Author Topic: DIY-SMU Project  (Read 15066 times)

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Offline djerickson

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DIY-SMU Project
« on: December 29, 2020, 05:14:18 pm »
I'd like to introduce my DIY Source-Measure Unit SMU project. http://www.djerickson.com/diy_smu
Youtube intro: https://youtu.be/B26SW3N2zoA

[attach=1]

It seems fundamental to have an accurate source for a wide range of voltages and currents, with the ability to measure both.  Source and measure are basic requirement for electronics test and measurement tasks and many scientific applications. This functionality should be available at a reasonable cost.

I worked on many DC and AC source / measure instruments for a number of industry leaders (Analogic Test and Measurement group, Teradyne DC Instruments group, Zoll and HP Medical) plus numerous startups and home projects. I always wanted to build a DIY Source Measure Unit: SMU.

Recognizing that this is a challenging project for DIY, now in retirement I finally have the time to develop the hardware, software, controls, and packaging. Fortunately the nerd stars are aligned for such a project. Precision 0.1% and better SMT resistors are readily available at low cost. Precision amplifiers, switches, ADCs and DACs are low cost and easy to apply. Digital isolators and DC-DC power supplies are small and readily available. Hand-built SMT is available and easy to DIY. Single chip CPUs and TFT LCDs with touch are powerful, low cost and DIY friendly.

I pored through old Keithley documents for their 220/240 series sources, and 236 and 237 SMUs and found their general architecture to be flexible and very capable. I suspect that most modern SMUs share the Keithley 236 general architecture.

So after a few years of planning and a year of detailed design, layout, and build, here is DIY-SMU.
   Voltage source and measure from tens of microvolts to +/- 150V in 3 ranges: +/- 1.5V, +/- 15V, +/- 150V
   Current source and measure from nA to .1 Amp in 6 ranges: 1uA to 100mA
   True 4-quadrant operation
   Source accuracy .01%
   Measure accuracy .005%
   Graphic LCD with touch screen
   Small, half-rack 2U package
   DIY friendly and low cost

It is not complete yet, and I plan to continue the project this winter. PC boards are built and working. An initial GUI is working.  It has a basic enclosure. My web page discusses the idea, requirements, design, and implementation. Check it out at www.djerickson.com/diy_smu

Thanks,
Dave Erickson

Offline fcb

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Re: DIY-SMU Project
« Reply #1 on: December 29, 2020, 05:37:20 pm »
Awesome!

The 236/237 architecture is a great place to start. Look forward to following this project.

We built a baby 2ch SMU (known internally as SMUSB), 1uA to 45mA, +/-12V. Went with a PC based front end rather than a display on the device.  My understanding is that some of the newer SMU's use software-in-the-loop to deal with some of the stability issues that crop up from time-to-time. Are you planning on guards?

TTi have a new SMU that's overdue.  So I suspect this will be a growing market.  I think Marcoreps was involved in project called OSMU?
https://electron.plus Power Analysers, VI Signature Testers, Voltage References, Picoammeters, Curve Tracers.
 
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Offline helgel

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Re: DIY-SMU Project
« Reply #2 on: December 29, 2020, 06:27:27 pm »
Nice project !  Congratulations ! I have a similar project going myself (https://poormanssmu.wordpress.com). When I started that project I was surprised to find very few attempts on similar projects out there. Sounds like your previous background and now retirement is perfect for such a project. With a full time job as software developer I unfortunately have less time on my own the project than I would like to, but it's still work in progress. I'll be following your project !
 
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Online prasimix

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Re: DIY-SMU Project
« Reply #3 on: December 30, 2020, 08:37:22 am »
Hi Dave, and thanks for sharing this project with us, looks great and very promising. About half rack enclosure (9.5"): you can check All Metal Parts from UK, e.g.: http://www.allmetalparts.co.uk/814-2u-95-inch-rack-mount-300mm-vented-enclosure-chassis-case-5055726240082.html

I would suggest putting a fan controller high on the TODO list. There is no reason that "tiny" fan that you're using is working all the time. The fact that many manufacturers are still saving on that component has no reason to be the case here :).

Good thing you realized that the Arduino Leonardo is not enough, even supported with extra processor on the Nextion (in charge of display). We had a similar thing: we started with Leonardo, then Mega2560 and Due (EEZ H24005 project) and finally finished on our own design based on STM32F7 with 8 MB (expandable to 32 MB) SDRAM with micro SDcard in the background for data logging, etc.

