Why my nFET measurements were bad

I’ve been bothered for the past week (or more) about why my FET measurements in Possible new FET lab for electronics course, , More thoughts on measuring FETs, and Measuring a high-voltage nFET were not coming out the way I expected. In particular, I was measuring much higher on-resistances than I expected from the data sheet, and I was getting different results when I made small changes in my measurement setup, like changing the current-sense resistor.

My measurements were all for Id vs. Vgs (or R=Vds/Id vs. Vgs). Today, I decided to try measuring Id vs. Vds for different Vgs values, to see whether an Ron made sense (straight lines for Id vs Vds, at least for small values of Vds).  Because I wanted to test with a wide range of currents, from very small to reasonably large, I could not use the function generator to sweep the desired voltage range—it can’t supply much current. Instead, I built the following test fixture:

The function generator provided the pFET Vgs with a triangle wave from -1V to -4.2V, which was chosen empirically to get the full range of current possible in the 10Ω resistor. The period was 8s, and the electrolytic capacitor was to smooth out the bumps from the discretization of the 8-bit DAC.

Before using the test fixture, I calibrated the voltage dividers plus unity-gain buffers as producing an output that was d*V_in+b.  Of the 4 amplifiers in the MCP6004 chip, I picked the three that gave the smallest offsets (b), wiring the inputs of the other amplifier to 3.3V and GND.  The amplifier was powered off the 3.3V output of the Teensy LC board.

Here are the I-vs-V plots that I got:

The hysteresis in the 2.43V and 2.63V Vgs curves is from heating the transistor, as the 2.43V curve peaked at 2.05W and the 2.63V curve peaked at 0.8W. The curves were traced counterclockwise.

The weird thing is that no matter what gate voltage we are looking at, there is a minimum Vds voltage, around 17mV.  No current flows until that voltage is exceeded, and then the voltage stays almost constant until the resistance of the channel limits the current.  If we try measuring the on-resistance with a tiny current, Itest, we get 0.017V/Itest as the on-resistance—the smaller the test current, the larger the on-resistance, and the resistance seems to be nearly independent of gate voltage (the phenomenon that confused me so much in my Id-vs-Vgs plots).

Enough current to measure the resistance depends on how strongly on the transistor is.  If it is barely on (Vgs=2.43V), then 200mA is enough, and the on-resistance can measured as around 160mΩ–215mΩ. At logic-levels (Vgs=3.35V), then we need around 450mA, and the on-resistance is around 49mΩ. When fully on (Vgs=9.15V), then 900mA may not be enough—the best estimate I can get there is around 25mΩ.

I redid the measurement with a 1.8Ω 50W resistor for the fully-on transistor.  This produced a curve much like the one for Vgs=3.35V, but with the current going up to 4.76A (with a power dissipation of about 1W in the nFET).  I estimated about 36mΩ on-resistance at Vgs=8.94V.  Of course, I’m not very confident of the 1.8Ω value, as wiring and breadboard resistance adds a substantial error at those low resistances, so the on-resistance may be even higher.  The datasheet reports on-resistance of about 6mΩ for Vgs=9V, measured at 20A, which is not a measurement I’m equipped to do.

The cause of the 17mV minimum for Vds is not clear—it has not appeared in any of the simplified models of FETs that I’ve seen. My current best conjecture is that there is a Schottky diode formed by the bonding wires contacting the silicon transistor.  There is usually  heavy doping of the silicon to avoid Schottky diodes at the bonding wires, but perhaps 0.02V was the best that they could do. Does anyone reading this know enough about power nFETs to either confirm my conjecture or offer a better one?

Incidentally, the requirement that the measuring current be large (around 0.5–1A) means that the simple FET measuring lab I was thinking of putting in the course won’t work.  For one thing, the students don’t have any power resistors for handling the current sensing. The only device they have capable of dissipating much power is their loudspeaker, and it is not a well-defined enough impedance to use for measuring current in the FETs.  I’m glad I haven’t written up that lab for the book yet!

