# resistor network calculation

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#### KamW

##### Advanced Member level 4 I am wondering how could I calculate voltages on resistor network ar maybe better resistor mesh. I have thick film resistor with large area. I am wondering what is the voltage distribution on the surface. I have assumed that there are a lot of nodes on surface, and calculated voltages from Kirchoff law. But even use of mat*lab for simple Kirchoff calculation is rather difficult, because of number of nodes, and number of equations. Does anybody know easier way to solve problem.

Regards
KamW

#### flatulent

##### Advanced Member level 5 relaxation method

Do what you did in making nodes with lumped resistors between. Then guess at the voltages at each node. Then step through the nodes and make them the average of the 4 (3 or 2 in some cases) node voltages around them.

This should take a few lines of codes in a few nested do loops. Continue iterating this do loop until the voltage on a few selected nodes change by less than a value you select each iteration.

Make sure that the nodes with values fixed by the external world (like a voltage source or ground) are not changed during the iterations.

#### KamW

##### Advanced Member level 4 flatulent thx for your response.
Unfortunatelly it was my fault. I haven't ask precision question. Yes your way is very good. I have been using this method before. With this method you could get precision result with teens of iterations. Additionaly if you add averages of nodes around the neighbour nodes you could get precise result in a few iterations.
Btw I have learnt this method as electron field calculation methods. I have forgotten names of this methods. Do you know the names. as I remember it was people names.
But return to my quesion
My problem is that I have to solve that mesh. I have to calculate voltages and current, additionally as for thick film i have RC circuit (exactly RQ) with grains and necks, and I am to calculate total impedance. So I have to find the way how to calculate it.
Especially if there is any way to reduce matrix dimmensions.

regards
KamW

#### flatulent

##### Advanced Member level 5 relaxation

The official name of the method involves the word relaxation. As far as your real problem, you should get a set of equations that when put into the determinant form for solution have mostly zero element values. I think that this is called a sparse matrix and has standard methods (which I am not knowledgable of) of solution.

Is there some way to cut down the problem to a smaller one by having the overall system replaced by a system of identical subsystems? This way you could wrap the mesh around on itself so that the top nodes were identical with the bottom ones and the left ones identical with the right ones and you would have a complete set of equations not dependent on the outside world.

After thinking more about this, could you use the trick that is used in transmission lines and strings of two port networks? You take advantage of the fact that the input impedance of the first block with the others loading it is equal to the others loading it.

You will end up with a function that has half poles. That is, the frequency response will drop at 3 dB per octave. This distributed RC network is used in signal processing.

#### KamW

##### Advanced Member level 4 It would be very comfortable to have identical nodes - like in old question what would be resistance of infinite 1 ohm mesh. I have no convenience to reduce number of identical nodes. I am going to simulate random phase layer. so I am to calculate whole net.
in n by n mesh, using standard kirchoff law I have n2 equations, and about n2 resistors (a little less, but lets say). so using matrixes I have aprox n2 by n2 matrix of resistors, and n2 by 1 matrix of voltages. problem is that every node depends on only 4 different nodes so in large matrix of resistors there is a lot of zeroes. It is hand-book kirchoff law use. I don't exactly remember matrix calculation, but I am wondering if could I generate any matrixes to get n by n voltage matrix, just like array of nodes, and somehow generate proper resistor matrix

According to transmision line. yes I have read some about transmision lines but I have problem with change one dimmensional line to surface problem.
In my oppinion there is no another way that solve whole equations.

regards
KamW

#### flatulent

##### Advanced Member level 5 two options

Are you required to find the solution by hand? Two CAD methods are to draw the network and run a SPICE simulation. The other is to get the set of equations and use a program like matLAB to find the solutions.

I suspect that you could use an ordinary computer program to generate the equations and save them in a file that you run through matLAB or to generate the net list for SPICE.

#### KamW

##### Advanced Member level 4 No of course I am not going to calculate network solution by hand. I am going to use mat*lab. It could make a lot of data. But I am afraid that I will loose control on data. Especialy with voltage matrix (n2 by 1 instead of intuitive n by n) it will be difficult to debug data.
And I think you are right. If there will be no another solution I am to write proper software to generate input data, and to get results .

regards
KamW

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