Resistance and Capacitance Measurement of the Long Wires in Lab 8 ------------------------------------------ Original Rev. 6-APR-2006 Current Rev. 11-APR-2006 This note is a report on the resistance and capacitance measurements of the stainless steel wire that is used in the long wire test setup in Lab 8. The resistance measurements were actually made at MSU on samples of this wire which were obtained from Fermilab. The capacitance measurements were made on the long wire test setup at Lab 8. Resistance Measurements ----------------------- A sample of the Fort Wayne Metals 4 mil 304V stainless steel wire was obtained from Fermilab. This sample was about 10 meters long and was brought back to MSU for resistance measurement. A careful set of 4 lead resistance measurements was made on March 31 and April 1. The sample being measured was about 2 meters long. It was loosely wound on a threaded cpvc spool and measurements were made at room temperature and at LN2 temperature. The results are: at room temperature 123.8 Ohms/meter at LN2 temperature 110.5 Ohms/meter Notes: - I cycled between room temp and LN2 temp 3 times looking for hysteresis or a permanent shift in the resistance at either temperature. At the 0.05% level I do not see any effects of that type. - The Ohms/meter number above for LN2 temperature does not take into consideration the change in length of the wire going from room temp to LN2 temp. I.E. I measured the resistance of the same physical piece of wire at both temperatures but only measured its length at room temp. - The accuracy of the above numbers is limited by my ability to measure the length of the wire between the potential leads. The sample is over 2 meters long and I estimate that I can measure its length to 2mm. - I verified that the sample was not under tension stress in the sample holder when it was at LN2 temp. - A previous note said that this 4 mil Fermi wire is actually 3.85 mil. I have not checked the diameter of this sample at that level of accuracy. - This measurement was made with the Fluke 8505A meter which was checked with the General Radio and Leads and Northrup standard resistors at: 10 Ohm, 100 Ohm, and 1000 Ohm. - The room temperature was between 22 and 23 C. These measured values are considerably higher than what was expected. On their web site the supplier of the wire, Fort Wayne Metals, gives the bulk resistivity of the wire as: 720 uOhm-mm. See: www.fwmetals.com/resources_specsheets/304v.pdf For the specified 4 mil diameter of the wire (0.0508 mm radius) the bulk resistivity value from Fort Wayne Metals implies that we should have expected a resistance per meter of 88.8 Ohms/meter. As shown above we measured 123.8 Ohms/meter Part of this difference may be due to the "4 mil" wire only measuring 3.85 mil diameter as reported by Doug. A 3.85 mil diameter wire with the bulk resistivity given by Fort Wayne Metals would have a resistance of 95.8 Ohms/meter but that still does not match what we measured. In the information on their web site, Fort Wayne Metals talks about using a stress relieving heat treatment on their 304V wire. "Thermal Treatment In wire form, 304V will gain tensile strength when stress relieved at 350-427 C. A reducing atmosphere is preferred but inert gas can be used. 304V will fully anneal at 1010-1121 C in just a few minutes. There is a carbide precipitation phenomenon that occurs between 427 and 899 C that reduces the corrosion resistance of the alloy. American Society for Testing Materials has described a test method to ensure the alloy has not been damaged." On 7-April-06 I measured the resistance of a 235 cm sample and then passed it to Reza Loleoo who will heat treat it in one of the sample preparation furnaces. He will cook it for 24 hours at 400 C +-20C in an inert atmosphere or a good vacuum. This sample measured 124.1 Ohms/meter before the heat treatment. Capacitance Measurements ------------------------ On 4-April-06 I measured the capacitance of long wires in the test setup in Lab 8. I used the MSU Philips PM6303A LRC meter for these measurements. The Lab 8 long wire setup is a 4x10 array of wires (10 wires in each horizontal row) with a 1x10 array under it for High Voltage tests. There is a shielding tent over the array. The wires in the array are spaced 5mm between rows and 5mm between columns. The 1x10 HV test array is 20mm below the 4x10 signal wire array. The aluminium foil shielding tent is about 2" above and 2" to the sides of the wire array. The wires are about 17.5 to 18 meters long (estimated). My intent is to use the upper 3 horizontal rows in the 4x10 array to model the two induction planes and one collector planes in the LArTPC. For this measurement I have labeled the wires in the following way. This diagram is looking at the connector side of the ceramic precision spacer at the North end of the wires. A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 Two things were initially noticed: The lead to lead capacitance in the ribbon cables that run into the North end wire termination is significant compared with the wire to wire capacitance - and thus it will need to be accounted for. There are broken solder connections (or connections that were never properly soldered) on the "C" row of the North end cable termination. In a good 3 plane model of the LArTPC I would like to measure both wire to wire capacitance and a given wire to everything else capacitance. Because of the broken "C" plane solder connections, on this trip, I will not be able to measure capacitances in a fully realistic model of the LArTPC. The "C" plane wires are not electrically connected at this time. In the values reported below I have separately measured and then subtracted the lead to lead capacitance of the ribbon cable. These values are just the wire to wire capacitance in the wire array. A typical value of the capacitance between adjacent leads in the ribbon cable was 20.3 pFd. Wire to Wire in the "A" Plane A1 to A2 53.4 pFd A6 to A7 54.3 pFd A2 to A3 53.8 A7 to A8 54.6 A3 to A4 54.0 A8 to A9 54.9 A4 to A5 54.2 A9 to A10 54.7 A5 to A6 54.5 A1 to A3 33.1 pFd A2 to A4 33.6 pFd A1 to A4 23.9 A2 to A5 24.4 A1 to A5 18.3 A3 to A5 33.8 Wire to Wire in the "B" Plane B1 to B2 56.2 pFd B6 to B7 57.9 pFd B2 to B3 57.1 B7 to B8 58.1 B3 to B4 57.5 B8 to B9 58.0 B4 to B5 57.7 B9 to B10 57.9 B5 to B6 57.9 B1 to B3 36.0 pFd B2 to B4 36.9 pFd B1 to B4 27.0 B2 to B5 27.8 B1 to B5 21.7 B3 to B5 37.1 From the "A" Plane, the more isolated plane of the two that could be measured, the average wire to wire capacitance is 54.27 pFd or assuming 18 meter long wire 3.01 pFd per meter. From the "standard" formula for capacitance between two long parallel wires where: D is the distance between the centers of the two wires, and d is the diameters of the two wires, and d/D is small then the approximation is: 12.064 C = ---------- pFd per meter for 4 mil diameter wires 2D spaced 5mm this gives Log ---- 6.05 pFd per meter d Why is my measured value of wire to wire capacitance only 1/2 of the expected value ?? Forge ahead and for the "A" plane measure the capacitance between a given wire in the "A" plane to all the other wires in the "A" and "B" planes. All of the other wires in the "A" and "B" planes is called the "Bus". Once again, in the values reported below, to remove the effect of the capacitance of the ribbon cable, I have separately measured the ribbon cable by itself and then subtracted it contribution. Wire in the "A" Plane to all other "A" and "B" Plane Wires A1 to Bus 124.9 pFd A6 to Bus 170.0 pFd A2 to Bus 158.2 A7 to Bus 171.9 A3 to Bus 166.0 A8 to Bus 166.7 A4 to Bus 168.8 A9 to Bus 160.7 A5 to Bus 170.2 A10 to Bus 129.5