[Update 2016 August 2: I didn’t really believe this set of results, so I did a negative control that I should have done earlier, replacing the nFET with a drain-source short.  It also shows the 0.02V minimum, indicating that this is a limitation of my test jig, not a property of the nFET! I’ll have to come up with a better test jig.]

2016 Santa Cruz Shakespeare season

This year, Santa Cruz Shakespeare is presenting two plays by their professional cast in their brand new Audrey Stanley Grove in Delaveaga Park, in addition to a play performed entirely by their unpaid interns. The main plays this year are Midsummer Night’s Dream and Hamlet, two of the most popular plays Shakespeare wrote, and the intern’s play is Orlando, an adaptation by Sarah Ruhl of Virginia Woolf’s novel.  I’ve now seen both the Shakespeare productions and will be seeing Orlando after it opens.  The company has posted photos of the Midsummer cast, but not (yet) of the Hamlet cast.

I always enjoy seeing plays in repertory, seeing the same actors in very different roles—there is too little repertory theater in the US nowadays, so the summers in Santa Cruz are a treat. I urge everyone to see both the Shakespeare plays this year, but if you can only see one, Hamlet is by far the better production. They made a number of changes to the play, in order to get equal roles for both genders, and I worried about what damage might have been done by making Hamlet, Polonius, Rosenkrantz, and Guildenstern all female roles (not women playing men’s roles, which is often done, but Hamlet as the princess of Denmark).

There were a couple of unedited lines in Hamlet that didn’t quite work (like referring to Polonius’s beard), but Kate Eastwood Norris was the best Hamlet I’ve ever seen—utterly convincing in all of Hamlet’s varied moods.  A lot of the lines that seem overplayed in most productions resonated with new depth.

The very simple set and effective lighting (having Hamlet’s shadow on one of the towers during a soliloquoy, for example) increased the impact of the lines. Having the fog come in during the performance was an unplanned, but mood-enhancing addition—I can’t promise that in future performances!  The costumes for Hamlet were not distracting, but the “Denmark” of this production seems to be set in no particular century and on no particular continent.

All the actors were at the top of their form opening night, and the audience gave a standing ovation (which is not all that common for Santa Cruz audiences—we tend to be a tough crowd). Even the Player King’s speech, which was left in, not hacked down to a couple of lines as in many productions, was moving.  (My wife agreed with Polonius that it was a bit too long, but was surprised at how a good performance made even the rather overblown lines resonate.)

Patty Gallagher did a marvelous job as Polonius—her Polonius was a wholly convincing pedantic counselor, and the gender swap making her Laertes and Ophelia’s mother instead of father may actually have made the role more believable. (Polonius has always behaved more like an old woman than an old man.) Having Ophelia cast as a black woman and Claudius as a black man did raise some questions about Polonius’s earlier relationship with Claudius and his dead brother.

There were some parts cut that we missed, like Horatio’s attempt to kill himself at the end, and some we didn’t (they cut out Fortinbras, who never seemed to belong in the play anyway).

In both plays I was impressed by Larry Paulsen (Puck and Philostrate in Midsummer Night’s Dream, the Player King and Gravedigger in Hamlet).  It is, perhaps, an unusual choice to make an older man be Puck, but his Puck was the best part of Midsummer Night’s Dream. Bernard Addison as Nick Bottom was also quite good (better than his Claudius in Hamlet, which was solid, but not inspired).  The two women, Katherine Ko as Hermia and Mary Cavett as Helena, were good, and for once the heights of the actresses matched the insults in their fight scene.  Kate Eastwood Norris was quite good as Penny (not Peter) Quince, with the extra byplay of having a crush on Nick Bottom adding to the normally rather thin lines for Quince.

But the directing and costuming for Midsummer were a bit lackluster—the fairies moped about the stage like hungover teenagers wearing boring pajamas.  Patty Gallagher as First Fairy bossed them around and had some rather stylized movements that seemed rather awkward—it might have been better to let one of interns have that role and given the fairies a bit of life.

