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How to build a 4 quadrant bench power supply, aka “poor man’s source measure unit”

NOTE: This document (currently) only contains unstructured research material. Might be useful for others.

Disclaimer: I’m an electronics newbee. Findings, solutions, suggestions, conclusions made in this document should not be viewed as accurate or even correct. They are mainly for my own use, learning and reference.

Introduction

I started out with a wish to have a power supply with both positive and negative voltages. You can get that by connection two “normal” supplies together. But you don’t get seamless transitions from – to +. Cheap and mid-range commercial bench power supplies also tend to have low accuracy in the lower range (uV and uA). You might find a general accuracy of 0.05%. That’s not bad, except when you start looking into detailed spec it’s often also a +2 to +4mV/mA offset to account for at the lower range.

A also want an electronic load. I then though about combining a power supply with an electronic load (sink and source capabilities) and soon found out that we’re now talking about a four quadrant supply. Add precision and dynamic range to this and you have a source measure unit.

When you combine seamless transition from + to – as well as both sink and source capabilities, the number of commercial offerings are dramatically reduced. Add accuracy and dynamic range to the equation it gets (very) expensive as well (for example Keithley 2450 smu)

Is it possible for a newbe to design and build a device like this? Or at least something similar with a bit less precision ?

  • Continuous adjustable between -30V(or -25V) to +30V(or 25V), with some simple sweep functions
  • 1-2A source and sink capability
  • Adjustable current limit (constant current)
  • 4-5 digit measurement precision for both volt and current (ultimate goal: 6 1/2 digits). Accuracy probably not very good in the first versions, especially in the extreme ends (requires stability and calibration)
  • Low offset down to 1mA / 1mA (ultimate goal: 100uV and 100uA)
  • 5″ color capacitive touch LCD display with numbers and graphs (https://github.com/hellange/poor-mans-smu)
  • Some physical knobs

A kind of four quadrant Keithley 2280s. It could be a “poor man’s source measure unit“. I accept that the first versions probably will have way lower accuracy.

My four quadrant endavour started out with a LT1970 (which was the closest I find for a IC supporting four quadrants), tried to learn how it works, identify it’s limitations and see if I can create a more “discrete” circuit without all of it’s limitation.

I’ll try to keep it as simple as possible. I want to understand each part of the design. I’ll rather replace multiple components with a single component even if it’s more expensive. Hopefully I won’t need too much advanced analog wizardry. Initially, some parts might end up as overkill. Some parts might unstable/inaccurate and not the ideal for the job.  Let’s find out… It’s part of the fun… Main goal is to learn about:

  • High precision analog circuits
  • How to achieve high accuracy
  • Stability (also long term)
  • High current (>500mA) using discrete output stages
  • PCB design
  • Combo of software and hardware

The display part is easy, I’ve done a lot of research on 5-7″ capacitive touch displays before (you can read more about that in the ‘display’ categories of my blog entries )

4 quadrant

Diagram ( from https://www.eevblog.com/forum/projects/simple-4-quadrant-psu-with-remote-sense-please-recommend-topologyschematic/ ):

Screen Shot 2018-08-28 at 16.00.03

Control loop

How Does a Power Supply regulate It’s Output Voltage and Current? “…To accomplish this most all power supplies have separate voltage and current feedback control loops to limit either the output voltage or current, depending on the load. To illustrate this Figure 1 [below] shows a circuit diagram of a basic 5 volt, 1 amp output series regulated power supply operating in CV mode.

loop

Seems like a lot of power supplies use variants of this conceptual model where the control of voltage is “OR”ed with the current control using diodes or transistors. The question is how this will work when you add an additional negative current limiter. Then the voltage and negative current control loop will “fight” each other… Who is under control ? How to obtain stability ? One of the first parts I want to learn about is how to design a stable and accurate control loop.

From LM12/LM318 Application Note 446 A 150W IC Op Amp Simplifies Design of Power Circuits “External current limit can be provided for an op amp as shown in Figure 19. The positive and negative limiting currents can be set precisely and independently down to zero with potentiometers R3 and R7. Alternately, the limit can be programmed from a voltage supplied to R2 and R6. The input controls the output when not in current limit. This is just the set-up required for an operational power supply or voltage-programmable power source“:

Screen Shot 2018-04-11 at 14.12.56

The power op amp, A4, is connected as an inverting amplifier. Its output current is sensed across R10. This sense voltage is level shifted to ground by A3, a differential amplifier that is made insensitive to the op amp output level by trimming R9. With current below preset levels, the outputs of A1and A2 are clamped by D1 and D2 with Q 1 and Q2 turned off. When the current threshold is reached, the relevant amplifier will come out of clamp, saturate the transistor on its output and take over control of the summing node. The clamp diodes limit the swing on the outputs of the current-control amplifiers while the transistors disconnect frequency compensation until the summing node is engaged. This ensures fast activation of current limit. Recovery back to voltage mode is also fast. The LM318 wideband amplifier is required for A1 through A3.”

According to a post in eevblog forum: “…Q1 and Q2 work as analogue switches, connecting a compensation RC network when either of the two current limit opamps is engaged…”

Relevant power supply related projects

There are a lot of power supply projects out there. Mostly single quadrant variants, but there is a lot to learn from them.

EEZ H24005 BENCH POWER SUPPLY (Arduino Shield for programmable DIY bench power supply with SCPI support).

eez_h24005_front_panel

Lots of design discussions on eevblog forum: DIY SCPI programmable dual channel bench PSU 0-50V/3A (now EEZ H24005) From arduini.cc: https://create.arduino.cc/projecthub/prasimix/diy-programmable-scpi-bench-power-supply-5e59d5. Consolidated pdf: https://github.com/eez-open/psu-hw/blob/master/Consolidated/EEZ%20PSU%20consolidated%20r5B13a.pdf

Screen Shot 2018-03-21 at 15.24.55

http://www.eevblog.com/forum/projects/diy-bench-power-supply-psl-3604/

PSL-3604_view (1)

http://www.eevblog.com/forum/beginners/mosfet-linear-regulator-circuit/

http://www.djerickson.com/ps-load/ Power Supply / Load or 2/4 quadrant voltage current source/meter design proposal

Screen Shot 2018-08-23 at 12.57.27

http://wahz.blogspot.nl – lab power supply Tom Biskupic goes through his power supply project from A to Z, learnings and mistakes. Very useful! Code etc. on github. “What I  really wanted was one of those Rigol DP832. Of course I could buy one but given I an am using this supply to learn about electronics it seemed a perfect opportunity to build one!…

https://gerrysweeney.com/fully-programmable-modular-bench-power-supply/ “back to the regulator stability topic, I have removed all the capitative loading around the driver and output circuit and instead reduced the bandwidth of the control loop by including frequency-dependnat negative feedback on both the voltage and current error amps. The aim was to significantly lower the gain of the loop above the point where the feedback becomes positive and the servo action becomes unstable….

Dave Jones uSupply

Dave jones uSupply, schematics (Rev B ,   Rev C). Current control uses filter 1uF/ 330R = 480Hz? at the output of the current sense (MAX4080T) which helps reducing noise. (Rev C replaces MAX4080 with “discrete” op amp diff amp and output filter changed to 0.1uF / 1K =15KHz? cutoff) Also uses a transistor to draw the output low in case of current limit. Instead of output from op-amp and diode.

Both revisions also use filter in the input of the voltage regulator (22uF) to “stabilize” the circuit.

Rev C is an update of rev B. It basically saves a lot of components (read: cost). For example: Replacing uCurrent and MAX4080 with INA219 and discrete op-amp based differential amplifier, replaced AD/DA to save cost and pins (more info in EEVblog #259 – PSU Rev C Schematic – Part 12 ).Now powered by only two li-ion batteries. Downside is a slight reduction in precision (10bit).

Screen Shot 2018-03-15 at 15.34.39

Rev B:

Screen Shot 2018-03-15 at 15.34.28

https://www.eevblog.com/forum/projects/lab-powersupply-markus-take/

Variant of Daves uSupply: http://www.instructables.com/id/Digital-Battery-Operated-Powersupply/

Ian Johnson

Project #021 – Home Built Bench Power Supply Schematics: http://www.ianjohnston.com/images/stories/IanJ/PowerSupply/BenchPsuSchematic.pdf

(Note also that Ian has designed (and sell) a precision programmable voltage reference Handheld Precision Digital Voltage Source – PDVS2) that can be a very useful tool.

Peter Oakes

https://www.element14.com/community/groups/test-and-measurement/blog/2014/09/15/the-modular-bench-power-system-the-essential-diy-build-for-every-ee-student-and-old-timer-alike

Screen Shot 2018-03-06 at 09.14.39

kerrywong

A Digitally Controlled Dual Tracking Power Supply

Screen Shot 2018-03-09 at 23.23.43

lt1970a

http://cds.linear.com/docs/en/datasheet/1970afc.pdf

Some limitation of lt1970 is that it cannot set current limits lower that apprx. 4mA. The current limit in general is only within 1%. Output current is max 500mA but requires careful PCB layout to dissepate heat. By adding output stage current can be 5A, but the lowest current limit will then be apprx. 40mA with a 0.1ohm shunt resistance.