I would love to see a video in the future that covers the following:
1. What does output enable/disable look like, that there are no over-/under-shoots.
2. How it behaves with a slightly higher capacitive load

Keep up the great work, maybe a combination of your SMU and Helgel Poor man’s SMU could become a new module for our EEZ BB3 in the near future. In that case it would get all the support for SCPI via USB and Ethernet, GUI editor, MicroPython scripting, MQTT, NTP, Node-RED that we already have.
 
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Offline djerickson

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Re: DIY-SMU Project
« Reply #4 on: December 30, 2020, 02:17:25 pm »
Thanks for the feedback. Yay, a half rack 2U enclosure! Will order one right away.

I agree, fan speed control is a must, and will be on the new CPU board.

For the last month I battled a 300KHz noise issue, 50mV sine wave, thought it was oscillation. It drove me crazy! It only occurs when the Out- or Out+ is grounded.  Turns out it's the 3W DC-DC common mode noise. I had a common mode choke, but that made it worse. I tried 3 manufacturers DC-DCs so far. They all have common mode noise: Meanwell is worst, then CUI, Recom is best. More testing.....

The output dynamics are very good when changing the output current, voltage, or resistive loads, and when clamping.

I've done a bit of testing with capacitive loads. With 1000pf to 1uF it rings or overshoots a bit, and settles in a few mS. It's good with large caps. Tuning the loop may help.

I need to thoroughly test the dynamics vs. the output and remote-sense relays and will report. If the OFF/ON transients are ugly I may be able to fix in software with some simple sequencing.

Thanks!
Dave

 
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Online prasimix

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Re: DIY-SMU Project
« Reply #5 on: December 30, 2020, 02:33:38 pm »
For the last month I battled a 300KHz noise issue, 50mV sine wave, thought it was oscillation. It drove me crazy! It only occurs when the Out- or Out+ is grounded.  Turns out it's the 3W DC-DC common mode noise. I had a common mode choke, but that made it worse. I tried 3 manufacturers DC-DCs so far. They all have common mode noise: Meanwell is worst, then CUI, Recom is best. More testing.....

Perhaps you should consider DC-DC converter built around SN6505 push-pull converter. It depends how much power you need on +/-15 V rails, probably not so much. I'm just start experimenting with it after giving up from Mean Well and TRACO. It looks like this (with 4x multiplier as suggested by Kleinstein):



I derived 5 power rails on the secondary side: +3.3 V for MCU/ADC, +/-5 V and +/-15 V for analog circuits.

 
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Online Kleinstein

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Re: DIY-SMU Project
« Reply #6 on: December 30, 2020, 05:31:17 pm »
The ready made DC/DC converters often have quite a lot of common mode injection. The smaller the transformers the closer the coupling and a higher voltage also makes things worse. 

I don't think the SN6505 is special, it just gives the chance to choose your own transformer. For a one off DIY unit one could use a relatively large core with some extra space to reduce the capacitance. A low voltage to start with also helps. For DIY winding I used 2 twisted wires for both halves of the dual winding. This should give relatively good symmetry and thus little voltage to drive the CM signal even without an extra shield.

CM injected signal is relatively difficult to filter, but usually a CM choke would be the way to go.  It needs a special type with 3 coupled inductors for a +-15 V output. So the CM choke on the primary would be easier.  There may be a resonance with the CM choke, if just at the wrong value / frequency.
 
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Offline djerickson

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Re: DIY-SMU Project
« Reply #7 on: December 31, 2020, 02:02:19 pm »
Thanks, Prasimix, appreciate the design idea.

DC-DCs and even AC transformers with low common-mode noise generally use multiple internal shields. Unfortunately my transformer design and build skills peaked with 1980 Ferroxcube potcores ;).
I suspect I can get it low enough by using enough of the good external stuff (low ESR ceramic and Electrolytic caps, Y-caps, beads, common-mode chokes...) plus finding the quietest off-the shelf DC-DCs, and careful measurements. I feel a test board coming on.

One of my project goals to be DIY-friendly, is to avoid custom transformers. I know of no off-the shelf transformers with shielding, other than medical grade AC ones. 