I guess I’ve been spoiled by having seen Danny Scheie’s 1991 production of Midsummer Night’s Dream in the Festival Glen by Shakespeare Santa Cruz—it is hard for a rather mundane, traditional performance like the one Terri McMahon directed this year to compete, even if there were some good additions (like the miming of the potions by Puck and Oberon).

On more mundane matters—the Grove is a comfortable place to see a play (but bring blankets—it gets colder even than the Festival Glen did), but it is rather inaccessible by public transit, bike, or walking (the two-lane access road to the park is very narrow and unlit). We ended up taking taxi and Uber, but cellphone reception in the Grove can be a bit spotty, so calling a taxi can be tough, and the taxi drivers don’t have any idea yet where Santa Cruz Shakespeare is, and the official address on Upper Park Road is misleading.  We ended up walking out of the park after Midsummer Night’s Dream, after the taxi we called got lost, and we met a taxi at the golf-club clubhouse after Hamlet, choosing there as a more findable location.

I like the new benches for the reserved seating, but they need cup holders or, better, little shelf tables on the back of the bench in front (which I saw they had started to install). The boxes for the groundlings are a bit confusing, as there was no indication whether any of them had been reserved by a group.  Perhaps they need a sign for each box, either saying in red “reserved” or in blue “open for groundlings”.

The bathrooms are rather hastily installed trailers, but they did have hot water, which one doesn’t always get in public bathrooms these days.

The Grove was finished on time (about 3 months from permission to start to opening night), if not quite on budget (they still need to raise about 16% of the cost of the Grove, being $219k short).  They are also looking for donations to fund next year’s production, since they are using a forward funding model, where the ticket sales and donations this year determine next year’s budget, rather than building up debt the way the former Shakespeare Santa Cruz company did.  (It was that debt to UCSC that killed SSC.)

So go to https://www.santacruzshakespeare.org/ and buy tickets, make donations, or both!

UCSC iGem 2016: Sugar Slugs

UCSC’s 2016 iGEM team has finally had their crowd-funding site go live at https://crowdfund.ucsc.edu/project/2548.  They have an interesting project this year:

Engineering a Better Future

The world of crop production is laden with agricultural co-products that are unfit for human consumption. The vision of the UCSC iGEM team is to develop a novel process for converting these co-products into the high-value sweetener, Erythritol. It’s simple, sweet, and best of all, zero-calorie.

Ever wanted a bioreactor you can control at the click of a button? Our team is also designing and building our very own autonomous bioreactor, the Taris V1. Whether its temperature, pH, nutrient uptake, or beyond, our bioreactor will also monitor and feed its internal conditions into an online interface where users can seamlessly track their data and change conditions as they see fit. Talk about convenience.

With its low cost and ease-of-use, we hope our Taris V1 bioreactor can serve as a platform for other teams across the globe to create innovative solutions to real-world problems.

Source: UC Santa Cruz | UCSC iGem 2016: Sugar Slugs

I don’t know much about what they are doing for the metabolic engineering to make the erythritol, but the bioreactor project is a rather fun “maker” project.

They have posted their budget on-line, and by far the largest cost is getting to the iGEM “Jamboree” in Boston in October. All the lab equipment is provided by UCSC (except the bioreactor they are designing and building), and all the student labor is free (in fact, they are paying summer tuition in order to take the iGEM course). So they have about $1000 for hardware, <$200 for reagents, and $31,300 for travel to the conference.  I think that they’ve over-estimated the price of flying to Boston, though, as Southwest flights are currently about $320 round-trip, and ground transportation at each end would probably add only about $200 to that, so 21 people  (20 undergrads and 1 instructor) should be able to do the travel part for under $11,000.  They’ve probably underestimated the lodging costs though, unless they are planning to pack like sardines into an AirBNB rental.

I’ve been thinking of going to the iGEM conference myself this year (on my own money, not crowd-funded), as I’ll be on sabbatical in October, and not teaching. I’ll have to make up my mind soon, though, as the cheap flight prices will probably go away.