It’s absolute current limitation seems to vary with load (must be verified). However, it’s a good candidate for a prototype, or a “VERY poor man’s smu”…

Block diagram:

Screen Shot 2018-01-02 at 08.16.02

4 quadrant power supply example from: EDN (2004):

Screen Shot 2018-08-28 at 16.05.53

More 1970 related design info in the online version of Electronic Circuit Design:

Screen Shot 2018-09-06 at 09.40.03

EasySMU

EasySMU is a single-channel ±12V/±40mA programmable-voltage/programmable-current source with accurate voltage/current measurement capability. DC2591A shows a demo application that uses 1970a even though the primary purpose of the EasySMU is to demonstrate the LTC4316 I2C address translator.  “EasySMU is a single-channel ±12V/±40mA programmable-voltage/programmable-current source with accurate voltage/current measurement capability

Screen Shot 2018-09-06 at 10.04.49

An interesting note about the gain resistor network: “Since the LT1970A power dissipation varies based on loading and output settings, most discrete resistors would exhibit mismatch as the PCB temperature gradients change. The LT5400-3 matched resistor network eliminates this mismatch.”

DC2132A is a high performance, compact, efficient DC bench supply

High Performance Portable DC Bench Power Supply: Save Money and Free Up Bench Real Estate by Building Your Own (2014)

dc2132a

The LT3081’s unique current-source reference and voltage-follower output amplifier make it possible to connect two linear regulators in parallel for up to 3A and over 24V of adjustable current and voltage output control. Linear regulators at the output suppress output ripple without requiring large output capacitors, resulting in a truly flat DC output and small size.” Also look at the discussion here: https://www.eevblog.com/forum/projects/linear-technology-dc2132a-cvcc-adj-bench-power-supply-board/

Relevant commercial power supplies (4 quadrant, SMUs or sink-capable)

The subsections below is a collection of relevant documentation for several commercial available supplies.

Keysight 66332A and 663xB

These are power supply that also contains “active downprogrammer [that] can sink up to the full rated current of the power supply, which quickly brings the power supply output to zero volts.“. Service manual Keysight 66332A Dynamic Measurement DC Source and Keysight Models 6632B, 6633B, 6634B System DC Power Supply

(but not negative voltage ?)

Principle of operation:

Screen Shot 2018-03-06 at 09.05.17

The CV/CC control circuits provide a CV control loop, a positive CC control loop, and a negative CC control loop. For any value of load resistance, the supply must act either as a constant voltage (CV) or as a constant current (CC) supply. Transfer between these modes is accomplished automatically by the CV/CC control circuit at a value of load resistance equal to the ratio of the programmed voltage value to the programmed current value. The negative CC control circuit is activated when a current source such as another power supply is connected across the output terminals and its voltage is greater than the programmed voltage. A low level CV_Detect*, CC_Detect*, or CCN_Detect* signal is returned to the secondary interface to indicate that the corresponding mode is in effect.

When the CV loop is in control, diode D328 is conducting current. Voltage regulation is accomplished by comparing the programmed voltage signal CV_Prog with the output voltage monitor signal Vmon. The Vmon signal is in the 0 to +5 V range, which corresponds to the zero to full-scale output voltage range of the supply. If the output voltage exceeds the programmed voltage, Vmon goes high and produces a more negative-going CV signal, which reduces the input to the voltage gain stage and lowers the output voltage. Conversely, if the output voltage is less than the programmed voltage, Vmon goes low and produces a more positive-going CV signal, which increases the input to the voltage gain stage and raises the output voltage. Depending upon the position of the sense switch, the output voltage is either monitored at the supply’s output terminals (local), or at the load (remote) using the +S and -S terminals with remote sense leads connected to the load. If the output voltage goes higher than the programmed value, the unit starts sinking current to reduce the output voltage.

When the CC loop is in control, diode D325 is conducting current. Current regulation is accomplished by comparing the programmed current signal CC_Prog with the output current monitor signal Imon_H. The Imon_H signal is produced by measuring the voltage drop across the current monitoring resistor and is in the 0 to +5 V range, which
corresponds to the zero to full-scale output current range of the supply. If the output current exceeds the programmed current, Imon_H goes high and produces a more negative going CC signal, which reduces the input to the voltage gain stage and lowers the output current. Conversely, if the output current is less than the programmed
current, Imon_H goes low and produces a more positive-going CC signal, which increases  the input to the voltage gain stage and raises the output current.

When the supply is sinking current, only the CV control circuit or the CCN control circuit can be active. In this case, the supply is acting as a load instead of a power source and will attempt to pull the output voltage down by drawing off current from the externally applied source. The current that will be drawn from the externally supplied source is
determined by the CC_Prog signal. When the current required to reduce the voltage is less than the programmed current value, the CV control circuit is active and regulates the output voltage. When the current required to reduce the voltage exceeds the programmed current value, the CCN control circuit is active. It regulates the output current by comparing the negative Imon_H signal to the inverted CC_Prog signal.

The service manual also contains full schematics.

Keysight 228A

The Keithley 228A is capable of bipolar source or sink (4 Quadrant Operation) up to a full 100 watts without derating, permitting it to act as a voltage or current supply or as an active load.

Schematics from Service Manual snapped from doc.xdevs.com :

Screen Shot 2018-04-12 at 07.57.08

The control loop is at the left hand side of the schematics. “U103A supplies a signal which drives the output in the polarity programmed by the operator. Comparators U106 through U109 supply a signal which balances the signal from U103A when the output approaches a programmed limit. The *voltage limits are set with a zero to +l.OlOV signal from the voltage DAC (Vdac) UllO. The acronymn DAC means Digital to Analog Converter. The 4current limits are set with a zero to + l.OlOV signal from the current DAC (Idac) Ulll. The positive limits (U107 and UlO9) are sensed by comparing the (DAC voltage) with the (feedback voltage) and attempting to keep feedback voltage less than or equal to the DAC voltage. The negative limits (U106 and U108) are sensed by comparing the (DAC voltage + feedback voltage) with ground and attempting to keep (DAC voltage +feedback voltagekgreater than or equal to zero or – (feedback voltage) less than or equal to (DAC voltage). Refer to Figures 6-3 and 6-4.

Seems to be using a summing amplifer from voltage and current measurement amplifers. Not using the diode-or concept I’ve seen in a lot of other devices?  Investigate…

Keithley 236

236

The 236, 237, and 238 Source-Measure Units (SMU) are fully programmable instruments, capable of sourcing and measuring voltage or current simultaneously. Link to Operators manual. The Service manual on Keithleys website does not contain full schematics. This one does: http://www.ko4bb.com/getsimple/index.php?id=download&file=06_Misc_Test_Equipment/Keithley/Keithley_236_237_Source_Measure_Unit_SMU_Service_Manual_and_schematics.pdf (thanks: https://www.eevblog.com/forum/testgear/keitley-236-teardown-and-review/ )

Block diagram (from the service manual) of the control loop:

Screen Shot 2018-08-24 at 10.13.06

Description from service manual: “Programming current and voltage sets the output voltage of the two digital-to-analog (DAC) circuits. Program ming current controls the output of the I DAC (U23 and U22), and programming voltage controls the output of the V DAC (U25 and U24). Programming current or voltage for zero output will result with a 0V output from the respective DAC. Programming for a full scale output will result with a -40V output from the respective DAC.

The output voltage from the I DAC is applied to current clamps through resistor networks. Op amp U13 and diode CR11 form the negative current clamp (-I CLAMP). The output from the I DAC is inverted by the xl amplifier U50. Op amp U17 and diode CR10 form the positive cur rent clamp (+I CLAMP).

The output from the V DAC is inverted by the x1 amplifier U12 (xO,1 for the 1.1V range) and similarly applied to current clamps through resistor networks. Op amp U15A and diode CR12 form the positive voltage clamp (+V CLAMP). The inverted output of U12 is again inverted by U19. Op amp U15B and diode CR9 form the negative voltage clamp (-V CLAMP).

During operation, only one of the four precision clamps will be on at one time to control the error amplifier (U14). The controlling function and the programmed polarity (+ or – ) will determine which clamp is on.”…

DAC used are  14 bit current output AD7538 from Analog Device (I’m a bit surprised it’s only 14 bit…). There are LT1007s at the DAC outputs. In the control loop, the voltage clamps use LT1057 and the current clamps use  AD744. Why are they different ?

Control loop schematics:

236

For larger version, check the end of the PDF service manual or a resized version I’ve checked into github.

Keithley 2400 smu

The Keithley 2400 smu output stage have multiple voltages. This is in order to avoid too much heat dissapation when large current and high voltage difference between supply voltage and output voltage.

