# Gas station without pumps

## 2014 February 18

### Still better I-V plot for Schottky diodes

Filed under: Circuits course,Data acquisition — gasstationwithoutpumps @ 00:32
Tags: , , ,

Last weekend I posted a voltage-versus-current curve for a 1N5817 Schottky diode, to confirm the theoretical formula $V = V_{T} \ln \left ( 1+ \frac{I_{C}}{I_{S}}\right)$, where IS is the saturation current of the diode, using the following setup

and measuring the results with an Arduino Leonardo.  I claimed that the resulting data fits the model well for over six decades (> 120dB):

Fitting over a wide range of currents is more robust than fitting over the narrower range that I can get with just one value for R2.
There is quantization error still on the voltages, but the overlapping current ranges give good data for most of the range. VT is now 26.1mV and IS is 0.91µA.
click to embiggen

I was a little dissatisfied at the low end, because of the low resolution of the Arduino analog-to-digital converter (only 10 bits).  This weekend I decided to repeat the measurements, but using a Freedom KL25Z board, which has a 16-bit ADC.  Of course, it doesn’t really get 16 bits of accuracy—the data sheet claims that when you use the hardware averaging of 32 samples in 16-bit differential mode (the most accurate) you get at least 12.8 equivalent bits and typically 14.5 equivalent bits. (For single-ended 16-bit, the effective number of bits is only guaranteed to be 12.2, and the typical is 13.9 bits.)  They claim a ±6.8LSB total unadjusted error.

My son helped me get the bare metal ARM system set up on my laptop, along with ADC and UART routines, so that I could write my own single-purpose data logger for this problem (he’s working on getting the KL25Z board integrated into the Arduino Data Logger, but it isn’t close to being ready yet).  My program used the longest sample times and hardware averaging of 32 samples, to get the most accurate conversions possible from the 16-bit ADC.  The first version of the program used differential inputs for the voltage across the diode (E20-E21), but single-ended readings (E21) for the voltage across the resistor.  I had to reduce the voltage for the test from 5v to 3.3v, because the KL25Z runs on 3.3v, not 5v. I got some rather weird results:

Two runs of measurement with R2=100Ω. The low-current measurements seem to be all noise.
click to embiggen

I could get decent measurement in the low-current range by using a larger resistor, so the problem was not noise in the measurement fixture or problems reading low differential voltages on the diode, but just with the small single-ended read for the current. It is pretty clear to me that the ADC does not work well when the input voltage results in less than about 50 counts.  (Note, that means that at the low end of the voltage range you only have about a 9.4-bit equivalent ADC.)

I modified the circuit to allow differential reading away from 0 for both the voltage across the diode and the voltage across the shunt resistor:

Adding an extra resistor ensured that the lowest voltage did not get too close to ground and I could use differential reads for both voltage (E20-E21) and current (E22-E23)/R2

This gave me a much cleaner reading, with problems only once the differential counts got below about 20:

Differential measurement with R2=100Ω. The low-current measurements have problems when the counts get small, but not nearly as severely as with the single-ended measurements.
click to embiggen

I replaced the 100Ω R2 resistor with a 15.56kΩ resistor (nominally 15kΩ), to extend to lower currents despite the noise in the ADC:

This plot extends the fit down to about 0.1µA, but only by adding an extra term—an offset to the voltage. I thought at first that overshoot to –11mV is an error in the analog-to-digital converter on the KL25Z, as I couldn’t see how my circuit could be back-biasing the diode.
Click to embiggen

I tried using larger resistors, but was unable to get any better data using them—I seem to be limited by the differential voltage measurement of the diode at the low end. I thought I might be able to improve the measurements by adding an instrumentation amp to increase the signal for low voltages.  But first I tried just hooking up a voltmeter, with no ADC or instrumentation amp connections.  When the voltage across R2 (100kΩ) is 0.31mV, the voltage across the diode plus R2 is only 0.05V, so there is -0.26mV across the diode.  The backwards voltage across the diode was not an artifact of the ADC!

I then tried looking at the voltage across the diode with my oscilloscope.  There is about 20mV of AC noise, independent of the DC voltage, until the diode has about 50mV across it (with the 15.5kΩ resistor for R2), by which time the noise has dropped to about 10mV (the Bitscope oscilloscope with the differential probe has a noise floor of about 3mV, if the two leads are connected together, so this is not just oscilloscope noise).  This noise seems to be white noise, not 60Hz hum pickup, so is probably coming from the diode.  This AC noise signal limits how accurately we can measure the DC current, and rectifying the noise could be the source of the mysterious “backwards” bias.