My personal pet peeve about switching power supplies is that common mode noise is not specified. They are often tested with their output common grounded, so common mode noise is minimized. The way I measure it is with a resistor (10-50 ohms) between input and output commons. Measure the voltage across the R with a wideband scope. This gives a decent indication of common mode noise as a current, good for comparative studies. 

Another quiet DC-DC design method is to use a HF sine wave or resonant DC-DC to eliminate having to clean up nS rise-time edges that switchers generate. But in all cases, shielded windings help.

Dave
 

Online prasimix

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Re: DIY-SMU Project
« Reply #8 on: December 31, 2020, 02:38:54 pm »
I'm agree with your approach/attitude that a DIY friendly project should have as few custom components as possible (preferably none). I suggested this DC-DC converter because it uses an off-the-shelf transformer from WE: 750315371. A whole converter with LDO's don't use a lot of space: IC6 is SN6505, IC5 is +15 V LDO, IC7 for -15 V and IC4 for +3.3 V.


Offline alm

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Re: DIY-SMU Project
« Reply #9 on: January 01, 2021, 10:53:06 am »
Awesome start! Have you considered replacing the DC-to-DC converter for the analog circuit with a simple linear power supply from a small off-the-shelf 15-0-15V transformer? I realize that this is less neat, more expensive and bigger, but it would remove the concern of common-mode noise.
 

Offline djerickson

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Re: DIY-SMU Project
« Reply #10 on: January 01, 2021, 08:44:35 pm »
Thanks for the advice, Alm. Using an AC transformer might be a last resort.

I dug into the issue and also looked with more detail at the SN6505 and your DC-DC design, Prasimix. I like your design, nice use of a voltage multiplier.

My design with a CM choke feeding a Meanwell 3W DC-DC had 3 volts(!) of 300KHz common mode noise on the DC-DC input. I have a handful of different DC-DCs and tested 6, 8 and 7 pin SIP parts. Meanwell is worst for CM noise and doesn't like the CM choke.  Tracor and Recom are best. CUI is in the middle. I'll buy more to test.

I think I found a fundamental issue: In an SMU design, the Out- is the common of the power supply, driven by the +/- 150V supplies common. When you ground it through a scope, for example, the path back to chassis ground is through the power supply, Amplifier, the DC-DC's Y cap,  plus the AC transformer's inter-winding capacitance, and a Y cap that I add.  The common mode inductor's 1mH plus those caps makes an pretty ugly impedance.  Bypassing the CM choke reduced it to just capacitance, no big inductor. It works much better.

In a 'normal' isolated instrument, grounding the floating ground to chassis should quiet the common mode. With a CM choke in the power path, both sides of the LC resonant circuit formed by the Common mode choke plus any Y caps would be kinda grounded. But you could imagine some weird stuff happening to your circuit-under-test when you apply that big-old LC circuit to your DUT. Not sure how DMMs deal with this. Then add in the SMU's complexity... Yikes!

So for now I'm gonna stick with "C good , LC bad". Will try to simulate this. All this funky "grounding" hurts my brain.

Thanks,
Dave
 

Online Kleinstein

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Re: DIY-SMU Project
« Reply #11 on: January 01, 2021, 09:39:40 pm »
The purpose of the CM choke is to add impedance for common mode voltage. So having some 3 V at the DCDC converter input side is kind of showing that the CM mode choke is working. The only thing to avoid is to get some series resonance from the coupling capacitance and the CM choke. So one may have to use a different type CM choke, possibly even 2 in series (one for the high and one for the lower frequency range). As a simple fix some 10K in parallel to the CM mode choke may help to dampen a resonance and make it a more well behaved impedance.
The DC/DC converter should be without an internal Y cap - it does no work well with a CM choke. If at all the capacitor would be separate from before the CM-choke.

The plan shows some capacitive dropper to provide +-15 V - it can be nice, though unusual.
 
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Offline arlo_g

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Re: DIY-SMU Project
« Reply #12 on: January 04, 2021, 01:22:10 am »
Hi Dave,
Your SMU project looks great, and your progress to date is awesome.  I like your focus on keeping things DIY friendly. 

The three suggestions/comments below are in no way intended as criticism. 

The voltage sense buffer opamp inputs are protected by BAV199 diodes.  The  leakage specified by some manufacturers of these diodes might be on the high side for the 1uA range: had you considered using the base collector junctions of bipolar transistors for protection diodes, the way that Keithley was known to do?  2n3904's (and surface mount versions) are supposed to have quite low leakage, but this performance might not be guaranteed.