2400_output_stage

Take a look at the Dave Jones  eevblog teardown: https://www.youtube.com/watch?v=DJ2nzvX2gBc. It uses AD847 as driver op-amp(?) for the output stage. This is a +/-15V device. That probably? means the the transistor output stage has gain. To keep complexity low, I plan to have no voltage gain in the output stage. This means that the +/-15V probably is a bit on the low side… Learn more…

Screen Shot 2018-02-02 at 14.28.05

Other devices used: AMP03(Precision, Unity-Gain Differential Amplifier), nais v214s solid state relay, AD7849 DAC, LT1112(Dual/Quad Low Power Precision, Picoamp Input Op Amps). Keithley Model 2400 review and VFD repair also have teardown details

Theory of operation (from 2400 service manual): “D/A converters control the programmed voltage and current, or voltage compliance and current compliance. Each DAC has two ranges, a 10V output or a 1V output. The DAC outputs are fed to the summing node, FB. Either the V DAC or the I DAC has the ability to control the main loop. If the unit is set for SV (source voltage), it will source voltage until the compliance current is reached (as determined by the I DAC setting), and the current loop will override the voltage loop. If, however, the unit is set for SI (source current), it will source current until the compliance voltage is reached (as determined by the V DAC setting), and the voltage loop will override the current loop. A priority bit in the Vclamp/I clamp circuit controls these functions. The error amplifier adds open-loop gain and slew-rate control to the system to assure accuracy and provide a controllable signal for the output stage, which provides the necessary voltage and current gain to drive the output. Sense resistors in the HI output lead provide output current sensing, and a separate sense resistor is used for each current range. The 1A range uses 0.2V full-scale for a full-range 1A output, while all other ranges use 2V output for full-scale current. Voltage feedback is routed either internally or externally

2400_analog_block

There are four voltage ranges: 0.2V, 2V, 20V, and 200V. The feedback gain changes for only the 20V and 200V ranges, resulting in three unique feedback gain values. A multiplexer directs the voltage feedback, current feedback, reference, or ground signal to the A/D converter. An opto-isolated interface provides control signals for both DACs, analog circuit control, and A/D converter communication to the digital section.

Agilent B2912A Source Measure Unit SMU

Agilent B2912A Source Measure Unit SMU Teardown: https://www.youtube.com/watch?v=pKX50E_14MQ AD8208 current sense, 30N06 N-channel mosfet (60V 30A), ixta10p50p P-channel mosfet (-500V 10A), ISO7240A optoisolator, fds8978 mosfet for switching? (optimized for low gate charge, low rDS(on) and fast switching speed), .. LM399 reference, OPA1611 (ultralow noise and distortion op-amp), ISO7240 and ISO7242 isolators, ADS1675 (24 bit delta-sigma precision ADC), AD8676 (precision op-amp with offset 12 μV, drift 0.2 μV/°C, noise 0.10 μV p-p), ADG413 and ADG452 switch, 8N60C output N channel mosfet, ADS1675 24bit ADC: http://www.ti.com/lit/gpn/ads1675,

Here is a screeenshot from Dave Jones video showing current shunt and the switching mosfet. Could it be the same arrangement as in http://www.imc-berlin.com/fileadmin/Public/Downloads/Whitepapers/eng-WPs/WP_Current_measurement_with__Auto-Ranging.pdf ???

Screen Shot 2018-01-11 at 08.45.07

Screenshot from the output stage:

Screen Shot 2018-01-11 at 09.13.52

Screen Shot 2018-01-25 at 15.15.54

Screen Shot 2018-01-25 at 15.21.14

Screen Shot 2018-02-01 at 09.23.50

Screen Shot 2018-02-16 at 08.35.42

Agilent N3304A

Schematics (PDF) for N3304A 300 Watt Electronic Load Module linked to from a eevblog forum entry: http://www.eevblog.com/forum/projects/diy-bench-power-supply-psl-3604/?action=dlattach;attach=206857.

Hameg HM8142 (two quadrant only)

Service manual with schematics https://docs-emea.rs-online.com/webdocs/0296/0900766b80296cf9.pdf. Note that a french version also contains a short one page very high level description of the operating principle (https://drive.google.com/file/d/0Bxd9xq3tnxpiNWxueGQ5blpsZDg/view)

Programmable voltage references/sources

Using programmable voltage references can also be handy when experimenting with circuits. A lot can also be learned about how to design stable and accurate circuits, an important part of a Poor mans’s SMU. Here are a few:

Ian Johnstons Handheld Precision Digital Voltage Source – PDVS2 “A handheld Precision Digital Voltage Source, true 0.0000V to 10.0000Vdc range, battery powered…an accuracy/stability down to the uVs it has a multitude of uses as a calibrator, reference & precision voltage source. ”  Uses 18bit DAC9881 and LM399.

PDVS2_1

A lot to be learned in Ian’s informative 3 part video starting here: https://www.youtube.com/watch?v=2Ssg05oFCbk&t=940s.

https://www.barbouri.com/2016/07/21/programmable-voltage-reference-v2-12-assembly/ “A precision programmable voltage reference circuit capable of 0.001 to 4.095 volt output in 1 mV steps with an accuracy of 100 uV.

ProgramableVoltageReferenceV2.12BothSide01-1024x425

High Precision Voltage Source (2017) “…showcasing an ultrahigh precision programmable voltage source using ADI/LTC products together. The AD5791 with the LTZ1000ADA4077, and AD8675/AD8676 can be used to provide a programmable voltage source that achieves 1 ppm resolution with 1 ppm INL and better than 1 ppm FSR long-term drift.

Screen Shot 2018-09-07 at 08.21.07

Scullcom Hobby Electronics – DC Voltage Calibrator  “In this project we will design and build a DC Voltage Calibrator, providing a voltage range from 0 to 10 volts in 1 milli volt steps. The user interface will be a TFT display with touchscreen.

sculldom

Design considerations

Unstructured collection of theory, construction ideas/principles, component selection etc…

Stability before absolute precision ?

Modern meters use precision reference, low temperature coefficient and then software calibration. Not necessarily high PRECISION (such as 0.01%) parts. For example if you know the gain of some stages are STABLE, you can design the electronics so that you can measure absolute gain in software. As long as your circuit allow for “setting up” the circuit for (auto)calibration. Ref (https://youtu.be/oXX6GhhoJls?t=821). ….add more on software calibration…

Interesting reading:  download.tek.com/document/LowLevelHandbook_7Ed.pdf

Precision, accuracy, resolution

I tend to mix the terms accuracy and precision. According to Fluke :

Precision: An instrument’s degree of repeatability—how reliably it can reproduce the same measurement over and over.

Accuracy: An instrument’s degree of veracity—how close its measurement comes to the actual or reference value of the signal being measured.

Resolution: The smallest increment an instrument can detect and display—hundredths, thousandths, millionths.

Counts and digits are terms used to describe a digital multimeter’s resolution. Today it is more common to classify DMMs by the total counts than by digits.

  • Counts: DMMs that offer higher counts provide better resolution for certain measurements. For example, a 1999-count multimeter cannot measure down to a tenth of a volt if measuring 200 V or more. Fluke offers 3½-digit DMMs with counts of up to 6000 (meaning a max of 5999 on the meter’s display) and 4½-digit meters with counts of either 20000 or 50000.
  • Digits: The Fluke product line includes 3½- and 4½-digit digital multimeters. A 3½-digit DMM, for example, can display three full digits and a half digit. The three full digits display a number from 0 to 9. The half digit, considered the most significant digit, displays a 1 or remains blank. A 4½-digit DMM can display four full digits and a half, indicative of higher resolution.

Precision and drift

Minimize Voltage Offsets in Precision AmplifiersVoltage-offset errors in precision amplifiers are partly caused by input bias currents. This article analyzes the problem and proposes a solution based on resistor networks, both discrete and integrated.

OPA388 Ultra-Low Offset Voltage: ±0.25 µV, Zero-Drift: ±0.005 µV/°C

http://www.eevblog.com/forum/metrology/t-c-measurements-on-precision-resistors/

Resolution

Theoretically resolution based on DAC/ADC bits:

16bit = 1/(2^16) = 1/ 65536 = 0.00001525…   @1V = 15.25uV @5V= 76uV

18bit = 1/(2^18) = 1/ 262144 = 0.00000381… @1V = 3.81uV @5V = 19uV

Already here we see that in order to obtain total 100uV resolution, we must change the max voltage used for low range measurements…  If using 16bits converter.

In practise, this is probably NOT possible to achieve. There are probably other part of the design that will contribute more to offset and noise. If not, we might increase resolution. later.

Accuracy

What is counts vs bits vs percent vs ppm ? The following table is from Understanding and Applying Voltage References (1999):

Screen Shot 2018-02-27 at 12.43.04.png

Percent (%) ppm
0.001% 10 ppm
0.01% 100 ppm
0.1% 1000 ppm
1% 10000 ppm

10ppms of 1V = 10uV ?

1ppm of 1V = 1uV ?,   15ppm of 1V = 15uV ?

Error budget

http://www.electronicdesign.com/power/whats-all-error-budget-stuff-anyhow “…many engineers in Europe were quite unfamiliar with the concept of an “error budget.” How can you design a good circuit without being aware of which components will hurt your accuracy?

https://www.edn.com/design/analog/4368505/Error-budgets-keep-your-analog-signal-path-honestSome programmers’ claims that you can calibrate out all errors in software may lull you into a false sense of security regarding the errors in your design…

Errors and Error Budget Analysis in Instrumentation Amplifier Applica AN539: “describes a systematic approach to calculating the overall error in an instrumentation amplifier (in amp) application

Screen Shot 2018-02-21 at 11.25.48

Screen Shot 2018-02-21 at 11.26.52

Self “calibration” ?

