There must be a very simple stupid answer to this and I could really use some help knowing what it is :/
Consider a mesh-current analysis problem where the circuit contains a current source. Every text and website I can find on the topic gives a nice simple example where the current source is along the junction between two meshes, and I understand how to set up a phantom voltage across this source, which is canceled out by adding the two equations for the meshes that adjoin.
However I do not for the life of me understand how to set up the equations for such a circuit where the current source is on the edge of the circuit. It's driving me crazy!
I've put an example of the sort of problem I mean at . I think (THINK) I can correctly deal with the 10A source on the top edge, but the dependent source on the bottom right corner has me utterly baffled. I assume KCL is used to determine that the current through the 1 ohm resistor is (2Vphi/5) +
10 but what's the current in the 5 ohm?
Or in general what is the plan of attack when faced with a current source at the periphery of a problem where mesh-current analysis has been mandated?
(This detestable text has no solutions for the "drill exercises", just answers. Useless).
Why should you care where the current source is? You have three loops, draw the current in all three loops (take care with your direction), and write you equations. Post them here. Tom
Because the algorithm given in the book for dealing with a current source in this type of problem can't be applied to this configuration
- how do I draw a supermesh around something that's on the outside?
I'm really confused. This again doesn't follow the algorithm in the text. if we define Ia as shown in the diagram, Ib as being counterclockwise in the top loop, and Ic as being clockwise in the right-hand loop, then
Ia =3D ??? Ib =3D 10 Ic =3D 2Vphi/5
According to the text I should be setting up voltage equations using the mesh currents, and I can only draw this up for the bottom left loop:
75 =3D 2(Ia+10) + 5(Ia - 2Vphi/5)
Both other loops have current sources in them, which I can't eliminate by drawing a supermesh around them.
Can't sleep until I work this out. This whole class of problems has me pissed off, not the least reason for which being the textbook:
- it has answers only for some problems (usually these days textbooks give answers for all odd problems, but this book has answers for only maybe 30% of the questions)
- worked examples are given only for the simplest possible case of each problem
- "drill exercises" are often more complex, but have only answers, no intermediate values or working. STUPIDITY.
If they want to sell solution manuals, f#$*#!ing well put the solution manual inside the textbook and add $30 to its price. Students don't have a choice anyway.
I still hate this textbook, but I had a glass of shiraz and attacked the problem again. Define Ib=3D10A running counterclockwise in the top mesh, Ic=3D2Vphi/5 running clockwise in the lower right mesh and Ia running clockwise in the lower right and we get:
75=3D2(Ia+10) +5(Ia-2Vphi/5) so 7Ia - 2Vphi =3D 55
I still hate this textbook, but I had a glass of shiraz and attacked the problem again. Define Ib=10A running counterclockwise in the top mesh, Ic=2Vphi/5 running clockwise in the lower right mesh and Ia running clockwise in the lower right and we get:
75=2(Ia+10) +5(Ia-2Vphi/5) so 7Ia - 2Vphi = 55
But Vphi=5(Ia-2Vphi/5) so Vphi=5Ia/3
hence 7Ia - 10Ia/3 = 55 Ia = 15
*sigh* not enough hours in the day, I tell you.
It would serve you to always represent your units.
75 is 75 v, 2 is 2 ohms. Not nit picking but it will help you realize what units you are working with. BTW: Ia is in the lower left. Good night. Tom
I don't really like mesh analysis much. There are several methods, but the one I like conceptually uses the idea of "spilling" in and out of a node.
In your schematic example, you have four nodes. The schematic is:
Okay, I admit it. It's not the best ASCII schematic around. Oh, well.
Node Vx is obvious. It is: Vx = 75V and we're done.
Node Vy spills outward through three resistors. Treat the resistors as conductances for this purpose. Also, the same thing happens in reverse (super-position), so that Vx, Vz, and gnd spill back into Vy. The spill in and spill out must be equal:
Substituting that into Vy equation and solving for Vy:
Vy = (Vx*Gx - 10A)/(Gx + Gy + 2/5)
The values of Gx=1/Rx, Gy=1/Ry, and Gz=1/Rz should be clear. Plugging in the values, that solves out to Vy=25V and using that with the solved Vz equation gives Vz=5V.
