EEVblog Electronics Community Forum
EEVblog => EEVblog Specific => Topic started by: EEVblog on November 19, 2015, 09:18:29 pm

Dave explains the fundamental DC circuit theorems of Mesh Analysis, Nodal Analysis, and the Superposition Theorem, and how they can be used to analyse circuits using Kirchhoff's Voltage and Current Laws we learned in the previous video here:
https://www.youtube.com/watch?v=WBfAEeEzDlg (https://www.youtube.com/watch?v=WBfAEeEzDlg)
The same circuit is solved using the 3 different methods. Will we get the same answer from each technique?
https://www.youtube.com/watch?v=8f2yXiYmRI (https://www.youtube.com/watch?v=8f2yXiYmRI)

Mesh for life. When we were learning this stuff, I almost failed my first test on Nodal(did not get the correct calc until 2 wks after class started, had to speed learn that). Then I ended up loving how it all worked when I figured it out, simultaneous equations FTW.

Nice! These videos will be very good materials for the freshmans at Universities (or high schools). (And funny to remeber my struggles)
One thing i don't understand: Why pepole like to use decimal fractions. At the nodal expressions, you can multiply the whole expression with 30, and the calculations will not contain any rounding error. Maybe it's just the matter of taste..

One thing i don't understand: Why pepole like to use decimal fractions. At the nodal expressions, you can multiply the whole expression with 30, and the calculations will not contain any rounding error.
For me it's one of nonfamiliarity.
4/30 th's doesn't instantly convey the same useful information that 0.133 does.
Same reason I prefer digital watches to analog, the digital watch gives me the time in exactly the format I think about it in.

In the first part (KCL method) it would be worth mentioning that I3 resolves to having a negative sign, which means I3 flowing *into* the node, and that would demonstrate the sum of the currents is indeed balanced.
PS: this video on the subject from MIT is also great:
http://ocw.mit.edu/courses/electricalengineeringandcomputerscience/6002circuitsandelectronicsspring2007/videolectures/lecture2/ (http://ocw.mit.edu/courses/electricalengineeringandcomputerscience/6002circuitsandelectronicsspring2007/videolectures/lecture2/)

One thing i don't understand: Why pepole like to use decimal fractions.
Interesting, I immediately thought "ah, here is an American who uses fractional measurements instead of metric", but if your flag is correct, nope.
I'd always assumed that people who prefer fractions do so because they are all the time dealing in "1/64th of an inch" etc. Guess I assumed wrong.
I can never remember how to solve equations fractionally, always prefer to just convert to decimal, even if it is an approximation.

Great Dave!
You explain it brilliant.
However in the nodal analysis there is an error. Va/30 should be 0.0333 not 0.333.
But you got the sum right. 0.1+0.05+0.333=0.1833. Thats advanced math ;D
Keep it up!

He did mentioned the error on the video later on.
Also when he was talking he did say 0.0333 even if on the board it was written wrong.
(edit, he says it at 11:10 time mark) and the correction after he is done explaining it at 13:50

This is a good start, but it does feel a little incomplete without mention of supernodes and supermeshes.

Sorry!
My bad. Shouldn't fast forward when the king is explaining :[
/Roger

For me it's one of nonfamiliarity.
4/30 th's doesn't instantly convey the same useful information that 0.133 does.
Same reason I prefer digital watches to analog, the digital watch gives me the time in exactly the format I think about it in.
I see. In our (at Hungary) education system, the way with the fractions is more preferred in all theoretical subject (even in high and grade school. But yeah, in the real world, you make way more bigger assumptions and simplifications.
We learn these methods in a subject, called "Signals and Systems". For me, it was very deep water at the first time. This is a typical homework: http://prntscr.com/94w25e (http://prntscr.com/94w25e)
How about another Universities? You have to do this kind of networks, or even worse?
Interesting, I immediately thought "ah, here is an American who uses fractional measurements instead of metric", but if your flag is correct, nope.
I'd always assumed that people who prefer fractions do so because they are all the time dealing in "1/64th of an inch" etc. Guess I assumed wrong.
I can never remember how to solve equations fractionally, always prefer to just convert to decimal, even if it is an approximation.
My flag is totally correct! ;)