I’ll be giving the iGEM team some money for their crowd-funding campaign, as it would be valuable for all of them to be able to attend the conference after the work they’ve put in—I know many of the students on the team this year, and they are the hard-working students that teachers love to have in their classes.

I urge others to make at least a token donation, to let them know that the hard work they are doing is recognized by the community.  Donations can be made through the UCSC crowd-funding site.

Disclaimer: I’m officially the “2nd PI” for the iGEM team this year, because the iGEM organization insisted on there being two faculty involved. I’ve done some advising on the bioreactor project also, though only through a few conversations with the lead designer on that team (who was also my group tutor for my applied electronics course in the spring).

LED strip power consumption

I mentioned in LED lighting for bathroom that the LED strips I had bought from China were much yellower than I expected and were lower-powered than the seller claimed.  I believe that they sent me a different LED strip than what they had advertised (a cheaper product using 3030 LEDs instead of 5050 LEDs), but that is a risk one takes in ordering through AliExpress.  Although I could have started a claim against the seller, I had already cut up and installed the strips, so I did not feel justified in asking for a refund.  The amount was small enough that I just wrote it off and ordered another set of LED strips through AliExpress, making sure they were from a different seller and were well described on the web page.

The new strips did indeed use the 5050 SMD LEDs that both strips claimed to use—the LEDs were substantially larger, through the strips were the same size.  I installed the new strips alongside the old ones, and they are substantially brighter and whiter.  It is also clear that the old power supply I was using was not able to handle the load of the new strips, reaching a current limit of about 1.5A with voltage dropped to about 11V (though it claimed to be 12V 2A). I have ordered a new 12V power supply, Mean Well SGA60U12-P1J, which is a modern, efficient power supply and should be able to deliver 5A. Will that be enough?

Because my old supply was being limited by the current it could supply, I did not have a good estimate of the power needed by either the new or old strips.  In both cases, the seller had said 14.4W/m, which is 1.2A/m @ 12V.  I know that spec is wrong for yellowish lights (they are smaller LEDs than the 5050 LEDs I’d ordered), but I was curious what the power consumption really was.

So I decided to measure a 5cm length of  each of the strips (5cm is the smallest unit for the strips, standard for most LED strips).  The 5050 strip has 3 resistors in each unit, so consists of 3 copies of a 150Ω resistor in series with an LED module that internally has 3 LEDs in series.  The yellowish strip has only one resistor in a 5cm segment, so consists of three LEDs in series with a 100Ω resistor. I can tell the resistor values, because they are clearly labeled SMD parts.

To make the test pieces, I cut the strips at the 5cm cut line, then used a razor knife and a pair of long-nose pliers to peel away the waterproofing from the copper pads. I soldered red and black stranded wires onto the pads, then used some heat-shrink tubing to insulate and stabilize the connection, providing a tiny amount of strain relief.

The newer 5050 strip is on the top. The incorrectly shipped 3030 strip is on the bottom.

I wanted to make I-vs-V plots for the LED strips using PteroDAQ, but the Teensy board ADC is limited to 3.3V, and the voltages I needed could go well over 12V (12V for the LED strip plus whatever I needed for the current sensing).  I could keep the voltage down for the current sensing by putting the current-sense resistor on the ground side of the LED strip.  If the 14.4W/m @12V figure from the seller is accurate, then I’d expect about 60mA for a 5cm section, so a current-sense resistor <55Ω would keep the voltage in a measurable range.  But to measure the voltage across the LED, I need a voltage divider.

My first attempt was to use a 62kΩ and a 15kΩ resistor to get a nominal divider ratio of 0.1948.  To check this ratio, I used the function generator to sweep over most of the 3.3V range, measuring the input and output of the voltage divider at each point with two channels of PteroDAQ.  I saw some weird non-linear behavior of the output of the voltage divider vs. the input, so I did a fit assuming that the ADC had a fixed offset voltage, besides the scaling of the voltage divider (this 2-parameter model worked better for tests that I’ll describe below than just a scaling by the voltage divider, so I used it for this initial test set also). Although I usually make PteroDAQ measurements in volts, I redid the measurements in raw ADC integer values, because the pattern of the values suggested a relationship to the binary encoding.