Which pretty much finishes it. I(Ry)=25/5=5A; I(Rx)=(75-25)/2=25A; I(Rz)=(25-5)/1=20A. Your B source of 2/5*Vy is clearly 10A and that leaves 15A for the 75V source. Labeled below:
I like that way of looking -- treat each node as spilling outward and inward through conductances, in or out via current source/sinks, and let the chips fall where they do. I don't like mesh as it doesn't sing in my mind like this way does.
I found the node-voltage method much simpler to wrap my head around, but I more frequently make mistakes with signs in this method :)
The text really isn't very helpful on the decision process either. They say basically pick whichever method results in fewer simultaneous equations. But since I'm doing them all on a calculator anyway, it makes no difference to me whether there are 2, 3, 5 or 10 unknowns. Though sometimes if there are lots of voltage or current sources, choosing one or the other can mean less work.
It's all very moot since the whole reason I am struggling with this stuff is because I don't do it manually. It's the work of a few moments to set up a circuit in PSpice and run two simulations to get a Thevenin equivalent or whatever I need. Come to think of it, there's probably some macro feature to do that automatically.
I'm self-taught, as this is just a hobby. By the time I was exposed to mesh analysis, I'd already learned to handle things using the nodal approach. I'd read "The SPICE Book" and that's how they illustrated the way spice looks at things. It made a whole lot of sense at the time. When I finally was exposed to the mesh approach because my son was taking an electronics class, I just kept going "Ewwww! No way! Why would anyone do this to themselves?" I could work through it, forced to it, but I didn't like it. What I'd already learned was so much easier to apply, both conceptually and in terms of manual labor as well.
Well, I'd actually like to hear an example if one ever does come to mind. I worked through quite a few problems with my son using mesh and was never exposed to a single case where I liked it better.
The nodal analysis I was exposed to is just a little bit different than what The SPICE Book exposed me to, but close. They don't usually express it as "spills" in and out, when talking about it, but instead take a slightly less intuitive and slightly more rigorous approach in their wording. It's just enough different from how SPICE appears to approach things and how nodal analysis does that I consider them very close cousins but not identical twins, so to speak.
But I don't ever recall making such mistakes with nodal analysis/the spice approach. I think I actually have MORE problems with signs in other cases (though I usually get them right, I think -- I'm not sure, anymore, because the nodal approach just works and works and works, when I need it and I don't seem to have errors with it so I just haven't gone back that often to see if I'd still have sign problems in mesh or branch analysis ... neither of which I developed much of a stomach for.)
It's easy -- I think branch analysis and mesh analysis are always harder on every problem done by hand. Unless you just love to play with matrices, Cramer's rule, and determinants. Carefully done, mesh analysis appears to play right into a nice matrix setup, so if you have matrix math handy on your calculator it can be a little less effort arranging terms to plug in. But if you are working by hand, paper and pencil, I don't like it at all. It's just _more_ work, not less.
I now remember a conversation with Dr. Fouts, who's famous for chimpanzee communications (he's well into his 70's now, but probably still at Central Washington University -- I make contributions to his institute there.) We were talking about some of the other approaches taken by other researchers -- the use of plastic chips of various colors or shapes, for example, to facilitate communication between humans and chimps in lieu of using hand-signs. Dr. Fouts was almost livid... angry... in response. He told me that it was cruel to the animals to do that, because, "What happens when they don't have their plastic chips around? How do they communicate?" He added that the chimps get frustrated and even angry when that happens. He felt it was cruel to teach an animal such boons in communication and force them to develop skills with tools they cannot always have around -- their hands.
We don't always have matrix math calculators at hand. But we usually do have paper and pencil, and if not even that we've got our fingers and dirt to play with. The nodal analysis approach won't leave you frustrated from a lack of tools, nor does it force you quite as often towards matrix math and Cramer's. And it "feels" right, too.
I'm still waiting to see the case where mesh results in fewer. hehe.
Read above.
Well, spice is a great tool. When you have it handy. There will be those times when it's not around.
Jon
-- I would have preferred this paper to be either much longer or much shorter, but I did not have the time to do either -- Stroustrup
I don't know if it's all schools or just this one, but the course is really presented as "this is what's happening inside your SPICE program". Not explicitly, but the implication is definitely there.