To reduce the noise, I put a 4.7µF ceramic capacitor in parallel with the diode, and redid all the measurements with 100Ω, 15.5kΩ, and 100kΩ resistors for R2.

Modified measurement circuit, adding a bypass capacitor to reduce AC noise on the diode and allow better DC measurement.

Now the signals are very clean down to nanoamp levels. I no longer need to add an offset to the voltage, as it is 0 to within the measurement repeatability. The noise from very small voltage differences for the 100Ω shunt resistor is still a bit of a problem, but that region is well covered by 15.5kΩ data. The curve was fit using just the 15.5kΩ and 100kΩ data, to avoid having to trim out the noise from the 100Ω data.
Click to embiggen

Lessons learned today:

• Higher-resolution ADCs do give smoother curves, with less digitization noise, but they aren’t a panacea for measurement problems. To get most of the resolution, I had to set the ADC to use long sample times and do a lot of averaging. I understand that Freescale Kinetis M series include 24-bit sigma-delta converters for higher precision at much lower speed (24 bits is 7 decimal digits), as well as the high-speed 16-bit successive-approximation converters. Unfortunately, they don’t have a low-cost development board for this series.
• Stay away from the bottom end of the ADC range on the KL25Z.  Scale single-ended inputs to have values at least 50, and differential inputs to have values at least 20.  There may be similar problems at the top end of the range, but I did not test for them.
I wondered if the problem may be switching from the large value for the voltage across the diode to the small voltage across the shunt resistor that was the problem. I tried putting in a dummy read between the voltage and the current reads, but that didn’t help at all. At first I thought that the low-count readings were good with the large shunt resistors, but this is probably an illusion: errors in the current measurement for small currents aren’t visible on the plot, because the voltage across the diode is not changing, and so large horizontal errors in the plot are not visible there.
• Watch out for AC noise when trying to measure DC parameters.  If there are semiconductor junctions around, the noise may be rectified to produce an unwanted DC signal.
• The differential ADC settings have a range of ±VDDA, not ±VDDA/2. This means that the least-significant bit step size is twice as big for differential inputs as for single-ended inputs. For some reason the Freescale documentation never bothers to express what the differential range is.
• Serial USB connections are a bit flakey—the Arduino serial monitor missed a byte about every 200–300 lines.  I looked for anomalous points on the plot, then commented out the lines that produced them—they were almost all explainable by one character having been missed by the serial monitor; e.g., I commented out “662401069     86      19” right after “660001069       865     17”,  because the last digit of the voltage (the second field) was missing.  The fields were a timestamp (in 24MHz ticks), voltage across the diode (in ADC units), and voltage across the shunt resistance (in ADC units).  [Actually, this was not a new lesson for me—I’ve had to do the same on almost all files collected from the Arduino serial monitor.  My son’s data logger code is better at not losing data, but it is still worthwhile to check for anomalies.]
• The 3.3v supply from the Freedom board is much cleaner than the 5v USB supply that I get from the Arduino (unless I use an external power supply with the Arduino), but I can only take about 10mA from the 3.3v supply before it begins to droop.  If I want  more than that, I’d better provide my own power supply (or at least my own LDO regulator from the USB 5v supply).

## 2014 February 9

### Better I-V plot for Schottky diodes

Filed under: Circuits course,Data acquisition — gasstationwithoutpumps @ 15:21
Tags: , ,

Yesterday I posted a voltage-versus-current curve for a 1N5817 Schottky diode, to confirm the theoretical formula $V = V_{T} \ln \left ( 1+ \frac{I_{C}}{I_{S}}\right)$, where IS is the saturation current of the diode, but I wasn’t really satisfied with the results, either in terms of dynamic range or the quality of the fit.

The voltage does fit nicely to the log of current, with IS=1.32µA and VT=27.1 mV. Given the quantization noise in the voltage measurement, these seem like a pretty good fit to theory. (click to embiggen)

One problem is that the serial variable resistor I used did not all really low currents.  I rewired it today so that I had a potentiometer providing the voltage, rather than a series variable resistor:

I also wrote a little Python program to merge different data files, so that I could combine files in which the resistance of R2 (for measuring the current) differed.

The resulting data fits the model well for over six decades (> 120dB):

Fitting over a wide range of currents is more robust than fitting over the narrower range that I can get with just one value for R2.
There is quantization error still on the voltages, but the overlapping current ranges give good data for most of the range. VT is now 26.1mV and IS is 0.91µA.

