Peak Envelope Voltage (PEV) Servo
Build a Geomagnetic Observatory ! GELLER Labs "Backyard Science"
Thoughts on a proton precession magnetometer design - a Proton Magnetometer Project. Build an Earth's field magnetometer.
The FDM MAGNETOMETER1 project is a low cost high performance proton magnetometer (a digital magnetometer) kit under development for universities and amateur scientists to be able to accurately measure and monitor changes in the Earth's total magnetic F field and to observe geomagnetic storms. Magnetic storms can cause large excursions in the field and are of concern to interests ranging from electrical power grids, radio communications, and satellite operations, to aurora watchers and amateur radio operators.
1 Filter Diagonalization Method "FDM" (harmonic inversion), see Jan 21 and Jan 23 entries, based on: Vladimir A. Mandelshtam, Howard S. Taylor, Harmonic inversion of time signals and its applications, Journal of Chemical Physics (1997), Volume 107, Issue 17, 1997, Pages 6756-6769
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Project Documentation, Links and References (very early stages)
Journal Notes:
G1 magnetic storm, global KP6 in the rear-view mirror: NOAA 7 day Costello Index PDF, NOAA K index PDF.
Monday, March 14, 2011
Overnight: PDF, TXT, return to geomagnetic quiet NOAA K index PDF. Looks like a return now to the relatively normal diurnal cycle following the events of last week PDF.
As we have discussed on numerous occasions, the free induction decay (FID) precession waveform peak envelope voltage varies over time, presumably because of the strong dependence of tau 1 on outdoor temperature (at the sensor stand). I am thinking there might be some advantage to stabilizing the FID peak amplitude with time and temperature, at a level compatable with the working ADC input range. There are many ways to change the peak amplitude, such as for example, changing the NBLNA gain, the polarization current, or the polarization time. Polarization time can be adjusted cycle to cycle by a program variable. Also, since we are operating relatively low on the polarization curve (well under five tau), there is plenty of adjustment range in polarization time which directly affects peak envelope amplitude. I am thinking that polarization time is the variable to use as the "plant" for a negative feedback loop. This relatively simple digital signal processing (DSP) can probably be easily done within the LabView program. Perhaps the feedback variable can be a running N point average of the most recent N peak values. More later.
Tuesday, March 15, 2011 Precession Waveform Peak Envelope Voltage Servo
Overnight: PDF, TXT The geomagnetic field was very quiet overnight.
I set up an amplitude servo as described above (3/14/11). This automatic gain control (AGC) functions by varying the polarization time as opposed to gain in a conventional AGC implementation. The polarization time works as a variable because our polarization time is about twice tau 1 of the working fluid. That is, were we to polarize for a longer time, up to say, about five time constants, the amplitude of the precession waveform envelope would increase (albeit more slowly after several time constants). After seven hours of operation, the loop is working very well. PDF The red curve represents polarization time in seconds. The blue curve is the peak voltage measurement of the precession waveform envelope. As can be seen by the two curves, as the amplitude began to fall, the polarization time was automatically increased to compensate and to hold the peak envelope amplitude at about 2.0 V. The AGC loop is currently using a 5 point moving average of the peak envelope amplitude measurement. The loop is disabled until enough points have been acquired (here 5) to generate the first valid moving average value (i.e. "priming" the digital filter). The blue curve represents actual shot-to-shot measurement values and is not averaged over more than one measurement cycle.
If nothing else, a properly set AGC loop will be convenient for running the instrument over a wide range of temperatures without needing to update the NBLNA gain setting. It might lead to improved results by keeping the amplitude high enough to make best use of a given number of digitizer bits. For a later study, it is presumed that the red curve follows the temperature of the working fluid in the powered coil of the counter-wound coil sensor pair. Note that the sensors are covered by a heavy plastic bag, in a sensor container, and the fluid is inside the PVC coil form of the powered coil. So, the temperature of the working NMR fluid, particularly with increasingly strong solar radiation as we go into the spring season, is probably somewhat different than the outside air temperature. Later (~8pm), the amplitude servo loop continues to work well PDF. As the outside air temperature drops below 38 F, the polarization time is moving towards shorter times to maintain the 2 V peak envelope amplitude, now down to ~1.8 seconds from this afternoon, when it was as long as almost 2.4 seconds. PDF
If we go with the precession waveform envelope amplitude servo, an automatic gain control (AGC), there will need to be a switch to turn it off and allow for manual polarization times for experiments, such as measuring the tau 1 of a working NMR fluid. See our notes on using a FDM proton precession magnetometer to measure tau 1 of a NMR fluid.
Wednesday, March 16, 2011
Overnight: PDF, TXT The geomagnetic field was very quiet overnight. The peak envelope voltage servo ran well overnight PDF. The red curve is the polarization time and the blue curve the measurements of peak envelope voltage. Both curves are plotted against number of data points, presently about 2 minutes per measurement. The servo loop is presently configured to hold a 2 V peak envelope voltage by automatically varying the polarization time. There is no direct connection to the measurement of the magnetic field, other than perhaps some increased accuracy at the highest resolution (probably due to a more optimal use of the ADC dynamic range).