The photoMOS switch on the highest current range(s) will suffer from drain resistance that varies with temperature and impacts current measurement accuracy, and to a lesser extent the drain resistance of CMOS switches on lower ranges will impact accuracy too.  Had you considered adding a calibration path such as e.g. a relay from the output net (inboard of output switching relay) to a precision resistor load?   Something in the 100-200 Ohm range would give good readback voltage resolution to estimate the total shunt resistance in the 100mA and 10mA ranges.    I see now that switches U17.1 - U17.4 on your schematic neatly sidestep the current shunt switch resistance by connecting the instrumentation amp inputs across the shunt resistors.

I think that your choice to drop current ranges under 1uA to keep things manageable makes a lot of sense.  Take the following suggestion as an idle thought experiment:  could the leakage of CMOS switches be managed for lower current ranges by using a t-network of three switches with one of them driving the intersection of the three to guard potential when the other two are open?  I think that this would cut channel leakage currents from the switches down by a large factor as the switch to the output net would have ~0V across its channel. Of course this wouldn't do much to reduce leakage in ESD diodes internal to the switches, substrate diodes, package material (and gate leakage?  hopefully the switches are in a process with thick enough oxide that this isn't significant) etc.

« Last Edit: January 04, 2021, 10:53:50 pm by arlo_g »
 
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Online Kleinstein

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Re: DIY-SMU Project
« Reply #13 on: January 04, 2021, 08:32:02 am »
The leakage current for the transistor junctions is not guaranteed - similar to the BAV199: typically very low, but not tested to a very strict level. Chance are the typical leakage is better with the BAV199.  so there is nothing gained from going from one untested part to another. The often best bet for tested low leakage may be 2N4117-4119, but these are not really cheap. The cheap plastic version is usually not tested to a strict value either.
 
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Offline djerickson

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Re: DIY-SMU Project
« Reply #14 on: January 05, 2021, 06:10:43 pm »
BAV199's are pretty good for low leakage, particularly at low voltages. Where the leakage really matters, I try to run them at lower voltages, such as by bootstrapping to the op-amp output.  If I *have to* I can select them. If I remember correctly, Phillips, (now NXP) has slightly better specs. I'd be interested in seeing any data on low leakage alternatives such as bipolar transistors or FETs.

T-network for switches, what a good idea! I remember that trick from the good-old-days as a solution to high frequency leakage, but sure, why not DC leakage?

Dave

 

Offline MLNSLM

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Re: DIY-SMU Project
« Reply #15 on: January 05, 2021, 08:30:12 pm »
Hello David

I have currently been working on a simple SMU myself.
I'm having some problems with overshoot when current-clamping.
I have looked at your schematics, the ones of Keithley etc. and some others but just can't seem to get the grip of it.
Now that I've read that you've done some simulations in LTSpice, I am kindly asking you (as the chinese would say) to share them with me/us? Maybe I can figure something out then.

Cheers and Nice Work!
 

Offline djerickson

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Re: DIY-SMU Project
« Reply #16 on: January 07, 2021, 11:35:19 am »
Sure, I just added the PSPICE simulation .ASC (schematic) file to the .zip file at:
http://www.djerickson.com/diy_smu/files/DIY_SMU_Files.zip
It simulates constant voltage with current clamping. You'll need to change it for Constant current.
The amplifier and crossover models are pretty complete. The voltage - sense amplifier has its own floating power. I'm not sure how to simulate that so I used a behavioral model for it.
Let me know if the simulation doesn't work.
Good luck!
Dave
« Last Edit: January 07, 2021, 11:48:14 am by djerickson »
 

Offline macaba

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Re: DIY-SMU Project
« Reply #17 on: January 08, 2021, 03:59:03 pm »
This is looking fantastic so far, I look forwards to seeing more.

Meanwell is worst for CM noise and doesn't like the CM choke.  Tracor and Recom are best. CUI is in the middle.

I'd be interested to see some numbers alongside part numbers for these, even if it's just relative.

