledge and skills become crystalised over time ... a bit like times table and You use it without really thinking about it.

So it is with maths ...and pretty much everything else  i had been taught...little bits..pebbles ( calculus) come to the fore in rounding off  comprehension and decision inherent in the profession.

[IanB]

Your system is MUCH different than ours.  The expectation on entry to a STEM program is pre-calculus in High School.  Some may have had differential calculus but not all.

Then the progression for the first two years (up to the AS degree):
Calc 1 - Differential
Calc 2 - Integral
Calc 3 - Linear Algebra and Numerical Analysis - a lot of matrix math.
Differential Equations - the end for the lower level stuff

Those courses are all 1 semester each and cover the entire lower level 2 year program.

Then we get into the things like Laplace Transforms, Fourier Analysis, Field Theory and so on, all as part of the
upper level (BS) program.  Every STEM major does the first 4 classes and then it splits.  Laplace and so on will be in the EE program and I have no idea what happens in the other majors.
 
So, in some ways it's a slow path - two years to get through differential equations.  BUT, the subjects are taught in depth - as though you intend to major in math.  Perhaps a little too much depth and not enough utility.

Yes, the UK system is a bit different. The main difference is that not all students continue to the equivalent of 11th and 12th grades (sixth form in the UK), and those students that do elect to study a limited range of subjects. Not all students elect to study mathematics, but those that do will be introduced [from 11th grade onward] to series, convergence, limits, differentiation, integration and real analysis. I think there may also be an introduction to complex numbers and linear algebra.

It is normally expected that students entering a STEM degree will have this foundation and can start studying more advanced material, although there have been some complaints that students today are not prepared as well as they were in previous generations.

For various reasons I got exposed to a richer range of subjects in my sixth form studies including group theory and modern algebra, statistics and confidence tests, differential equations and numerical methods.

[mtdoc]

Your system is MUCH different than ours.  The expectation on entry to a STEM program is pre-calculus in High School.  Some may have had differential calculus but not all.

Then the progression for the first two years (up to the AS degree):
Calc 1 - Differential
Calc 2 - Integral
Calc 3 - Linear Algebra and Numerical Analysis - a lot of matrix math.
Differential Equations - the end for the lower level stuff.

Not really true. First of all many universities are on the quarter system- not semesters-  so calculus is completed in one year. Secondly, most top universities expect entering STEM students to have completed calculus in high school (grade 12) i.e. before entering college. Also, AS degrees are only given out in junior colleges not in 4 year colleges and universities.

Every STEM major does the first 4 classes and then it splits.

Not always true. For example, the biological sciences often only require Calculus 1 and 2 (often done in high school as stated above). Sometimes true for other sciences as well.
 

[Simon]

Do I correctly remember that a constant current fed into a parallel resistor and capacitor would bring about a steady state across the resistor and capacitor in five time constants? Much in a similar way to a voltage applied to a resistor capacitor series circuit brings the capacitor to a full charge after five time cycles? I'm sure I read this somewhere but the Internet provides scant and argumentative information and I have read so much printed matter I can't find it anymore.

[rstofer]

I have never thought about the problem using a current source.  Were it not for the resistor, the charge would be linear but, of course, the resistor is taking increasing amounts of current as the capacitor takes charge.

So, AFAICT, the equation is still related to 1-e^-t/RC.  So, at 5 time constants, the capacitor is about 99% charged.

I have attached an LTspice file and a screen shot - the time constant is 1 ms so at 5 ms we're pretty close to fully charged.

[Andy Watson]

Do I correctly remember that a constant current fed into a parallel resistor and capacitor ...

Yes.
Think about the constant current source and resistor as its Thevenin equivalent - now put the capacitor back in series - you have the more usual RC circuit which will charge to 99% within 5 time constants.