Mastering Mesh and Nodal Analysis with KVL for Complex Circuits

[M P]

I bet you smiling now ;)

 

[gneill]

Check the sign of the term.

 

[M P]

View attachment 76995

Check the sign of the term.

before I go further -55.74 - 20.06j + 0.25 V40 - 0.05 j V40 ?

 

[gneill]

before I go further -55.74 - 20.06j + 0.25 V40 - 0.05 j V40 ?

I'm not seeing where that's coming from. Sorry.

Did you make a V30 substitution? Really you should eliminate V40 instead, since you need V30 to find the current through Z4.

 

[M P]

thank you I will do as suggested and see how it goes..

 

[M P]

thank you for all your help

 

[Ebies]

can you please confirm if I have conducted my kvl loops correctly as per diagram on post #9

V1 - I1Z1 - Z4(I1-I2) = 0...Eq 1

-V3 - Z5(I2-I3) - Z4(I2-I1) = 0...Eq 2

I3Z3 - V2 - Z5(I3-I2) = 0...Eq 3

 

[gneill]

It all looks fine except for the sign of the Z3 term in the third equation. I3 causes a potential drop in Z3.

 

[Ebies]

thnx gneill

 

[Ebies]

I3(-Z3) - V2 - Z5(I3-I2) = 0...Eq 3 new and revised eq 3

 

[gneill]

I3(-Z3) - V2 - Z5(I3-I2) = 0...Eq 3 new and revised eq 3

That'll work. Or,

-I3*Z3 - V2 - Z5(I3-I2) = 0

 

[Ebies]

when using mesh analysis to determine the voltage drop direction, do you use conventional current flow or do you use the clockwise current you chosen at the beginning when assigned your clockwise mesh currents...? I am asking so I know when to add or subtract when doing the "KVL" walk... I am a bit confused about what the sign needs to be when walking the "KVL" loop and you encounter components... spent a lot of time going through my books and watching online tutorials and its confused me even more now

 

[gneill]

when using mesh analysis to determine the voltage drop direction, do you use conventional current flow or do you use the clockwise current you chosen at the beginning when assigned your clockwise mesh currents...? I am asking so I know when to add or subtract when doing the "KVL" walk... I am a bit confused about what the sign needs to be when walking the "KVL" loop and you encounter components... spent a lot of time going through my books and watching online tutorials and its confused me even more now

While you can use either direction to achieve valid equations, you must be consistent in your choice. Once you've made a selection of current direction for a mesh you must not change it, otherwise where loops "touch" the current sums through the shared components will be compromised.

This is why it's common practice to simply choose all the mesh current directions to be one direction (say, clockwise), so that you can get in the habit of doing things the same way every time. It helps to avoid mistakes if you don't have to think about how the current directions interact at the mesh boundaries. It also makes it possible to write the mesh equations directly by inspection in the form of a matrix equation. Then there's practically no thinking involved at all, just apply the trivial algorithm! I'm sure you'll come across this method shortly.

That said, sometimes a particular problem may make it advantageous to choose a particular direction for a given loop (say if you are to find a current that's given a defined direction through some wire or component). Then you need to apply the mental effort to keep the current directions consistent and worry about their directions at the mesh boundaries.

 

[Ebies]

Thanks gneill yet gain for the response, I comprehend the mesh current concept now, what I do not understand however is: you know between the individual terms for a single equation: how do you decide if it's a "+" or "-" term? I watched a lecture last night which said it is always "+" for example: IL1Z1 "+" Z4(IL1-IL2) "+" V = 0. Yet what the gentleman said in the lecture can not be true as it will change the result of the equation no? in our books it states the following: "In writing the mesh equations, imagine you are walking around the mesh in the direction of the current loop. Then use the convention that all voltages pointing in the direction you are walking are positive and those pointing in the opposite direction are negative", now reading that it does not really explain how you decide on the sign of any single term within the equation as it does not tell me how to consider the direction of voltage drop (whether it will be gain or a drop). This is really my only sticking point with mesh analysis and any help or guidance will be greatly appreciated...

 

[gneill]

The way I look at it is that the mesh current is causing potential drops across resistances as it flows through them. If you "walk the loop" in the direction of the mesh current, then each passage through a resistor is a drop (negative term) for that current. Naturally, voltage sources always produce a potential change according to their fixed potential as you "walk" through them.

You can, if you wish, write down drops as positive terms instead. Mathematically this is equivalent to multiplying the entire equation by -1. An equation remains valid if you multiply both sides by the same value. It's pretty easy to write the terms down in this fashion, the only tricky bit being to remember that a voltage rise caused by a source should be written as a negative term, and vice versa (because a "drop" is positive and a "rise" is negative in this paradigm). You also need to remember to treat the signs of the potential changes due to the boundary currents accordingly.

Personally, when I write a mesh equation manually I write drops as negative terms. Thus I don't have to do any mental gymnastics when it comes to walking through sources or dealing with boundary currents. Once I've recorded the equation I can always multiply through by -1 to pretty it up.

 

[Ebies]

Thank you very much for the speedy reply Sir, you are a star and your help and guidance are greatly appreciated!