 

Offline djerickson

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Re: DIY-SMU Project
« Reply #18 on: January 09, 2021, 01:18:07 pm »
I ordered a handful of different DC-DCs and will test them when they arrive next week.
Dave
 

Offline jbb

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Re: DIY-SMU Project
« Reply #19 on: January 10, 2021, 11:28:24 pm »
Hi there

Glad you’ve brought this to the EEVblog forum. An SMU is one of those pieces of gear which is very useful but often too expensive. Having a DIY offering is great.

The crossover design is clearly very important. I was really pleased to see your crossover design because it’s really clear how it’s meant to operate and separates the control dynamics from the separate force and clamp circuits.

(I also really liked the output buffet/disconnect for the 2Q power supply on your site. Very nice approach.)

I see the +clamp and -clamp opamps have anti-windup diodes which should help the force -> clamp transition. Do you have any anti-windup on the force opamp to help with the clamp -> force transient? (I had a poke around in LTSpice and found that the basic ‘just add Back to back Zeners’ concept is a no go because their leakage current wrecks the DC accuracy.)
 
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Offline djerickson

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Re: DIY-SMU Project
« Reply #20 on: January 11, 2021, 02:14:52 pm »
Regarding the crossover: The original Keithley 236 crossover design is quite nice for 1990 technology. I discuss it on my web site. For greater detail, read (expired) Keithley Patent 5,039,934, a nice education on crossover design.   A big advantage of it is that it uses one integrator for both current and voltage, good to avoid integrator wind-up.  I talk about it at length. The precision, fast error op-amps before the integrator switch very quickly (microseconds) using a simple precision diode circuit.

I think the disadvantage of using a single integrator is that your voltage and current loops need to have similar loop gains in order to have good dynamic response on both.

While at Teradyne, I learned of a different but similar crossover. It used fast comparators and an R-S flip-flop to switch the error voltages into the integrator, and with hysteresis.  I wonder if they used this more complex approach to avoid the Keithley patent.

My 3 op-amp crossover approach assumes that DACs are cheaper (it uses 3 DACs  vs. 2) and provides fully independent control over the HI and LO clamp levels. I see this as a useful feature. I tested this circuit a few years ago on my PS-Load project (2-4 quadrant power supply) and was happy with its performance.

Thanks,
Dave
 

Online Kleinstein

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Re: DIY-SMU Project
« Reply #21 on: January 11, 2021, 02:53:04 pm »
The same loop gain is not the problem with using a single integrator. One can adjust the gain of the voltage and current channels before one combines them. The difficulty comes if the regulator is more than a simple integrator  - the ratio of an additional proportional would be fixed. Possible differential parts would likely be added before the signals are combined.
 

Offline arlo_g

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Re: DIY-SMU Project
« Reply #22 on: February 11, 2021, 02:18:50 am »
Here are a couple more ideas around the SMU design that might or might not be useful.

1. Guarded cabling: high performance SMU's from the big test equipment players use triaxial connectors to maintain a coaxial guard around output signals and a coaxial shield at safety ground potential. The Trompeter TRB style connectors used by Keithley and HP/Agilent/Keysight are quite expensive. Coaxial guarded connectors and cabling would provide much of the low current performance, but exposed outer conductors on connectors would be a serious safety concern when driven to way beyond the usual 42Vdc safety limit by a SMU.

FAKRA connectors, a plastic shrouded connector family based on SMB coax connectors, might be an inexpensive and safe choice for guarded SMU cabling. These mostly seem to have gold plated center conductors, but nickel or worse plating on the outer conductors so they might only be as good as BNC connectors at best in terms of thermocouples on the guard connection. I have yet to handle a FAKRA connector though, so it could be that the plastic shrouds are really unpleasant in use, and the 100 connection cycles claimed by some manufacturers might be optimistic. Anyways, all of this guarding stuff probably only matters for currents <<1nA.

2. Class G variation on the output stage. Keithley's 237 and more recent SMU's use class G topologies in their output power amplifiers to reduce power dissipation (and also to support higher current at low voltage ranges).  There is a supply connection that is already available in your SMU design, Dave, that allows the maximum amplifier power dissipation to be halved: the output common.  I sketched out an output amp stage in LTspice that demonstrates the idea, see schematic below. Ground symbols in that highly simplified testbench represent the output common of the real SMU. For the simulated case of -100mA constant current load, M4 dissipates the bulk of the power for -150V < Vout < 17V and M3 takes over from 17V < Vout <150V.  M1 and M5 behave similarly for an opposite sign of load current.