I would like to design a system so that measurement errors caused by offsets, gain nonlinearity, drift can be (to a large extent) adjusted for in software. I probable need some extra components for this, such as switches, muxes and a good reference. I still, however, want to use precision components with as low drift as possible.

DESIGN FOR SELF-CALIBRATION OF INSTRUMENTATION “In a self-calibrated measuring method the input/output relation of a measuring system is directly determined by the self-calibration algorithm with the use of the internal reference quantities and elements, and the measuring errors are self-corrected by the corresponding signal and data processing algorithms…

https://meettechniek.info/measurement/self-calibration.html (2014) “Electronic circuitry used in measurement equipment are subject to a certain deviation who influences the stability and accuracy. Offset, drift en variations in gain due to temperature changes, aging and power supply changes cause measurement uncertainties of sometimes unacceptable proportions. By making use a self-calibration circuit and protocol the accuracy of a measurement is vastly increased…

 

Maxim AP261 Calibration-Multiplexers Ease System Calibration (Maxim AppNote 261)IC switches and multiplexers are proliferating, thanks to near-continual progress in lowering the supply voltage, incorporating fault-protected inputs, clamping the output voltage, and reducing the switch resistances. The latest of these advances is the inclusion of precision resistors to allow two-point calibration of gain and offset in precision data-acquisition systems…

From reference design (Ultrahigh Sensitivity Femtoampere Measurement Platform): “To minimize any offset errors due to the ADC, an ADG1419 single-pole/ double-throw (SPDT) analog switch shorts the input of the resistor divider to ground and allows the software to measure the offset error due to the ADC and resistor divider. When offset cancellation is enabled, the software subtracts the measured offset from every reading. Any remaining offset is due only to the ADA4530-1 circuitry

From AN1711 APPLICATION NOTE SOFTWARE TECHNIQUES FOR COMPENSATING … ADC ERRORS “This document provides some methods of calibrating the ADC. Some ADC errors like Offset and Gain errors can be cancelled using these simple software techniques…

Screen Shot 2018-02-03 at 23.21.12

Improve DAC integral nonlinearity through gain correction (2011)Linearity errors are the most challenging to handle of the three since, in many applications, the user can null out the offset and gain errors, or compensate for them by building end-point auto calibration into the system design. Linearity errors, however, require more complex correction.

ADC Calibration (National Instruments, 2009) “…a method used to compensate for an internal DMM gain error, is a feature exclusive to the NI 4070/4071/4072 DMM that allows you to appropriately trade off measurement speed for long-term accuracy…

Calibrating Amplifiers and ADCs in SoCs “…in real world, there are many errors that get introduced into the system affecting the ADC’s output. The most important errors and the ones that we are going to discuss in this article are the offset and gain errors…

APPLICATION NOTE 4170 Improve Current Measurement Accuracy by Skewing the Input Offset Voltage on Current-Sense Amplifiers “…presents a method that introduces known input VOS by suitably sizing input resistors for current-sense amplifiers.

The ABCs of ADCs: Understanding How ADC Errors Affect System Performance “Offset and gain errors can easily be calibrated out using a microcontroller (µC) or a digital signal processor (DSP). With offset error, the measurement is simple when the converter allows bipolar input signals. In bipolar systems, offset error shifts the transfer function but does not reduce the number of available codes…. There are two methodologies to zero out bipolar errors. In one, you shift the x and y axes of the transfer function so that the negative full-scale point aligns with the zero point of a unipolar system….

Software calibration reduces D/A converter offset and gain errors “In reality, the accuracy of the output voltage is subject to a number of factors, including gain and offset errors from the D/A converter and from other components in the signal chain. The system designer must compensate for these errors in order to get the highest possible output accuracy.

Built-in Self-Test and Calibration of Mixed-signal Devices (2011 thesis)

Software tricks

Averaging

Oversampling and decimation (Atmel application note)By using a method called ‘Oversampling and Decimation’ higher resolution might be achieved, without using an external ADC. This Application Note explains the method, and which conditions need to be fulfilled to make this method work properly…

Measurement

Probes: Probe consideration for low level measurements

Measurement range switching

In order to obtain high dynamic range I probably need to switch between current shunt resisors. Maybe also when measuring volt. Can I get away with two ranges ? Switch using relay? or are there other ways ?   Switchin extra resistor on/off in parallell ? Or use them in series such as http://www.imc-berlin.com/fileadmin/Public/Downloads/Whitepapers/eng-WPs/WP_Current_measurement_with__Auto-Ranging.pdf:

Screen Shot 2018-01-10 at 19.40.33

Additional info about range switching in DMMs…

Switching Low-Level Signals to a DMM (National Instruments, dec 2017)  “This document will describe the fundamental principles that affect low-level measurements, which relay types best address these principles…

how-do-multimeters-auto-range-without-blowing-up-their-analog-switch

Must I use relay for the current switching, or can I use mosfets such as described here: http://www.electronic-products-design.com/geek-area/electronics/mosfets/using-mosfets-as-general-switches ?

Dave Jones explains range switch in his uSupply (direct link)

Current shunt resistor selection

Write about heat, selecting low value vs accuracy… etc…

References !!!!

Do I have to care about “burden” voltage is is that only relevant for “external” measurement ?

??? Could I have a “separate” current measurement that is floating with battery supply? Just use uCurrent configuration ? uCurrent uses 10k (nA), 10(uA), 0.01ohm(mA) with 100x gain. I don’t need nA.     0.1ohm for mA with 10x gain… ? Or just 1ohm…   100uA will then give 100uV… with 2x gain = 200uV.

When using low value current shunt to measure large currents, even the solder join makes a difference. That brings you to kelvin connections. Optimize High-Current Sensing Accuracy by Improving Pad Layout of Low-Value Shunt Resistors : “…note the 22% error associated with the solder resistance without using Kelvin sensing. This is an equivalent solder resistance of about 0.144 mΩ.”

Dave Jones explains current shunt and how to select values for gain etc. for his uSupply (direct link)

 

Current measurement

Question: Should I have two measurements, one for current limiting and one for actual “presented” current measurement ? If less precision is needed for the current limit, maybe it makes sense to separate the two. Dave Jones does that in his uSupply…

Read the Current sensing tutorial (from EET). From: A Current Sensing Tutorial—Part II: Devices :

Difference amplifier(DA) “In summary, a DA can be utilized for either high-side or low-side sensing. When used for high-side sensing, error can be introduced by the finite common-mode and differential-mode input impedances… However, a DA places a load on the system bus voltage due to its finite common-mode and differential-mode input impedances. This load draws current from the system bus voltage, which introduces uncertainty in the measurement…

Instrumentational amplifier(IA): “The first advantage over a DA is the ability to easily change the differential gain… Secondly, the inputs are connected to the non-inverting inputs of a buffer amplifier… One disadvantage: input common-mode voltage of IAs is limited by their supply voltage. Therefore, IAs typically is utilized for low-side measurements

Current sense amplifiers: “Current shunt monitors are devices that place little load on a system and allow for sensing current under high common-mode voltage conditions… typically have fixed gains. The exceptions include current output devices, which require an external precision resistor to set the gain…

Current Sense Circuit Collection (Linear Technology ApplicationNote 105, 2005) compiles solutions to current sensing problems and organizes the solutions by general application type.

Screen Shot 2018-03-12 at 08.20.14

Current Sensing Circuit Concepts and Fundamentals (AN1332)

Difference and Current Sense Amplifiers (MT-068 tutorial) “…A simple… difference amplifier can be constructed with four resistors and an op amp… There are several fundamental problems with this simple circuit…

Current Sensing: Low Side, High Side, and Zero Drift (Texas Instruments video) Info about high side measurement and what too look for in specs (from 2:45)

10uA-100mA, 0.05% Error, High-Side Current Sensing Solution Reference Design “This TI Precision Verified Design provides the theory, component selection, simulation, complete PCB schematic and layout, bill of materials, and measured performance of a split-supply, high-side four decade current sensing solution that can accurately detect load currents from 10uA-100mA.

High-Side Current Sensing with Wide Dynamic Range: Three Solutions (2010) “This article will focus on providing current-sensing solutions that can help designers accurately monitor wide-ranging dc currents in the presence of high common-mode voltages. Special attention will also be devoted to temperature performance

Calculating Accuracy in High-Side Current-Sense Amplifiers (2016) “…Determining the optimum value for the current-sense resistor (RSENSE) is crucial. Larger RSENSE values increase the series IR voltage drop and power loss, but minimize the effect of the offset voltage error…

From Choose the Right Current-Measurement Technique for Your Application :

Screen Shot 2018-02-21 at 13.53.55

“I discussed that the common-mode voltage level is critical in determining the implementation … As the maximum common-mode range increases, it typically means a reduction in the achievable accuracy. For example, Texas Instruments’ INA210 current-shunt monitor has a maximum common-mode voltage of 26 V and offers an input offset voltage of 35 µV. Input offset is one of the most important device parameters when determining measurement accuracy. Now compare the specifications of the INA210 to those of the INA283 current-sense amplifier. Its common-mode range extends up to +80 V (as well as down to –16 V), with a maximum input offset of 70 µV.”

