Mesh analysis

[Simon]

Attached is a photo of an exercise I am doing. I'm trying to work out if I have written the equations out correctly. My main concern is V3 that is just dumped in there. Unfortunately most books and examples online seem to give very simple networks usually it's a three-way network with The voltage source on each of the outer branches and the centre branch is a resistor.

[f5r5e5d]

http://cirlab.det.unifi.it/Sapwin/ could be helpful for checking but you may still need to do some algebra since computer algebra systems don't always order/factor things the way you want

free CAS aren't up to the standards of Maple, Mathematica but can still sometimes be helpful in circuit analysis

https://www-fourier.ujf-grenoble.fr/~parisse/giac.html

[Simon]

Is it a simulation program ?

[f5r5e5d]

read the page? - SapWin is a schematic entry driven Symbolic Transfer Function generator, with the option for substituting real values and doing Bode Plots

but it is the Symbolic Equation output that is unique, valuable for verifying hand mesh analysis

[Simon]

I see well the beta 4 won't launch, I'll try 3

[Simon]

Because i don't have a frequency i can't convert the complex impedences into henrys. I'm really justying to check I wrote the equations right. I am using wolfram alpha to sole the equations

[jm_araujo]

I'm a bit rusty on my equations, but it it seems that the terms related to Z4 (1st and 2nd line) are with the wrong sign (Z4 in the diagram is "-j5").

[Simon]

Yes it is certainly wrong in the first line, thank you

[orolo]

Save for the Z4 sign, I get the same equations.

The system is triangular: in eq1 you can put I1 in terms of I2, in eq3 I3 in terms of I2, and in eq4 I4 in terms of I2. Divide eq2 by j, substitute I1, I3 and I4, and solve for I2.

[f5r5e5d]

I'd guess the expectation is for you to use superposition, simplifying the circuit for each Vsource considered independently with the others shorted

properly done the full mesh/nodal analysis will give the same answer but superpostion lets you easily do it "by inspection" with just series/parallel, I, V divider relations

[Simon]

No the question specifically wants me to use mesh and then nodal.

Sent from my phone so mind the autocorrect.

[lordvader88]

I've never done this stuff with reactance added in, only just resistance. I'm good at math but lazy. If I ever get serious about this stuff on a real EE level I''ll be going along by proper course syllabus for 1-2nd year EE

[Simon]

I've never done this stuff with reactance added in, only just resistance. I'm good at math but lazy. If I ever get serious about this stuff on a real EE level I''ll be going along by proper course syllabus for 1-2nd year EE

Yea that is what this is. With inductances it all works the same, it's just that the math is complex number math. I just use wolfram alpha for that, tutor is quite happy with me to do that. It's all a giant waste of time but one has to tick boxes in order to get to the useful stuff.

[Simon]

I am now asked to do nodal analysis on this circuit. The problem for me is what do I do about the branches from the top power supply that is not even referenced to ground. I have tried various permutations of equations none of which look like they will produce the same current as the mesh analysis.

[Simon]

my equations so far are like the attached.

[SingedFingers]

I've never done this stuff with reactance added in, only just resistance. I'm good at math but lazy. If I ever get serious about this stuff on a real EE level I''ll be going along by proper course syllabus for 1-2nd year EE

Yea that is what this is. With inductances it all works the same, it's just that the math is complex number math. I just use wolfram alpha for that, tutor is quite happy with me to do that. It's all a giant waste of time but one has to tick boxes in order to get to the useful stuff.

Can confirm. Did EE degree. Never used this once. Usually you just use a rough calculation and finger in air estimate, stick it in a SPICE variant and frig the values with empirical methods.

Ergo, I can't remember how you do this but I'll stick with the thread in case I learn something useful

[Simon]

This is what annoys me so much. I am forced to jump through these hoops when in actual fact the knowledge is completely useless to me. My time would be better spent working on my own customer projects or learning something pertinent to what I am doing like programming in C. But instead in order to get all of the formal qualifications required to either land myself a better job later or be better at what I would like to do on my own I have to start at this level doing advanced physics that nobody uses any more. It's extremely annoying and I've got deadlines on it as well or rather I have to do two modules a year but this is one question out of one third of one module and with the time it is taking me there is a fat chance of that and it's all over stuff that is completely and utterly useless.