Note that I have only run DC sweeps on this circuit, and a lot of component choices are far from careful.  There are no gate protection diodes, no caps for dynamic gate drive, the gate biasing resistor values are suspiciously low and my transistor selection consisted of grabbing the first FET's and BJT's that I saw in the LTSpice library that had roughly the right max Vds/Vceo.

Connecting the amplifier "supply" to output common through D3 and D10 is weird, but those diodes are only conducting in quadrants where the output amp is serving as an active load. All of this class-G business might not be worth the trouble for a single channel SMU, but it could make it easier to support two channels in a box.
 

Offline jbb

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Re: DIY-SMU Project
« Reply #23 on: February 11, 2021, 04:08:58 am »
Isn’t fancy guarded cabling with triax connectors used for really low current measurement? As I recall, Dave decided not to go hunting nA for cost reasons...

On class G: that would cut down dissipation... I think some commercial SMUs use like +-30V rails in there to get a low-V higher-I range too.
 

Offline wizard69

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Re: DIY-SMU Project
« Reply #24 on: February 13, 2021, 03:52:03 am »
I'd like to introduce my DIY Source-Measure Unit SMU project. http://www.djerickson.com/diy_smu
Youtube intro: https://youtu.be/B26SW3N2zoA

[attach=1]

It seems fundamental to have an accurate source for a wide range of voltages and currents, with the ability to measure both.  Source and measure are basic requirement for electronics test and measurement tasks and many scientific applications. This functionality should be available at a reasonable cost.
I'm with you there.    I would have been happy with a voltage only SMU and frankly one that does ±24VDC would have been fine.   In fact I'd love to see a precision voltage SMU that effectively is a USB dongle.   I'm not even sure that sort of functionality can even be squeezed into a dongle.
Quote
I worked on many DC and AC source / measure instruments for a number of industry leaders (Analogic Test and Measurement group, Teradyne DC Instruments group, Zoll and HP Medical) plus numerous startups and home projects. I always wanted to build a DIY Source Measure Unit: SMU.
Looks like you have an incredible work history.
Quote
Recognizing that this is a challenging project for DIY, now in retirement I finally have the time to develop the hardware, software, controls, and packaging. Fortunately the nerd stars are aligned for such a project. Precision 0.1% and better SMT resistors are readily available at low cost. Precision amplifiers, switches, ADCs and DACs are low cost and easy to apply. Digital isolators and DC-DC power supplies are small and readily available. Hand-built SMT is available and easy to DIY. Single chip CPUs and TFT LCDs with touch are powerful, low cost and DIY friendly.
Plus somebody in China will rip off the design, build it with cheap or slave labor and sell it for half what we can buy the parts for.   

By the way I'm not a big fan of Touch screens on instrumentation.   Just a personal thing.
Quote
I pored through old Keithley documents for their 220/240 series sources, and 236 and 237 SMUs and found their general architecture to be flexible and very capable. I suspect that most modern SMUs share the Keithley 236 general architecture.

So after a few years of planning and a year of detailed design, layout, and build, here is DIY-SMU.
   Voltage source and measure from tens of microvolts to +/- 150V in 3 ranges: +/- 1.5V, +/- 15V, +/- 150V
   Current source and measure from nA to .1 Amp in 6 ranges: 1uA to 100mA
   True 4-quadrant operation
   Source accuracy .01%
   Measure accuracy .005%
   Graphic LCD with touch screen
   Small, half-rack 2U package
   DIY friendly and low cost
Half rack is good but I wonder if 1/3 rack is possible.    Bench space is always an issue.   Beyond that I'd prefer good support for computer communications than anything else.   You still would need voltage and current displays on the front panel but a computer connection would be nice.   Bluetooth is probably asking too much.
Quote
It is not complete yet, and I plan to continue the project this winter. PC boards are built and working. An initial GUI is working.  It has a basic enclosure. My web page discusses the idea, requirements, design, and implementation. Check it out at www.djerickson.com/diy_smu

Thanks,
Dave Erickson

Thanks Dave!   I will have to check out your web site in the future.   It is already late and I need to dig out my truck tomorrow.

In any event this sounds like a most interesting project.   It is something that could be very useful.    What is nice is that I learn something new every time I tune into such threads, even if I never build it, I gain.   
 


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