Extending Beyond the Max Common-Mode Range of Discrete Current-Sense AmplifiersThe simplest approach to monitor high voltage highside current sensing is a design with a low voltage current sensing amplifier with external input voltage dividers, for example, if a 40V common mode voltage amplifier is selected for a 80V application, the 80V input common mode needs to be divided down to 40V common mode voltage. This voltage division can be accomplished using external resistor… …As voltage dividers has serious consequences with output error and degradation in performance, another alternative approach is to shift the ground reference of the current output amplifier to the high voltage common mode node…

Precision Current Sensing Solutions Guide Describes considerations and criteria for specification and selection of resistor, difference amp. Includes a lot of resistor details: “This solution guide provides guidance for the selection of low-ohmic components that are constructed from materials that satisfy the design requirements of precision current measurement circuits operating in environments with a high degree of temperature variation.  Guidance is also provided for selection of a high-quality difference amplifier.

Current measurement amplifier

Differential opamp vs instrumentational opamp from allaboutciruits: building-a-differential-amplifier and the-instrumentation-amplifier

Differential op amp

Precision, Low-Side Current Measurement (TI tech note)

Difference Amplifiers—the need for well-matched resistors (2012)

Use differential amplifier (with bi-directional current sense), examples:

TS1102-50EG5 ( 50x, 0.5% gain error max, 200uV offset max )…are self-powered
and feature a wide input common-mode voltage range from 2 to 27 V.
ONLY UNIDIRECTIONAL and self powered. Not for me.

INA226 ( 1x, 0.1% gain error max, 10uV offset max ), From: https://www.mouser.se/publicrelations_techarticle_curentsensemonitoring_2015final/TI INA226 is one of the highest precision current sense monitors on the market today, with an offset voltage of just 10µV and a common mode range of up to 36V.  Not for me. No analog output.

INA219B ( 0.5% gain error max, 50uV offset max ) No analog output ?

INA210-INA215 (different gains) VCM=-3V to 26V. I need better specs on negative side.

INA149 “precision unity-gain difference • Common-Mode Voltage Range: ±275 V amplifier with a very high input common-mode • Minimum CMRR: 90 dB from –40°C to +125°C voltage range”. offset:350uV, max:1100uV. Offset drift: 3µV/°C,max 15 µV/°C. ( VCM –20 to +25 when supply voltage is +/-5V. @15V VCM becomes +/-275V ) From: http://www.ti.com/lit/ds/symlink/ina149.pdf (page 15:): “…the sense resistor imbalances the input resistor matching of the INA149, thus degrading its CMR. Also, the input impedance of the INA149 loads RS, causing gain error in the voltage-to-current conversion. Both of these errors can be easily corrected… addition of a compensation resistor (RC), equal to the value of RS…  if RS is less than 5 Ω, degradation in the CMR is negligible and RC can be omitted.”. Video from TI: https://www.youtube.com/watch?v=4by0NI3Pc9g . 

AMP03AMP03 VCM = ±10 V ?

AN-1308 Common-Mode Step Response of Current Sense Amplifiers:

AD8274 Gain of ½ or 2. Offset 100uV- 500uV. Offset drift 6μV/°C (a bit high). 86/92 dB minimum CMRR . Low distortion. “Excellent gain accuracy 0.03% maximum gain error 2 ppm/°C maximum gain drift “. VCM = ±40 V. (Offset is a bit high but as long as the drift is not bad, maybe its usable with some software cal…)

(*) AD8276 Unity gain, Offset 100-500uV. Low offset voltage drift: ±2 μV/°C maximum (B Grade) Low gain drift: 1 ppm/°C maximum(0.5 – 2) (B Grade) gain drift 5ppm/C. Gain error:0.01% max:0.05%, CMRR:86 dB, VCM = ±27 V? Or is 27V too low? Alternative AD8274…  (this one looks interesting… at least for prototyping)

AD8278 Gain of ½ or 2. Offset 50uV- 250uV. Low offset voltage drift: ±1 μV/°C (0.3uV – 1uV )B grade, Low gain drift: 1 ppm/°C maximum (B Grade) 80db CCMR, VCM = ±27 V. AD8279 is a dual version. AD8278 has better spec that 8274/8276, but still only 27V VCM…

(*)AD629 B is better than A. “The AD629 is a difference amplifier with a very high input, common-mode voltage range. It is a precision device that allows the user to accurately measure differential signals in the presence of high common-mode voltages up to ±270 V.”  . unity gain. “…allows the user to accurately measure differential signals in the presence of high common-mode voltages up to ±270 V” AD629 is improved over INA117Measuring −48 V High-Side Current Using the AD629 Difference Amplifier, AD8603 AD780 Reference, and AD7453 12-Bit ADC Single-Supply ComponentsOp Amp. Offset 100uV, max: 500uV, max drift:10uV/C, Gain error:0.01mV max0.03mV. Alternative part: AD8479 : 2x wider Common-mode range, higher input impedance, lower voltage drift and gain error, with R-R Output (x2 offset…). From AN-1531:

Screen Shot 2018-02-15 at 12.42.39

The AD629 looks promising. Expensive, but I only need one.

AD8479 cm=+/-600V, “…difference amplifier with a very high input common-mode voltage range”. Gain error: 0.005mV max 0.01mV. 1mV max offset (double that of AD629).

AD8210 The AD8210 is a single-supply, difference amplifier ideal for amplifying small differential voltages in the presence of large common-mode voltages. More: http://www.analog.com/media/en/training-seminars/tutorials/MT-068.pdf. “The operating input common-mode voltage range extends from −2 V to +65 V”. Only down to -2…. Not usable for me ?

AD8207 for bidirectional current sensing applications. “The AD8207 is a single-supply difference amplifier ideal for amplifying small differential voltages in the presence of large common-mode voltage. The operating input common-mode voltage range extends from −4 V to +65 V”.  Only down to -4…. Not usable for me ?

Parametric search at TI http://www.analog.com/en/parametricsearch/11081#/p4133=Difference%20Amplifier

Instrumentation op amp

A Designer’s Guide to Instrumentation Amplifiers 2ND Edition

I believe that offset and gain linearity is important to obtain good accuracy. Some examples:

AD8230 Gain error: max 0.04%@2x/10x/100x, typ 0.01%, Vos max: 10uV, VCM = −8 V to +8 V, voltage range 750 mV, price $10. Requires external resistors for gain other than x2 ? Guess we need precision resistors… too low common mode ?

LTC6915 Gain error: max 0.075%@x1/x2, max 0.5%@2..32, typical 0%. Vos max: 10uV price $8. +/-5V supply. CM=rail-to-rail, which is too low for my application.

No current sensing examples are shown in the datasheets for instrumentationl opamps, only thermocoupler bridge. Is it overkill i my use ?  Or not suitable at all ?  Did I get something wrong ? CMRR  problem ?

PGA281: (5uV,max 20uV offset, 0.03%typ/0.15%max gain error, multiple gains) Example:10 µA-100 mA, 0.05% Error, High-Side Current Sensing

Current sense amplifiers

High-Side Current Sensing: Difference Amplifier vs. Current-Sense Amplifier (2008)

Integrating the Current Sensing Resistor

Performance of Current-Sense Amplifiers with Input Series ResistorsWhen discussing functional operation, a current-sense amplifier can be considered an instrumentation/differential amplifier with a floating input stage. This means that even when the device is powered from a single-supply with VCC = 3.3V or 5V, it can amplify input differential signals at a common-mode voltage well beyond these power supply rails. The common-mode voltages in a current-sense amplifier can, for example, be up to 28V (MAX4372 and MAX4173) and 76V (MAX4080 and MAX4081).

Precision High Side Current Sense Amplifiers: “…We will compare two high-voltage parts, the AD8206 bidirectional difference amplifier and the AD8210 bidirectional current-sense amplifier.Both devices offer the same pinout, and both perform high-side current-shunt monitoring, yet their specifications and architectures are different. So, how does one consider which device is best-suited for the application?”…. “Current-sense amplifiers with this architecture [AD8210] are generally useful only if input common-mode voltage remains above 2 V or 3 V, and if the application doesn’t require that the input common-mode voltage go all the way to ground (or below)….”  !!!!

MAX9922/23 https://www.maximintegrated.com/en/products/analog/amplifiers/MAX9922.html “…ultra-precision, high-side current-sense amplifiers feature ultra-low offset voltage (VOS) of 25µV (max) and laser-trimmed gain accuracy better than 0.5%. The combination of low VOS and high-gain accuracy allows precise current measurements even at very small sense voltages.”. “The +1.9V to +28V current-sense input common-mode voltage range”…. Not usable for voltages closer to zero ?

Curren sense amplifiers (TI)

LT1991/LT1996

LTC6102 10uV max offset (will not use, only unidirectional..).

LTC6103 has 450uV offset… Two unidirectional sense amplifiers can be combined into bipolar:

Screen Shot 2018-02-13 at 09.50.18

LTC6104 is bidirectional with higher offset: “…high voltage, high side, bidirectional current sense amplifier…. ±450µV maximum offset”

LTC6101

AD8217 High Resolution, Zero-Drift Current Shunt Monitor. Mentioned in: (High-Side Current Sensing with Wide Dynamic Range: Three Solutions (2010)) VCM:4.5 V to 80 V Not enough range for my use.

