Poor Man's Resistor Problem - Page 1
Forum section: electronics / general

author: zhtoor
author_rank: Frequent Contributor
timestamp: July 06, 2017, 09:47:01 pm
content: Hello everybody,here is an interesting problem to solve for a poor man (that's me) :-the poor man has only limited number of resistor values say R1, R2, R3 and R4,the resistors are specified for t-ppm tolerance and c-ppm TCR.now the poor man posits the following problem:-given an arbitrary network with n-nodes, and an NxN matrix whereas each element of thematrix is 0, inf, R1, R2, R3 or R4. where 0 being a short circuit, inf being an open circuit.q1: what would be the resistance between node i and node j (i, j selected from 1..n, i<>j) ?q2: what would be the expected tolerance of this value Rij ?q3: what would be the expected tcr of this composite resistance between i, j; ie Rij ?q4: say Rij and Rjk are resistances from i to j and from j to k respectively, what would be the expected ratio accuracy of Rij , Rjk ?q5: what would be the temperature coefficient of this tracking ratio ?once this problem is solved, here are the next level of questions:-nq1: given R0, the target resistance value, and N, the number of nodes, what combination produces a value Rij closest to R0 ?nq2: the network so obtained above to be minimized wrt. to number of resistors, wrt. to expected TCR ?nq3: given a ratio K, and N, the number of nodes, what i,j,k produce the ratio Rij / Rjk as close to K as possible ?nq4: the network so obtained above to be minimized wrt. to number of resistors, wrt to expected TCR tracking of the ratio Rij / Rjk ?regards and comments from learned members of this forum required.

author: ahbushnell
author_rank: Frequent Contributor
timestamp: July 06, 2017, 11:44:33 pm
content: how do the resistors connect together?

author: zhtoor
author_rank: Frequent Contributor
timestamp: July 06, 2017, 11:51:35 pm
content: Quote from: ahbushnell on July 06, 2017, 11:44:33 pmhello, there are 25 nodes in the 4 cols by 4 rows shown, the resistors (or shorts, or open ccts) are connected between these *nodes*.regards.

author: ManateeMafia
author_rank: Frequent Contributor
timestamp: July 07, 2017, 12:42:57 am
content: This probably isn't helpful but your problem reminds me of this paper.http://www.isotechna.com/v/vspfiles/pdf_articles/Method_for_Calibrating_Resistance_Thermometry_Bridges.pdf

author: zhtoor
author_rank: Frequent Contributor
timestamp: July 07, 2017, 12:47:59 am
content: Quote from: ManateeMafia on July 07, 2017, 12:42:57 amthank you sir.interesting... looks like the poor man needs input from new zealandregards.

author: ahbushnell
author_rank: Frequent Contributor
timestamp: July 07, 2017, 01:46:44 am
content: Quote from: ManateeMafia on July 07, 2017, 12:42:57 amSo it looks like this. Because of symmetry there are only six problems to solve. They are in red.

author: alm
author_rank: Super Contributor
timestamp: July 07, 2017, 02:38:07 am
content: That is assuming all resistors have the same value. That would basically be a freshman circuit analysis problem. The way I read the start post, each one of them can be 0, inf, R1, R2, R3 or R4. Otherwise the grid with all open circuit or all 0 Ohm would be very easy to solve. This makes the problem more annoying to solve. Just brute force.