Choosing a correct resistor
From MariachiWiki
A coincidence box provides everything what is needed to run a set of detectors including a power supply. Because different detectors require slightly different voltages to operate the box provide a place to put resistors to adjust the voltages. Here the procedure is described how to choose correct values for these resistors. You are assumed to know what voltage you want for a particular detector (e.g. that can be learned by plotting an efficiency curve).
First is where to put resistors. The photo will help you to understand that.
Step 1
This step can be skipped if you already have some resistors in the box but don't take them out yet.
The resistors we are talking about are electrically connected sequentially with a DC-DC converter of a detector (the DC-DC converter is an electronic chip which converts low voltage on its input to high voltage on its output which is needed to operate a photomultiplier tube).
This chain is then connected to a 7V power supply inside the box. See schematics in the picture. The input of the DC-DC converter can be well approximated by a constant R0=100 Ohm resistor. That's all the information that we need to guess what should be a value r0 of the resistor.
If the desired voltage on input to a DC-DC converter is Vd:
r0=R0/Vd*(7-Vd) (1).
E.g. if you want 5.8V you would put r0=100/5.8*(7-5.8)=20.7 Ohm.
Step 2
You install this resistor (see the photo above), measure the real voltage V with a multimeter and might find out that it's different from what you wanted (the voltage can be measured between a ground screw and a screw holding the correspondig red wire, see the photo as well). This happened because the real value R of the resistance on the DC-DC input is different from the assumed 100 Ohm. Now it can be found from the voltage measurement and calculation: the current through the chain is I=(7-V)/r0 (Ohm law applied to the resistor r0), hence R=V/I=r0*V/(7-V). E.g. you measured V=5.9V. That means that real value of R was 20.7*5.9/(7-5.9)=111 Ohm. Now the next approximation for the resistor can be make using formula (1) again: r1=111/5.8*(7-5.8)=23 Ohm. Calculation of R is not necessary. You can combine everything in one formular for the corrected value of the resistor:
r1=R/Vd*(7-Vd)=r0*V/Vd*(7-Vd)/(7-V) (2).
In our example r1=20.7*5.9/5.8*(7-5.8)/(7-5.9)=23 Ohm again.
A few advices
- don't forget to turn off a coincidence box when you work on connectors/resistors!
- if power cables are already connected to a coincidence box it's important to check what connectors correspond to what detectors. Usually we enumerate connectors starting from the back wall of the box (from top to bottom in the photo) so that the first connector (screw) corresponds to the detector #1, the second one to detector #2 and etc. But it always worth cheking! It can be done either by tracking wires (outside the box they should be labeled) or by running an acquisition program and disconnecting power wires one by one in the box noticing what detector stops counting.
- if you alredy have some resistors in your coincidence box you can follow the following step by step procedure for each detector:
- Connect a detector and measure the voltage with the currend resistor (see the photo above on measuring voltage). It will be V for the formula (2).
- Remove the resistor and measure it. You'll get r0 for the formula (2).
- Vd in the formula (2) is the desired voltage you know from the calibration.
- Calculate r1 and put this value resistor back in the box. If your resistor is a bit different from the exact calculated value you can find what voltage you should expect using my excel calculator.
- Check the voltage. According to my experience it should match the expected one within 0.1V.
- Any resistors with 0.1watt or bigger power handling capacity can be used (they don't have to be as fat as in the picture ;)
Links:
- Resistor Color Codes
- Resistor Calculator. An Excel, hopefully selfexplanatory, file to perform the above calculation.