Afternoon: After 820 plotted two minute measurements (with a 97% success rate for a 2e-5 amplitude threshold), the statistical mode (most common value) for the figure of merit (FOM) is a very respectable 1e-7 (~5 pT). The average FOM is 2e-6 (~107 pT). The peak envelope voltage servo continues to run without problems PDF (red curve polarization time in seconds, blue curve peak envelope voltage). Recall that the peak envelope value comes directly from the precession waveform filtered envelope calculation, a calculation entirely independent of the FDM routine. Here are the corresponding FDM figure of merit (FOM) PDF and FDM amplitude PDF plots. Keep in mind that all of this very recent work represents fine tuning "around the edges" and is believed to have little affect on the most important plot of the F scalar with time.
Thursday, March 17, 2011
Overnight: PDF, TXT The geomagnetic field was quiet overnight. The peak envelope voltage servo continued to run well PDF.
Friday, March 18, 2011 - The new PEV Servo sheds light on how to set the NBLNA gain!
Overnight: PDF, TXT The geomagnetic field was quiet overnight. The peak envelope voltage servo continued to run well PDF. There were some larger excursions that past days. There have been large and relatively fast temperature variations compared to the 5 point moving average. The 5 point moving average takes about 10 minutes at the slow (normal) measurement cycle of about 2 minutes per cycle.
With a rare day of spring like temperatures, the peak envelope voltage servo called for polarization times near 3 seconds to maintain the desired 2 V peak envelope voltage. This decrease with longer times (riding out to several tau on the polarization curve) causes an effective drop in servo loop gain. Today's performance curves PDF show that the tracking (holding the desired 2 V peak envelope value (blue curve) with automatic changes in polarization time (red curve) became sloppier with longer polarization times. Long term readers of our journal will recall that after many minor improvements of past months, we reduced the gain of the NBLNA to celebrate larger precession signals (larger peak envelop voltages). So what is a good NBLNA gain? Well, I think the peak envelope servo is starting to answer that question. The NBLNA gain should be set so that for a given working fluid, at the most undesirable ambient temperatures with regard to tau 1, the servo does not call for about more than 2 to 2.5 tau 1 at that working temperature. As described above, this ensures adequate dynamic range and loop gain with good tracking of the desired peak envelope voltage. So, as we approach summer it is time for us to turn our NBLNA gain back up a bit! Then, a return to cooler temperatures should cause the PEV servo to call for very modest polarization times (probably well under one second).
Saturday, March 19, 2011
Overnight: PDF, TXT The field remains quiet with only the slightest increase of activity. NOAA Costello 7 day index PDF.
The peak envelope voltage (PEV) servo continues to run well. PDF Over the next days and weeks, I will start increasing the NBLNA gain to keep the servo running below about a 2.5 to 3 second maximum polarization time. I anticipate the system will run in cooler weather with polarization times below one second. Improved the PEV Sevo controls (lower right) PDF.
Sunday, March 20, 2011
Overnight: PDF, TXT peak envelope voltage (PEV) servo PDF, PDF2, evening PDF.
I added a description of the PEV servo to the PART VII software article (which still needs updating in several other areas).
Monday, March 21, 2011
Overnight: PDF, TXT peak envelope voltage (PEV) servo PDF. The polarization time in seconds (red curve) generally follows the outdoor air temperature combined with solar heating from direct sunlight at the counter-wound sensor stand. For this curve, the minimum temperatures were on the order of ~20 F (before data point #577) and ~30 F (before data point #1321). The maximum was ~40 F (not recorded). The polarization time needed to achieve a desired peak envelope voltage (2 V) decreases with lower temperatures. This is believed to be due to a lower tau 1 with lower temperature, hence a higher percentage of protons in the working NMR fluid become aligned for a given polarization time. With warmer temperatures, the servo calls for longer polarization times to maintain the desired peak envelope voltage. The response is non-linear, either because the dependance of tau 1 with temperature is non-linear and/or because the polarization curve relating percentage polarization to polarization time is a non-linear curve. An open question is how to align the system to allow for closed loop operation from the coldest expected temperatures to the warmest temperatures in full sunlight.
I added a computation of Tau 2 computed from the precession waveform filtered envelope. In the upper left, the time of peak voltage and time where the envelope has fallen to 1/e (e^-1) are displayed. These times are both corrected for the N point moving average, presently N=600. The difference, a good approximation of Tau 2 (also, believed to be a strong function of temperature), is displayed next to the filtered envelope Max value. The Tau 2 value is recorded to the data files. PDF The Tau 2 data is added to our Excel post processing plot, here just a few points with the new data, PDF.
Also, I moved the present computed value of the polarization time to under the set time. When the program is started with the servo enabled, the actual value is the operative time. If the servo is turned off during operation, the program will hold the last computed value. I might change this back to a switch between servo operation and a fixed set value.
Project Documentation, Links and References (very early stages)
QUESTIONS/COMMENTS/notice of typos, etc. send email to joegeller @ gellerlabs dot com
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