The error in the output voltage measurement shows a distinctive pattern, corresponding to the high-order bits of the ADC value.

These results were unexpected, so I decided to explore further, replacing the 62kΩ:15kΩ voltage divider with a 10kΩ potentiometer and using it at various settings.  It was with this data that I decided that a constant offset was needed to get the voltage divider fits to work well:

With the 10kΩ potentiometer, the patterning of the errors is barely visible, and the errors are much smaller than with the 62kΩ:15kΩ voltage divider. The offset was chosen for the d=0.0581 divider, but worked well for all the dividers.

Given that the patterned errors were now much smaller than the random noise (which I had already minimized by using 32× hardware averaging), I suspected that the problem was not an inherent non-linearity of the ADC, but poor behavior of the ADC due to the high impedance of the source.  I tested this two ways: first, by adding a resistor between the voltage divider output and the ADC pin (which should increase the source impedance without changing the voltage being measured) and second, by using a unity-gain buffer to provide a low-impedance source for the ADC pin.

With a 15kΩ resistor between the potentiometer voltage divider and the ADC input, I got patterned errors similar to what I first observed with the 62kΩ:15kΩ divider, but the offsets needed to get good fitting did vary a bit with the divider ratio:

The problems with the 62kΩ:15kΩ ADC measurements were caused by the high-source impedance, since adding extra impedance to the 10kΩ voltage divider created similar problems.

I also tried 62kΩ added between the voltage divider and the ADC pin, but that caused huge problems with reading the value.

Adding a unity-gain buffer between the voltage divider and the ADC pin cleaned up the problem, though there is still a little patterning of the error.  Here I modeled the offset as occurring in the unity-gain buffer, so that the offset is just on the divided-down channel, not on the other channel.  This has exactly the same fitting power as a model that provides the same offset on both channels, but this model is more explicable, since op amps are known to have input offset errors, and the 580µV error estimated here is well within the ±4.5mV spec for the MCP6004 op amp.

The divider ratio of 0.1942 is for the 62kΩ:15kΩ divider, which has a nominal ratio of 0.1948.

So I was finally ready to measure the voltage and current for my LED strips. I put the LED strip in series with a current-sensing resistor, measuring the current-sense voltage with channel A0 and the divided-down and buffered LED+current-sense voltage with channel A1. Because my function generator is not capable of generating a 12V output, I put it in series with a 9V power supply, so it only had to generate -2V to +4V.  Of course, since it has an output impedance of ~50Ω, and I was asking for up to 60mA, the function generator needs to generate higher voltages at the source, to compensate for the 3V IR drop.

At 12V, we get 55.2mA/5cm or 1.1A/m for the 5050 warm-white strip and 18.1mA/5cm or 362mA/m for the 3030 yellow-white strip.

Note that for the 5050 strips, about 3.05W/m (of the 13.2W/m, so 23%) is wasted in the current-limiting resistors, and for the 3030 strips, 655mW/m (of the 4.34W/m, so 15%) is wasted.  These losses are normal for LEDs with current-limiting resistors, which is why higher-power LED lights use switching regulators to control the current through the LEDs, rather than current-limiting resistors.

I have 1.92.9m of each type of strip in the bathroom cove, so the total current needed is about 2.794.25A, well below the 5A limit of the new MeanWell power supply, but large enough that the power-supply will be in regulation and efficient (efficiency of the power supply is claimed to be about 88%).  Assuming that the efficiency is as claimed, the new LED lighting should take about 3851W, considerably less than the 120W of the fluorescent fixtures that it replaces, but with about the same effective brightness and a more pleasing color.