The measurements at the high-current end had to be redone with an external power supply for the Leonardo Arduino board (not just USB power), as the reference voltage for the A-to-D converter dipped as the load increased. There is a tiny effect still when using an external power supply, but only at the very highest current level, and it is buried in the noise.

At the low-current end, we can see the flattening of the curve from the “1+” term that is often omitted from the model.  The resolution in the voltage is poor there, but the current knee can be fairly accurately set by using a large value for R2.

I should probably characterize the base-emitter junction of a PNP and an NPN transistor this way also, for setting the appropriate resistances for the log amplifier in the loudness circuit.

## 2014 February 8

### More on loudness circuits

Filed under: Circuits course — gasstationwithoutpumps @ 21:07
Tags: , , , ,

My son got interested in a loudness circuit again, and we tried coming up with one that that would take few components. We decided on having a 3-stage system: a preamp to get voltage up, a peak (or trough) detector with low-pass filter to extract the envelope, and a log amplifier to convert to a dB scale. We were planning to use a Schottky diode, rather than a precision rectifier for the peak detector.

Block diagram for loudness sensor using peak detector.

The gain of the first stage was set by looking at the sensitivity of the SPU0410HR5H‐PB silicon microphone and the maximum loudness that the system should be able to record. The mic has -42±3dB sensitivity referenced to 1V/Pa.  That means it has 7.94mV/Pa.  The loudest sound for the mic should be the sound level at a rock concert, approximately 120dB referenced to 20µPa—that is 20Pa.  So the microphone should have an AC output of about 160mV.  Because he is planning to work with a 3.3V power supply, a gain of 10 should just keep the signal within the rails.

Here is the loudness circuit, before the component values have been determined.

To get a gain of 10 (actually –10), we need R2=10*R1.  The R1 C1 time constant determines the cutoff for the high-pass DC-blocking filter.  A reasonable cutoff frequency is 10–20Hz, giving an RC time constant of  8–16msec.  Picking a cheap value for C1 (0.1µF),  gives us R1≈100kΩ and R2≈1MΩ.

The peak finder is just a Schottky diode charging C2 through R3, with R4 slowly discharging it.  Because the signal does not spend a long time at the peak, we want R3≪R4, so that we can catch the peaks. We also want a moderately rapid attack (to catch percussive sounds quickly) and a fairly slow decay, so that low-pitched sounds do not appear as fluctuating loudness.  We also want R4 to be sized so that the log amplifier has a good dynamic range.  We probably want to keep the currents through Q1 to between 0.2µA and 2mA, which suggests R4≈1kΩ, and R3≈47Ω.  To make the R4*C2 time constant around 0.1 sec, C2 would have to be 100µF, which costs about 50¢, so it may be cheaper to put in another op amp to separate the peak detector from the log amplifier, using a smaller C and larger R for the peak detector, followed by an op amp, then the low resistance for the log amplifier.

Modified loudness circuit with unity-gain buffer to separate peak detector from log amplifier.

Now we can make C2 be a reasonable size (say 0.1µF) and scale R3 and R4 to match (say 100kΩ for R4, to get a discharge time constant 0f 10msec, and 1kΩ for R3, to get a charge time constant of 100µsec).  This also limits the current drawn from U1 to 1.65mA (well less than the 15mA short-circuit current).

R5 can now be made fairly small (say 470Ω) to give us a large dynamic range on the amplifier.  If Q1 is an NPN transistor with characteristics like the S9013 transistor that I tested when I was playing with log amplifiers, then the output should range from Vref-0.65v up to almost Vref, which at 3mV/dB gives a range of over 200dB (which we certainly won’t get—the log amp may be good to 80 or 90dB.  If the ADC has 10-bit resolution on a full-scale range of Vref, then the steps are about 0.55dB (a 12-bit ADC would have steps of about 0.14dB).

Note that the log amplifier provides $V_{BE} = V_{T} \ln \left ( 1+ \frac{I_{C}}{I_{SO}}\right)$, where IC is the collector current, ISO is the saturation current of the base-emitter diode, and VT is the thermal voltage $V_{T} = \frac{k_{B} T}{q} \approx 26 mV$ at 300º K.  I should be able to estimate VT and ISO from the log amplifier measurements I made earlier. (I get VT =25.6mV and ISO=7.9E-15A for S9013.)