AD8418 Bidirectional, Zero-Drift, Current Sense Amplifier, CVM 2 V to +70 V

AD8206 difference amplifier for amplifying small differential voltages in the presence of large common-mode voltages. The operating input common-mode voltage range extends from −2 V to +65 V. Gain=20. Offset 2mV????  Too high…

LTC1787  “…delivers greater than a 12-bit dynamic range with ultralow 40µV input offset voltage compared to a typical 250mV fullscale input voltage. A fixed gain of 8 is set by onboard precision resistors”. Gain = 8. Se also: Sense Milliamps to Kiloamps and Digitize to 12 Bits – Design Note 227. Seems to be powered by the shunt voltage…. or is it different when biasing for bidirectional ???

http://cds.linear.com/docs/en/product-selector-card/Currentsense.pdf :

Screen Shot 2018-01-23 at 17.55.17

lmp8601/2/3 -22 to 60V CM. Gain x20, x50 or x100. 0.5% gain error (a bit high?)  “…devices are fixed-gain, precision current-sense amplifiers … The input common-mode voltage range is –22 V to +60 V when operating from a single 5-V supply….ideal parts for unidirectional and bidirectional current sensing applications.Could be a candidate if I accept 22V min voltage…

MAX4081 76V, High-Side, Current-Sense Amplifiers is the bidirectional version of MAX4080 that Dave Jones uses in rev B of his uSupply. ±0.1% Full-Scale Accuracy. 5/20/60 x gain versions available. More info Maxim APPLICATION NOTE 3888Accuracy is not very good…

PGA281 is a high-precision instrumentation amplifier with a digitally-controllable gain and signal integrity test capabilityWith ±15 V supplies the PGA281 can accept common-mode voltages of ±12.5 V, making it a suitable choice for high-side current sensing only as long as VBUS falls within the common-mode voltage range… Could be a candidate for a first version with reduced voltage span ?

Precision gain stages

Additional opamps… ?  Where must we have gain stages ?  Define +/- range in DAC and ADC, shunt resistors etc. before settling on gain.

Using integrated matched resistors… Accuracy, stability, drift…

more info…

Protection

EEVblog #373 – Multimeter Input Protection Tutorial

APPLICATION NOTE 4555 Circuit Guards Amplifier Outputs Against Overvoltage

From section 3.4 in 10 µA-100 mA, 0.05% Error, High-Side Current Sensing : “…protection for the system against ESD (electrostatic discharge), EFT (electrical fast transients), and surge (simulates a lightning strike). This protection is provided by a Schottky diode and two TVS (transient voltage suppressor) diodes. The BAT54-V-GS08 Schottky diode ensures that no current flows through the split supply when the power terminals are connected in reverse polarity. This diode protects against reverse voltages up to 30V……Since the split supplies to the PGA281 can reach up to ±18 V, the TVS diodes should have a breakdown voltage slightly higher than 18V. The diodes must also be bidirectional and should have a very fast response time in order to provide sufficient protection against fast transients. Based on these requirements the SMBJ20CA was chosen to provide up to 600 W of protection.

Can this me used to protect 36V opamps? https://assets.nexperia.com/documents/data-sheet/BZB84_SER.pdf

Reverse Current/Battery Protection Circuits (2003): “…The most recent MOSFETs are very low on resistances, and therefore, are ideal for providing reverse current protection with minimal loss…

Screen Shot 2018-02-07 at 13.57.32

How to protect circuits from reversed voltage polarity! (video)

AND8230/D – Application Hints for Transient Voltage Suppression Diode Circuits

Op Amp Input Overvoltage Protection: Clamping vs. Integrated (2016)

DIODE-CONNECTED FET PROTECTS OP AMPS

APPLICATION NOTE 4035 Overvoltage Protection (OVP) for Sensitive Amplifier Applications (Maxim)

Prevent System Damage Via Fast, Accurate Over-Current Detection (2014)An over-current detection solution can be easily created using a simple, low-cost operational amplifier (op amp), external gain setting resistors, and a low-cost comparator…

Dave Jones uSupply TVS diode explaination (direct link in video)

DACs – Digital to analog conversion

I probably need 3 bipolar channels.  One for voltage control, two for positive and negative current limits. Then you can set different values for negative and positive currents.

I was first thinking about 16bits resolution. For voltage that means max 305uA resolution for a swing of -10 to 10V. I want at least 100uA resolution. Do I need to have multiple measurement ranges, or do I need to go to 18 or 20 bits DAC ? For current limit, it’s probably sufficient because I need multiple ranges there anyway (I believe)…

+-10V 18 bit gives 76uA resolution, 20 bit gives 20uV resolution.

This is, however, if everything else is perfect. Which it’s not. But I don’t want the converters to be the bottleneck. I want to be sure that they are not the limitation.

True 18-Bit DAC for Extreme Precision Applications (Linear Technlology 2010)

Some possibilities:

Linear Technology http://www.linear.com/product/LTC2704  bipolar 4 channel 16 bit converter. Linear DAC product selector: http://cds.linear.com/docs/en/product-selector-card/2PB_dacsfc.pdf “…six output spans—two unipolar
and four bipolar…SPI serial interface. INL is accurate to 2LSB[LTC2704-16]. DNL is accurate to 1LSB for all versions

Analog Device http://www.analog.com/media/en/technical-documentation/data-sheets/AD5764.pdf. AN1411 application note: High Accuracy, Bipolar Voltage Output Digital-to-Analog Conversion Using the AD5764 DAC “… integrated output amplifiers, reference buffers, and proprietary power-up/power-down control circuitry...digital offset and gain adjust registers per channel… guaranteed monotonicity, integral nonlinearity (INL) of ±1 LSB, low noise, and 10 μs settling time. “. .  Others experiments with this: https://www.laserlance.com/projects/arduino-dac-library-and-shield/ (shared PCB at oshpark: https://oshpark.com/profiles/Laser-Lance. ±2 ppm FSR/°C max.

AD5765 Complete Quad, 16-Bit, High Accuracy, Serial Input, ±5 V DAC. More or less same as AD5764 except only 5v ????

AD5763 2 channel 16 bit bipolar

Try this parametric search at analog.com: 16bit <2LSBINL bipolar DAC

AD5781 True 18-Bit, Voltage Output DAC ±0.5 LSB INL, ±0.5 LSB DNL (recommended for new design)

AD5791 20 bit. Arduino shield: http://41j.com/blog/2015/10/ad5791-board-rev4/. Evaluation kit: http://www.analog.com/en/design-center/evaluation-hardware-and-software/evaluation-boards-kits/EVAL-AD5791.html. Note that there are two revisions of that evaluation board. Last post in https://www.eevblog.com/forum/metrology/an-arbitrary-output-voltage-divider-for-a-precision-voltage-reference/ shows a video of a “slapped-together AD5791 + LTZ1000”

The following are DACs that I have tested:

AD5761 (single channel)

I also tried this 1 channel DAC, mainly because it’s recommended for new designs in the analog webpage and I got some samples from Analog Devices. Wasn’t too difficult to get it up’n running. In my crude setup I found that it drifts some quite a few uVs. Note that the temperature coefficient in bipolar mode is +/-15uV. Might be a bit much for my application.

Code for arduino at Github.

DAC8734 (TI)

DAC8734 quad bipolar 16 bits dac https://www.youtube.com/watch?v=uYl_jqJeGtA

http://element1445.rssing.com/chan-35362995/all_p4.html

Schematic+SPI+DAC8734

I really wanted to use this DAC. But I never managed to “tame” it. More about by problems here: DAC8734 drawing too much current from analog supply and gives completely wrong output values. My theory is that I, at one or several stages, has done something wrong and “killed” the device.

How accurate?  16 bits ? Is it possible to “control” drift etc by measuring with a 24bit AD converter and (slowly) compensate drift in software, such as described in A Standards Lab Grade 20-Bit DAC with 0.1ppm/°C Drift (2001)

Screen Shot 2018-04-09 at 16.29.57

ADC – Analog to digital conversion

More info!

The following are ADCs that I have tested:

DAC1220 24-bit Sigma-delta ADC with internal reference https://github.com/hellange/Protocentral_ADS1220

Voltage references

In order to obtain accurate values, there is a need for a voltage reference. A nice overview of various voltage references:  https://xdevs.com/review/dcvref_table/, for example unheated ones:

Screen Shot 2018-09-19 at 15.07.37

The DAC8734 evaluation module has 2.5 and 5.0v references onboard. However, these are not the most accurate devices. Read more about them e.g. here: http://www.ti.com/lit/ml/slyc147/slyc147.pdf

What seems to the most used ultra stable voltage references are LTZ1000/LTZ1000A and LM399 (more insight here: https://xdevs.com/article/kx-ref/). Some general insight/opinions regarding references  e.g. here:  https://www.eevblog.com/forum/projects/dc-voltage-references-battle-overview-of-market/

The LM399 is used in http://www.ianjohnston.com/index.php/videos/20-video-blog-022-handheld-precision-digital-voltage-source together with a 18 bit DAC. I guess this means the LM399 should be sufficient for my use. Several sources indicate that it needs some “burn-in” to become stable…

How to Choose a Voltage Reference (2009) “…to measure voltage, you need a standard to measure against. That standard is a voltage reference. The question for any system designer is not whether he needs a voltage reference, but rather, which one?..“. Example table:

Screen Shot 2018-02-02 at 23.23.15

Voltage references hold steady (2010) “Decades ago, these references provided initial accuracies of only ±10%, whereas modern reference ICs can provide initial accuracies of 100 ppm, or 0.01%

Will the right voltage reference stand up? “In a perfect world, you are done as you find the IC chip with the correct output voltage for your ADC. However, in our non-perfect world the voltage reference chip has initial output errors, and an inherent inability to drive the ADC’s reference pin directly….