The nearly straight lines for the I-vs-V plots can be approximated as a resistance and a threshold voltage, which works well for higher voltages, but underestimates the current for low voltages:

The simple resistance models are within measurement accuracy above 10V—measurement accuracy is limited by the changing of LED characteristics with temperature.

Average annual power use

I just got my “True Up” bill from PG&E—it has been about a year since the solar panels were installed. During that time, the panels generated about 2.63MWh of electricity (7.2kWh/day): 77kWh more than we used during the year. PG&E reimbursed me $2.11 for the extra electricity, but wiped out the $106 of Net Energy Metering credits that we had accrued from generating electricity during peak time and using electricity during off-peak times.

Next year, we’ll be facing a minimum delivery charge of about $120 for the year. If we follow the same peak/off-peak usage, that means that we could use about another $226 worth of electricity without increasing our bill (other than losing the $2.11 credit). That would be about 1.5MWh off-peak, or only 660kWh peak consumption. What that translates to for us is that I will be buying a dehumidifier for our house, to reduce the condensation on the walls. Current Energy Start rated dehumidifiers remove about 1.85 liters of water per kWh used, and I don’t think we need to remove 2775 liters of water a year (7.6 l/day) from our house, so the dehumidfier will add nothing to our electricity bill.  Based on reviews (in Consumer Reports and on Amazon), we’re looking at the 30-pint Whynter RPD-321EW Energy Star Portable Dehumidifier, is it has good performance in cool rooms (our house gets quite cool in winter, especially when we’re both at work) and is relatively easy to empty (we don’t have a convenient way to rig up a drain hose).

We are fairly light users of electricity by US standards. We used about 2.63MWh a year, but the US average is 10.932 MWh/year, and the California average is 6.744MWh/year [https://www.eia.gov/tools/faqs/faq.cfm?id=97&t=3].  PG&E also reports what people in our area use: similar houses use 6.042MWh/year, and efficient similar houses use 3.262MWh/year [https://pge.opower.com/ei/app/myEnergyUse].

Part of the reason we use so little electricity is that we rely on natural gas for heating, hot water, cooking, and clothes drying, using about 433 therms a year.  Here we are not particularly efficient: PG&E reports that similar houses use 548 therms/year, but efficient similar houses use only 293 therms/year [https://pge.opower.com/ei/app/myEnergyUse]. Shorter showers and setting up a clothes line would probably reduce our usage, but heating is the biggest chunk, and our house is already as cool as we are willing to live in.  We’ve invested in insulation over the years, but there is only so much you can do with a poured-concrete house for sane amounts of money.

A therm is about 29.3001 kWh, so our natural gas use is about equivalent to 12.7MWh—much more energy usage than our electricity!

We’ve been planning to buy carbon offset credits for our energy usage this year (see previous estimates in Solar lies).  Nothing for electricity of course, since we had a slight surplus there.  According to PG&E, natural gas produces about 6.1 kg CO₂ per therm (and their electricity generation is about 238 g/kWh, only slightly more than the 208g for the same amount of energy from natural gas) [http://www.pge.com/includes/docs/pdfs/about/environment/calculator/assumptions.pdf].

I calculate approximately the following CO₂ production from our various uses this year:

• 2.64 MT (metric tonnes) for natural gas
• 3.37 MT for plane flight to Illinois (2 roundtrip tickets) [https://carbonfund.org/individuals/]
• 6.97 MT  for plane flight to Montreal (3 roundtrip) [https://carbonfund.org/individuals/]
• 0.5 MT Other transportation (bus and train)
• 13.5MT Total

My wife and I have considered taking another trip this year, to Boston, which would add another 4.9MT. Note that flying is by far the most energy intensive thing we do—reducing travel is probably the only way we could significantly reduce our carbon footprint.  As carbon offsets, we’re considering projects like https://www.cooleffect.org/content/project/efficient-cookstove-project/, which cost $6–$10 per MT.  Do any of my readers know of good carbon offsets that aren’t scams or just enabling polluters?