[IanB]

I would not agree that it's useless. You may not need to go through the calculations of a solution very often, but you will want to be able to replay the solution method in your mind without thinking too hard about it. It is the conceptual understanding that is important.

For example, your question above: "V3 is not even referenced to ground". Doing this exercise successfully will help illustrate why "ground" is just a notational convenience and does not play any part in the actual solution.

[Simon]

Well unfortunately the pages and pages of drivel that I have been given to study from don't clearly explain what to do in a situation like V3. Without it having some sort of reference to somewhere the current into the node is infinite, so I have to tight down to somewhere. I also can't simulate it because I'm not giving a frequency of the voltage or the inductance of the impedances and any simulation program works on an AC voltage with a frequency and inductance values not complex numbers so I effectually have no way of resolving this. It's actually a giant waste of time studying the material I have been given. Given that this is just a massive box ticking exercise I may as well just go straight to the assignment and do my best to solve them using the study material if necessary. If I miss learning something because it is not covered in the assignment then so be it. I've spent the last month reading pages and pages of mathematical explanation which have gone straight through my head and have completely obfuscated the actual principles that I'm supposed to be learning.

[snarkysparky]

I think octave ( free matlab equivalent ) will solve complex matrix equations easily.

In these problems you have to attack them by shutting off the brain momentarily and just write down the equations. Don't try to consider each circuit as a special case, just concentrate on getting the equations correct.  So V3 will just be another term in there.  When you have the equations correct then next step is to solve them.

""But instead in order to get all of the formal qualifications required to either land myself a better job later or be better at what I would like to do on my own I have to start at this level doing advanced physics that nobody uses any more""

You may use it and not know that you are doing so.  See learning all that theory changes how you think about things even if you don't do the calculations.  You should consider if you really want to torture yourself with a engineering degree if you have no taste for the theory. 

BTW this class was the first in my EE program and they tried really hard to get those who don't really want it to drop out at that point.  It was a tough one.

[Simon]

Well I'll go back through my coursework and try and find example similar to what I have. The problem with trying to shut off and just write equations is that there are up to 4 combinations of equtions I can write, only one is right.

[sibeen]

OK, I'm an old fart and have done this for quite a few years, and I'll state that it's not useless. It is actually trying to teach you a few simple rules. KVL = mesh and KCL = Nodal.  Learn these grasshopper and they will stand you in good stead for the rest of your lifer

Now to your nodal equations. KCL states that the currents into and out of a node sum to zero.

So we have node 1 which is at the top of Z4, (node 2 at top of Z5). I'm assuming here that the 'earth' is at the bottom of Z4, but in reality you can throw that wherever you want.  Node 1 has 4 currents into / out of.

Branch 1 = (N1 - V1)/ Z1.    A simple ohms law.

Branch 2 = N1/Z4. as the bottom of Z4 = 0 volts (earth) then N1 - 0 = N.

Branch 3 = (N1 - N2)/ Z2. A simple ohms law.

Now the tricky branch 4. Here the question is trying to teach you something.  Nodes 1 and 2 are connected by a voltage. This means that whatever the voltage is at node 1 then the voltage at node 2 will be V3 less than. Doesn't matter what all the other branches are doing - Node 2 will be V3 less than Node 1.

N1 = N2 + V3

This is showing you that in this Nodal instance you only need to actually solve for N1. N2 is just going to be V3 less.

[Simon]

Well granted the tutor has said he intends rewriting some of the module so maybe the module material is the mess i think it is. I can see where the principles can be useful but I am getting questions that are more complex than the material explains and all I need to understand is the principles not use this to solve massive stuff. The classic example is just like this but without V3.

So my understanding is that we are producing equations that define currents in and out, so if N1= N2+V3 then what is the current in that branch ? or is it ok to just state a voltage in the equations ?

[IanB]

So my understanding is that we are producing equations that define currents in and out, so if N1= N2+V3 then what is the current in that branch ? or is it ok to just state a voltage in the equations ?

Well the current law says the currents into and out of a node sum to zero, so once the currents through Z1, Z2 and Z4 are discovered, the current through V3 will be whatever is required to make the sum around the node equal to zero.

[orolo]

The voltage source forces a constant current from a to b through the -5i resistor, letting pass an arbitrary current 'k'. So a nodal analysis could be like this: