---------- Forwarded message ---------- Date: Fri, 30 Jun 2000 01:45:31 +0300 (IDT) From: "Peter L. Peres" To: pic microcontroller discussion list Subject: Re: [EE]: Relay question...the continuing saga Hi Bob, wrt your doubts: I did the calculation on paper for 2 x 2 and 3 x 3 matrices. In the morning, not now ;-). The trick to solve the mes(s|h) is to observe that the lowest resistance point appears when you measure between the centermost line and column. From this start adding rows and columns outwards. >Each time we add a new row and column we create at least one new 3*Rrelay >sneak path. Yes. For a 3 x 3 matrix you have 1/R and 2/(2R) + 1/(4R) in parallel. For 4 x 4 you have an asymmetrical matrix that is harder. 5 x 5 is again "easy" etc. In general the matrix simplifies to a sum of fractions of R in parallel with 1R for N%2 and the (N+1)%2 case should be harder to express. When N%2 then a great deal of shorts can be made in the equivalent schematic and the fraction sum simplifies neatly. The equivalent maximum I for some matrix sizes is: 2 x 2: I = 1.(3) x I0: 1.098: 0.235: 0.176 3 x 3: I = 1.8 x I0: 1.609: 0.191: 0.106 4 x 4: i ~= 2.285 x I0: 2.484: -0.199: 0.087 5 x 5: I ~= 2.777 x I0: 2.995: -0.218: 0.078 6 x 6: I ~= 3.272 x I0: 3.401: -0.129: 0.039 7 x 7: I ~= 3.769 x I0: 3.737: 0.032: 0.008 8 x 8: I ~= 4.2(6) x I0: 4.025: 0.241: 0.056 The fourth column is the result of ln((N-1)*N) and the fifth the error it gives in approximating the calculated Imax/I0. The sixth is the same error normalized. I don't think that ln((N-1)*N) is the limit but it seems to approximate to within 20% for common (small) matrix size values ?. (the numbers in column 2 were calculated right now using circuit simulation - use numbers at your own risk) I cannot see where this is going. Maybe someone else can ? BTW I seem to remember that some core memory addressing scheme I saw in an old book worked on similar principles ?! But I am not sure of this. I got the idea back then from a typical problem of the kind teachers give to students so as to torture them, with resistors, not relays ;-) So I did remember somewhat correctly that my 5 x 4 matrix drew about 2 x I0 ;-). One can still drive a 6x6 matrix of 8 mA relays with a PIC64 I think. Peter http://www.piclist.com hint: The list server can filter out subtopics (like ads or off topics) for you. See http://www.piclist.com/#topics