Voltage regulators

A Guide to Choosing the Right Ultra – Low IQ Low Dropout Linear Voltage RegulatorsThe following paper discusses the tradeoffs between achieving low [quiescent current] and good dynamic performance when choosing an LDO…

How to pick a linear regulator for noise-sensitive applications “A lownoise power solution is essential to preserving signal accuracy and integrity. This article addresses criteria and parameters to consider in designing such a power solution, including important specifications for picking a linear regulator

AN159: Measuring 2nV/√Hz Noise and 120dB Supply Rejection on Linear Regulators – The Quest for QuietLow noise amplifiers and analog-to-digital converters (ADCs) do not have infinite supply rejection and the cleaner the regulator output is, the higher their performance. These are just a few applications where linear regulators are required to provide quiet power supply rails, but how does one ensure that the regulator is performing as advertised?

Power Management for Precision Analog (TI) using linear 36V 150mA/200mA negative and positive regulators  TPS7A30 and TPS7A49. “The TPS7A30 family is designed using bipolar technology, and is ideal for high-accuracy, high-precision instrumentation applications where clean voltage rails are critical to maximize system performance. This design makes the device an excellent choice to power operational amplifiers, analog-to-digital converters (ADCs), digital-to-analog converters (DACs), and other high-performance analog circuitry”.”…TPS7A30/49 development kits remove switching noise and increase the performance of data converters, operational amplifiers, clocks and other signal chain devices…” (http://embedded-infos.blogspot.no/2011/02/texas-instruments-introduces-new.html)

TPS7A30TPS7A49 –35V & 36V –200mA Ultra-Low Noise, High PSRR, Low-Dropout Linear Regulator. Noise 15 μVRMS, PSRR: 72 dB

TPS7A33 /TPS7A470 –36V & 36V 1A Ultralow-Noise Negative Voltage Regulator.  Noise:16 μ/4μVRMS, PSRR:72 dB”…ideal to power operational amplifiers, analog-to-digital converters (ADCs), digital-to-analog converters (DACs), and other high- APPLICATIONS performance analog circuitry

ADP7118 20 V, 200 mA, Low Noise, CMOS LDO Linear Regulator. Noise:11uV, PSRR of 88 dB at 10 kHz. “This high input voltage LDO is ideal for the regulation of high performance analog and mixed-signal circuits operating from 20 V down to 1.2 V rails.

ADP7182 –28 V, −200 mA, Low Noise, Linear Regulator “This high input voltage LDO is ideal for regulation of high performance analog and mixed signal circuits operating from −27 V down to −1.2 V rails.

Ultralow Noise, High Rejection Low Dropout Regulators (from Analog Device)

ADP5070 switchmode preregulator ++ ( http://www.analog.com/en/design-center/evaluation-hardware-and-software/evaluation-boards-kits/eval-adp5070.html, “For more details about the dc-to-dc converters, refer to the ADP5070 and ADP5071 data sheets. For further information on the LDO regulators, refer to the ADP7142 and ADP7182 data sheets. These data sheets must be used in conjunction with this user guide when using the evaluation board. “) together with ADP7142 and ADP7182

Screen Shot 2018-09-06 at 14.49.40

LTC3265 dual supply: https://www.digikey.com/en/product-highlight/l/linear-tech/ltc3265-low-noise-and-high-voltage-dual-supply-with-boost-inverting-charge-pumps. “LTC3265 is a low-noise dual polarity output power supply, which includes a boost charge pump, an inverting charge pump, and two low-noise positive and negative LDO post regulators. The boost charge pump powers the positive LDO post regulator while the inverting charge pump powers the negative LDO regulator. Each LDO can provide up to 50 mA of output current. The LDO output voltages can be adjusted using external resistor dividers

LT1963/LT3015

LT3042 ” high performance low dropout linear
regulator featuring LTC’s ultralow noise and ultrahigh PSRR
architecture for powering noise sensitive RF applications” (solution:http://www.linear.com/solutions/5762)

Voltage regulator noise experiments: Simple circuits reduce regulator noise floor (EDN)

Can You Use the Voltage Reference to Power Your ADC Driver?

Small, Low Current Power Supplies by Rod Elliott

 

Output (op amp) higher current

Can we get away with an op amp driving a MOSFET output stage directly? What about stability, ringing, overshoot,gate capacitance…

How to Buffer an Op-Amp Output for Higher Current (2016)

Do-it-yourself: Three ways to stabilize op amp capacitive loads (2017)

Practical Techniques to Avoid Instability Due to Capacitive Loading (Analog Dialogue)

Screen Shot 2018-01-25 at 12.52.49

Simulation Shows How Real Op Amps Can Drive Capacitive Loads (Maxim AN5597)

Driving capacitive load with op amps (Microchip AN884)

Op amps with capacitive load capabilities, ex: lm8261(single +/-30V),  LM8272(dual, +/-24V). More about them here: Unlimited Capacitive Load Drive Op Amp Takes Guesswork Out Of Design

Could I simply use a LTC6090 140V Op Amp with a audio amplifier MOSFET output as indicated in the datasheet ? LTC2057, or other high voltage opamps from linear: http://cds.linear.com/docs/en/product-selector-card/2PB_6015f.pdf ?

Screen Shot 2018-03-10 at 14.58.29

So whereas an IC designer would say, “An output capacitor puts a pole in the ac response,” [Bob] Pease would use the time-domain equivalent by saying, “An output capacitor puts a lag in the ac response.” So when you realize the capacitor is putting in a delay, you can start to see why the system will tend to oscillate.” – http://www.electronicdesign.com/power/what-s-all-capacitive-loading-stuff-anyhow

https://electronics.stackexchange.com/questions/69506/stability-problem-in-unity-gain-opamp

Practical Techniques to Avoid Instability Due to Capacitive Loading (Analog Dialogue, 2004)

Simulation shows how real op amps can drive capacitive loads (2013)

Designing a *linear* MOSFET driver stage

Ask The Applications Engineer-25: Op Amps Driving Capacitive Loads describes noise-gain manipulation, out-of-loop compensation, in-loop compensation

Do-it-yourself: Three ways to stabilize op amp capacitive loads, overview:

Screen Shot 2018-02-06 at 07.26.43

AN-1645 LM4702 Driving a MOSFET Output Stage , page 14:

Screen Shot 2018-01-15 at 14.32.11

https://training.ti.com/ti-precision-labs-op-amps-stability-1:

Screen Shot 2018-01-08 at 20.05.10

Simulation: https://www.circuitlab.com/editor/#?id=3x7yrp

Slew rate

Do I need to control/reduce the slew rate ? http://www.ti.com/lit/ug/tidu026/tidu026.pdf

Stability and avoid oscillation

Why Op Amps Oscillate—an intuitive look at two frequent causes (2012) and Taming the Oscillating Op Amp (2012) and Taming Oscillations—the capacitive load problem (2012)A simple non-inverting amplifier can be unstable or have excessive overshoot and ringing if the phase shift or delay created by the op amp’s input capacitance (plus some stray capacitance) reacting with the feedback network resistance is too great…” 

https://www.apexanalog.com/resources/techseminar/stability_and_compensation.pdf

https://www.allaboutcircuits.com/technical-articles/negative-feedback-part-1-general-structure-and-essential-concepts/

Operational amplifier stability compensation methods for capacitive loading applied to TS507

https://www.eevblog.com/forum/beginners/first-bench-supply-ripplenoise-problems/

A good discussion of how to obtain stability in an electronic load. https://www.eevblog.com/forum/projects/dynamic-electronic-load-project/25/. Should also be relevant for power supply (especially a 4 quadrant power supply!)

Current limiting / constant current mode

Have problems with current limiting circuit. Have tried variations of diode or transistors as used by other designs. Unstable.

Reading:

https://www.eevblog.com/forum/projects/current-limiting-stability-problems/ “…my voltage control works fine, but I have problems with my current control. I use the schematics of David’s power supply  with an LT3083, but with an ASC712-5 current sensor. Everything works fine…but when it limits the current, the voltage goes down and the current as well….an oscillating current control loop.

