Using Laplace to analyse circuits

[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.