I make a lot of silly algebraic mistakes of this sort. The reason I get signs wrong in the node method is because you have a lot of situations like this:
V1---r1---V2---r2---V3 | r3 | V4
Let's say we define current flow to be V1->V2, V2->V3 and V2->V4. Well, the very first term of the expression will be (V1-V2)/r1, but because it's entering the node it will be negative, and the obvious step is to rewrite -(V1-V2)/r1 as (V2-V1)/r1. I often make mistakes there.
OMG Cramer's rule... I learned it nearly 20 years ago, and never used it, and was re-exposed to it in this course, but could not apply it with a gun to my head.
I think the difference between his situation and mine is that if I'm reduced to scrawling algebra in the dust, I won't have the physical tools to do anything with the results anyway. I guess after the alien abduction and anal probing, maybe I can impress my captors by doing circuit analysis in the steam on the operating theater windows?
True...ish. Rationally, I really only use this information in the design phase, and since design no longer means Bishop Graphics I'll always have CAD tools available when I need them.
Well, "The SPICE Book" is recommended by Mike Englehardt who is the long time maintainer/programmer/electronics guru of LTSpice... and he's one to know, I think. And right on page 15, an example is worked that uses the nodal approach.
My guess here, if I had to make one, is that mesh analysis, because of how the equations lay out neatly looking like they are matrix-ready at the outset, that a lot of people just assume that is how spice approaches things. They may be wrong about that guess.
But I'm not the expert here. What I do know about spice is that it doesn't only use one tool. It must "linearize" around operating points, move the dots for a tiny dt, re-linearize again around the new operating point, etc. Deep inside, I suspect spice programmers use all the tools they can muster including ways of recognizing when one approach or another is more likely to yield better accuracy per unit time. So maybe spice uses more than one approach. But if only one, then from The SPICE Book I take the idea that they approach it nodally.
I don't even think that way, at all!! Make NO assumptions.
V2 spills away through r1, r2, and r3. V1 spills in through r1. V2 spills in through r2. V4 spills in through r3. That's all there is. No signs, yet. Just perspective. Putting it into a concrete equation is trivial:
V2*(G1+G2+G3) = V1*G1+V4*G3+V3*G2
Done. It reads: "V2 times the sum of the conductances away from it equals V1 times the conductance inward plus V4 times the conductance inward plus V3 times the conductance inward." What's hard? And notice that I didn't start by thinking in any particular direction. On the contrary, I decided that everything flows in ALL directions at once. They flow IN and OUT at the same time so it's not possible to mess up on signs. Well. I think so.
Solving for v2, if you know the rest: V2 = (V1*G1+V4*G3+V3*G2)/(G1+G2+G3)
What's even neater is that this reads nice, as well. "The voltage at V2 is equal to the sum of the surrounding voltages times their conductances divided (which is amps) times the equivalent parallel resistance of those conductances (which is what 1/[G1+G2+G3] is.)"
It's just nice stuff everywhere you look.
Mesh doesn't form beuatiful pictures in your mind. Nodal does.
Hehe. Yeah. I had to refresh my memory, too. It's handy, though, if you don't want the complete solution and just need a selected value or two.
;)
Well, I guess I find myself without a calculator or computer while doing design more often than you. I don't carry laptops, TI-92's, etc., to dinner at a restaurant... but if I'm stuck waiting in the lobby for other guests to arrive first, I can sit there with pen and paper and do stuff without feeling "locked out" by not having my favorite calculator or computer around. Other times, I'm being driven somewhere (might be a few hours' trip) and if I've forgotten (more common these days) or otherwise didn't "bring my tools" with me, I can think and strategize about things and even work out some of the numbers when I want to.
Okay. You think you will always have your plastic chips around when you want them. I can go with that. I guess things have worked out often enough with me that if I depended on them exclusively I'd be frustrated a lot more than I actually am. It's nice to need only your brain and a few marks in the sand, at times.
Okay, yeah. Bad sentence. I meant, "The voltage at V2 is equal to the sum of the surrounding voltages times their conductances (which is amps) times the equivalent parallel resistance of those conductances (which is what 1/[G1+G2+G3] is.)" That _divided_ was my lower functioning brain reading '/' and telling my fingers to do something faster than my higher functioning part could read 1/conductance and see ohms and then tell my fingers to write _times_... Weird thing is, both got their way with me. ;)
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