Along the way, I realized that I had never plotted a voltage-versus-current curve for the Schottky diodes, to confirm the theoretical formula $V = V_{T} \ln \left ( 1+ \frac{I_{C}}{I_{S}}\right)$, where IS is the saturation current of the diode.

I did those measurements this morning, using a 1N5817 Schottky diode, a series resistor, a series potentiometer, and an Arduino (Leonardo) board.  I measured the voltage across the resistor (to get current) and across the diode.

The voltage does fit nicely to the log of current, with IS=1.32µA and VT=27.1 mV. Given the quantization noise in the voltage measurement, these seem like a pretty good fit to theory. (click to embiggen)

When my son gets the Data Logger working with the KL25Z boards, I’ll probably want to redo these measurements with higher precision. Note that both VT and IS depend on temperature, and I did not measure the temperature (probably around 18ºC). IS normally doubles for every 10ºC temperature rise, so any measuring device relying on these characteristics would need to have temperature compensation or calibration to correct for temperature.  In any event the IS values for the Schottky diodes are much larger than for the base-emitter junctions, so voltage drop across the diode is much smaller for a given current—which is why we use Schottky diodes!

## 2013 July 18

### Improved rectifier with Schottky diodes

Filed under: Circuits course,Data acquisition — gasstationwithoutpumps @ 22:32
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In the Improved rectifier post, I gave the following circuit for an inverting rectifier and showed traces of its performance using diode-connected S9018 NPN transistors as diodes:

Only one of D1 and D2 can be conducting.

With a constant amplitude triangle wave input (about 2.6v peak-to-peak),  the circuit had some pretty serious glitches:

frequency positive glitch negative glitch
3kHz 40mV 40mv
10kHz 80mV 80mv
20kHz 120mV 100mv
30kHz 160mV 140mv
40kHz 200mV 180mv
50kHz 220mV 210mv
60kHz 250mV 260mv
70kHz 260mV 300mv

I claimed that I could reduce the glitches  by replacing the NPN transistors with 1N5817 Schottky diodes.  The diodes arrived today, and I tried them out with the same 10kΩ resistors and 30kHz triangle wave as before:

(click to embiggen) With the 1N5817 Schottky diodes, the glitches at 30kHz are much reduced—only about 68mV of overshoot when turning off, which is half of the glitch with the S9018 NPN transistors as diodes.

I noticed that there was a bit of phase shift for the 30kHz signal, as well as the small overshoot. I tried adding capacitors in parallel with the resistors to improve the performance at 30 kHz (both to correct the phase shift and to keep the gain at -1).

This circuit works well up to 30kHz, and is still somewhat functional at 100kHz

C2 seems to adjust the overshoot, and C1 then needs to be set to fix the phase and gain.  I had the best results at 30kHz with C1=330pF and C2=220pF:

(click to embiggen) With capacitors in parallel with the feedback resistors, the phase shift is mostly corrected and there is less than 20mV of overshoot—the turn-on and turn-off corners are softened somewhat.

Unfortunately, there is no easy way in the BitScope software to set the offset of the traces precisely. You can do a lot of range changing and clicking the left or right sides of buttons (and start all over if you accidentally hit the middle of the button), but the offset is only displayed to 2 decimal points, but can be adjusted somewhat finer, making it hard to guess exactly what it is set to. As result, I’ve not been able to measure the overshoot or undershoot when it is less than 10mV—I’m never sure exactly what I’m measuring with respect to, and visually similar settings result in ±10mV in the estimate. In any event, the errors in this version of the improved rectifier are at least 5× better than in the version with the S9018 diode-connected transistors.

The circuit works well throughout the audio range, and can be pushed to 100kHz, though the “corners” have gotten soft enough that clipping to the threshold voltage is no longer very precise at (about 60mV off @ 80kHz—undershoot, not overshoot). At 100kHz, the output signal is still pretty good, but there is about an 85mV error in the threshold, and the corners are so rounded that the output almost looks like a sine wave:

(click to embiggen) Waveform at 100kHZ (sine wave input), showing the soft corners at that frequency. The output does not get down to the threshold voltage, but only to about 85mV above threshold.

I can get better performance at 100kHz with smaller capacitors (100pF and 220pF, instead of 220pF and 330pF), but at the cost of some overshoot at 20kHz and 30kHz.  I suspect that the right values for the capacitors depend heavily on what op amp is used (especially its slew rate), but since I only have MCP6002 (and the equivalent MCP6004) op amps, I’ve not tested this suspicion.