I Would very much have liked to have Dave as a Teacher when we learned this stuff.
Out teacher at the time made us....sleep. Total opposite of Dave :+

One thing i don't understand: Why pepole like to use decimal fractions. At the nodal expressions, you can multiply the whole expression with 30, and the calculations will not contain any rounding error. Maybe it's just the matter of taste..
Well, I prefer decimal fractions because they are more familiar to me and I instantly know that 0.698 is smaller than 0.763 compared to 4211/6029 vs 6011/7877. Also, addition or subtraction is much easier (to me). I once got scolded by a math teacher because I converted all probability results into percents. My reasoning was (and still is) that it is easier to understand. So I was happy when I could use decimal fractions in university (for subjects other than math).
Also, decimal fractions can be calculated faster with a simple calculator.

Mesh for life. When we were learning this stuff, I almost failed my first test on Nodal(did not get the correct calc until 2 wks after class started, had to speed learn that). Then I ended up loving how it all worked when I figured it out, simultaneous equations FTW.
Ha! I'm the same. Obviously, the two approaches are equivalent, but unless there's something about the specific circuit that makes nodal the obvious "easy" approach, I go mesh every time.
I don't know why. I just like it better.

The fractions are beneficial when calculating circuit topologies in closed form, and which can be then reduced to a simpler form. With the decimals the simplification and reduction may not be obvious and using the decimals may prevent the deeper understanding of the circuit.

Well done Dave! Awesome episodes! :+ :+ :+ More like this please! And don't keep apologising for the maths when its a "Fundamentals" Friday. ;) Just lay it on the line.
Followups are definitely warranted with examples of more complicated practical circuits with nonresistive components (e.g., diodes, transistors, opamps). Perhaps you could choose something from the forums: a circuit that someone here is having trouble making sense of.
And then if you could incorporate AC, complex impedance, caps and inductors, you'd have much of first 2 years of uni level electronics eng covered. Just a thought... I realise that such an undertaking would involve a lot of work. But if anyone could do it you could. I'd donate a few $s to help make it happen.
PS. As a show of support I've already sent you a small donation for these videos. There needs to be more educational content like this, widely available and explained by someone who is a good communicator, well respected, and knows what they're talking about. You fit the bill, Dave.

At 15:57, "You can't have a mesh within a mesh..." can be modified somewhat to allow for cases where the first mesh is encompassed by the third (undrawn) mesh. The key is that they need to be independent. Of course, this is most easily done by staying away from using surrounding meshes when the circuit gets complex. Otherwise you will get answers like 1 = 1 or I_{1} = I_{1}.
Let's call the outside mesh current I_{3}.
Algrebra for each mesh:
Mesh 1: E_{1}  R_{1}I_{1}  R_{2}I_{3}  R_{1}I_{2} = 0
Mesh 3: E_{1}  R_{1}I_{1}  R_{1}I_{3}  R_{3}I_{3}  E_{2} = 0
Substituting values:
Mesh 1: 1  10I_{1}  10I_{3}  20I_{1} = 0
Mesh 3: 1  10I_{1}  10I_{3}  30I_{3}  10 = 0
Collecting like terms:
Mesh 1: 1  30I_{1}  10I_{3} = 0
Mesh 3: 9  10I_{1}  40I_{3} = 0
Solving for I_{3} (because we are interested in I_{1}):
Mesh 1: I_{3} = (1  30I_{1}) / 10
Mesh 3: I_{3} = (9  10I_{1}) / 40
Combine the partial solutions:
(1  30I_{1}) / 10 = (9  10I_{1}) / 40
Solving for I_{1}:
4  120I_{1} = 9 10I_{1}
Combine like terms:
110I_{1} = 13
Or:
I_{1} = 13 / 110 = 0.11818...
It's like magic!