A/D System Dynamic Range by Larry Cochrane Some basics: Lets start with what dynamic range means. To keep it simple dynamic range of a A/D system is the lowest signal to the highest signal a system can handle. Dynamic range is usually measured in Decibels or db. To calculate db you would use the following formula: nDB = 20 log Eo/Ei where nDB the number of decibels corresponding to the voltage gain or loss, Eo = voltage output and Ei = voltage input. If we take a look at my Amp/Filter card the Eo = +- 10 or 20 volts and the Ei is around 1 millivolt (this is the amount of background noise you get if you short the input). This gives a dynamic range of around 86db Eo = 20 /Ei = .001 = 20000, Log 20000 = 4.3 * 20 = 86db Earthquake Dynamic Range: Earthquakes have huge dynamic ranges from small ones under 1ML to the big ones that the ML scale can't even handle. For each ML there is 10 times more amplitude (~32 times more energy). The difference between a ML of 2 to ML 6 would be the equivalent of a voltage gain of 10000 (10*10*10*10) or 80db. ML 1 to a 7 would be 120db (I think the ML scale bottoms out in the high 7's). Sensor Dynamic Range: This is a hard one. It depends on a lot of things like how well the sensor is made (internal noise), the sensor location, and what type of events you will be receiving. The sensor location has to do with the local ground noise and the micro seismic 6 second background noise. The type of events also depends on your location. If you are "lucky" to live near active faulting you will be seeing the full range of events, from the little ones to the BIG ONES. If you are receiving teleseismic (far) events only you probably will not be seeing large dynamic ranges. On my Lehman the background noise is a round 20 microvolts (using a 6 pole 10 hz low pass filter). As an experiment I connected my o-scope across the pickup coil (a 240vac relay coil) and moved the boom trying to simulate a large local quake and was able to generate about +- 200 millivolts. This would give a dynamic range around 86db. I'm sure it would be higher if I didn't live in a very noise location. Amplifier / Low-pass filter Noise: This would be the electronics that connects between the pickup coil (or other type of sensor) and the A/D converter. This is a little easier to measure. Short out the input and look at the background noise at the output. Then apply a signal to the board and find out how much voltage swing you can get out of it before it saturates. As I calculated above, my board has a dynamic range of about 86db. Any amp/filter board with a very low noise input amplifier should be able to get this type of dynamic range. My board uses a LT1007 with a noise figure of 60 nanavolts p-p between .1 and 10hz. The Analog To Digital Converter: Like the Amp/Filter electronics it is easy to calculate the dynamic range of a converter based on the number of bits. To calculate the dynamic range of a A/D convert you would use the following formula: Total Counts / background noise counts = Counts, then Log counts * 20 # of bits Total counts Dynamic Range Voltage resolution (note 1) -------------------------------------------------------------------------- 8 256 48db 39.0 millivolts 10 1024 60db 9.76 " 12 4096 72db 2.44 " 14 16384 84db 610.3 microvolts 16 65536 96db 152.6 " 20 1048576 120db 9.5 " Notes: 1) Based on a +- 5 volt (10 volt) maximum input for full output count. 2) Background noise count for 8 to 12 bits usually would be 1. On higher bit counts chips the background noise of the A/D chip should be considered. Over All System Dynamic Range: Just like a chain is no better then the weakest link, the same can be said for any A/D system. If you have a sensor that only as, lets say 60db of dynamic range, and the amplifier and A/D converter has 80db range then the overall dynamic range will be set by the sensor or 60 db, you will be losing 20db. If the sensor and the amp have a 86 db range and the A/D converter only has 48db (8 bit system) range then overall system dynamic range will be set by the A/D converter or 48db. You will be losing 36db of dynamic range. What all this means: What all this boils down to is how well your system will pick up events. If you have a system with low dynamic range, your system will saturate very quickly with even a moderate local event, if you have the gain turned up to pick up teleseismic. If you have the gain set lower so the moderate events don't saturate, you will be missing the teleseismic events. With higher dynamic range systems you will be able to pick up both type of events with out any problems. Larry Cochrane Redwood City, Ca USA PSN