ADD CURRENT LIMIT TO THE BUF634 (2000)  “…For stability, the bandwidth of A2 must be less than approximately one-fourth the bandwidth of A3, and R1 C1/(2π) must be less than approximately one-fourth the bandwidth of A2…

Screen Shot 2018-03-13 at 17.25.09

Dave Jones uSupply (direct link to where he explains the current limiting circuit)

Peter Oakes take on current limiting(direct link to video where he explains current limit)

Martin Lorton student power supply (direct link to where he explains current limit)

https://www.eevblog.com/forum/beginners/supply-lm350t-instead-of-lt3080/ Some info about how to “OR” the current and voltage control signal: “……The problem with the transistor as shown is that it adds voltage gain to the error amplifier for the current control loop making it much more difficult to frequency compensate…. Usually this is done with a pair of diodes but in the past when they were more available like the 2N404A, PNP emitter followers with high Vbe breakdown could be used.  Or use diodes and PNP emitter followers… 

https://www.eevblog.com/forum/beginners/lt3083-current-limiting-how-does-it-work/

https://e2e.ti.com/blogs_/archives/b/precisionhub/archive/2016/08/12/how-to-design-current-sensing-and-protection-with-off-the-shelf-op-amps

http://wahz.blogspot.nl/2015/06/lab-power-supply-current_13.html and related posts discusses various approaches to current limiting. Trial and errors.

Screen Shot 2018-04-03 at 09.15.06

Output stage

I’ll try to use only one N and one P mosfet at the output in order to keep things simple. Sure it’s possible to use several in parallell, but it add complexity. Read more e.g. Application Note AN-941 : Paralleling power mosfets

How to Make Linear Mode WorkTheoretically, linear mode operation is very easy. Simply bias the gate to deliver some desired amount of current or power, and stay within the manufacturer’s Forward Safe Operating Area (FSOA)… The reality however is that linear mode operation is one of the trickiest power applications of all, turning many “simple” designs into a reliability nightmare

Linear MOSFET and Its Use in Electronic Load (2016) “I tested a few of the IRFP150N’s individually in linear mode and they all failed when the power dissipation reached between 45W to 60W… There is a class of so called linear MOSFET (e.g. IXYS‘ Linear L2™ MOSFETs) which is specifically designed to operate in linear region with an extended FBSOA…

AN-272 Op Amp Booster Designs (2013) “This application report describes the output “booster,” or post amplifier, designs required to achieve needed voltage or current gain in applications that require substantially greater output voltage swing or current (or both) than IC amplifiers can deliver

Biasing

Diode ? constant current source ? current mirror ? Need to learn more…

https://electronics.stackexchange.com/questions/42927/purpose-of-these-two-transistors  shows this configuration (for a headphone amp):

Screen Shot 2018-01-26 at 10.29.37

From https://electronics.stackexchange.com/questions/138920/source-potential-for-mosfet-with-grounded-substrate :

Screen Shot 2018-01-26 at 11.21.20

Page 4 in http://www.simonfoucher.com/McGill/ECSE330%20Electronics/Notes/4.4%20MOSFETS%20in%20IC%20CSA%20CGA.pdf

Screen Shot 2018-01-26 at 11.31.08

Fundamentals of MOSFET and IGBT Gate Driver Circuits explains a lot about mosfets, driver circuit, optimize turn off, turn on etc. Here is one of the diagrams:

Screen Shot 2018-02-01 at 08.06.42

Which transistor

Linear Mode Operation and Safe Operating Diagram of Power-MOSFETs :

Screen Shot 2018-01-26 at 14.39.30

AN-1645 LM4702 Driving a MOSFET Output Stage (2013) contains info about distortion in different mosfet combos. Also a bit on output stage in general including gate resistor choice and snubber (section 7).

Relevant reference designs for high precision design

TI Designs: TIDA-01012 Wireless IoT, Bluetooth® Low Energy, 4½ Digit, 100-kHz True RMS Digital Multimeter Reference Design A bluetooth low energy reference design that also “…implements basic DC voltage and current measurement modes as well as true RMS AC voltage and current measurement modes inherent in most handheld DMMs in the market today.”

Ultrahigh Sensitivity Femtoampere Measurement Platform…provides a reference design for realworld application by partitioning the system into a low-leakage mezzanine board and a data acquisition board

10uA-100mA, 0.05% Error, High-Side Current Sensing Solution Reference Design “...we are showcasing an ultrahigh precision programmable voltage source using ADI/LTC products together. The AD5791 with the LTZ1000ADA4077, and AD8675/AD8676 can be used to provide a programmable voltage source that achieves 1 ppm resolution with 1 ppm INL and better than 1 ppm FSR long-term drift.

High Precision Voltage Source (Analog Dialogue, 2017)The AD5791 with the LTZ1000ADA4077, and AD8675/AD8676 can be used to provide a programmable voltage source that achieves 1 ppm resolution with 1 ppm INL and better than 1 ppm FSR long-term drift

A Standards Lab Grade 20-Bit DAC with 0.1ppm/°C Drift (Linear Technology, 2001)A useful development would be a practical, 20-bit (1ppm) DAC that is easily constructed and does not require frequent calibration…

 

User interface

Not sure how the UX should be made. 5″ capacitive LCD with some extra buttons

Display

Something like Keithley 2450 sourcemeter ?

2450_3 2450

From https://www.youtube.com/watch?v=WkAuFc9k08g :

Screen Shot 2018-02-07 at 14.51.47Screen Shot 2018-02-07 at 14.51.14Screen Shot 2018-02-07 at 14.51.02

Keisight sourcemeter and multimeters:

Keysight-B2961A-enlarged34460a

I feel the Keysight sourcemeter has too small digits.

Keithley 2280s power supply:

2280S-32-6_PWS_front_0

Maybe a combination of 2280s and 2450…

 

Statistics / graphs

Live trend graph with limited samples is easy. Trend graph based on ALL samples over long time is more difficult i.e. due to limited sampling memory. Some resources?:

https://stackoverflow.com/questions/45855209/reduce-dataset-to-smaller-size-keep-the-gist-of-information-in-the-dataset

Is decimate the right thing to use ?… probably not with the data I have that can be noisy and irreular ??? Standard algorithm seem to have to much filtering…

 

Resources

TODO: Some of the references might be moved to corresponding sections in main text…

Analog Engineer’s Pocket Reference

Screen Shot 2018-03-07 at 10.09.44

PCB Layout considerations

The PCB is a component of op amp design “Most analog designers are familiar with how to use ICs and passive components to implement a design. There is one additional circuit component, however, that must be considered for the design to be a success—the printed circuit board on which the circuit is to be located…

The basics: How to layout a PCB for an op ampApplications engineers tend to overlook printed circuit board (PCB) layout during circuit design. It is often the case that a circuit’s schematic is correct, but does not work, or perhaps works with reduced performance. In this post, I will show you how to properly lay out an operational amplifier (op amp) circuit PCB to ensure functionality, performance, and robustness…

AN 1258 Op Amp Precision Design: PCB Layout Techniques “…techniques for improving the performance, giving more flexibility in solving a given design problem. It demonstrates one important factor necessary to convert a good schematic into a working precision design…

How to layout a PCB for an op amp…That’s when I realized that PCB layout isn’t as intuitive as I thought…

How to layout a PCB for an instrumentation amplifier “… it is easy to make mistakes in the PCB layout that might degrade circuit performance. …shows a PCB layout with three mistakes we at TI commonly see when reviewing INA layouts…”

Isolate analog and digital circuits /opto isolation

Optocouplers for SPI: http://www.analog.com/media/en/technical-documentation/technical-articles/Isolating-SPI-for-High-Bandwidth-Sensors-MS-2689.pdf

Ground plane…

Partitioning and layout of a mixed signal PCB tries to explain why separate ground for analog and digital circuitry might not be the correct solution.

MAX14931 vs ISO7241 for ISP communication. Which to use… https://electronics.stackexchange.com/questions/149980/ucontroller-spi-over-optoisolator

SI866x “…Silicon Lab’s family of ultra-low-power digital isolators are CMOS devices offering substantial data rate, propagation delay, power, size, reliability, and external BOM advantages over legacy isolation technologies…

ATmega328PB Isolated Application Board An ATmega328PB breakout board with digitally-isolated SPI, I²C, or generic GPIO. $3 on tindie.

328isolator.jpg

Decoupling

http://www.analog.com/media/en/training-seminars/tutorials/MT-101.pdf

The decoupling capacitor…is it really necessary? “…I collected data for about a week, and none of my results matched expectations. I made numerous changes in an attempt to improve performance, but nothing worked. Finally, I decided to add the decoupling capacitor. As you might expect, this solved the issue…

#257: Power Supply Decoupling & Filtering: why we use multiple caps in different locations

EMI

http://www.analog.com/media/en/technical-documentation/application-notes/an139f.pdf “PC-board layout determines the success or failure of every power supply project. It sets functional, electromagnetic interference (EMI), and thermal behavior. Switching power supply layout is not black magic, but is often overlooked until it is too late in the design process

Protoboards

Protoboard for opams: http://www.ti.com/lit/ug/sbou162a/sbou162a.pdf

Another opamp protoboard: http://www.twovolt.com/category/test-gears-instruments/

https://bashtelorofscience.wordpress.com/2017/06/05/universal-op-amp-circuit-pcb/

Screen Shot 2018-03-09 at 22.37.46

 

Voltage regulators

Electronics

Several pdf presentations for electronics. Starting with http://scipp.ucsc.edu/~johnson/phys160/lecture1.pdf. More about opamps and output stages: http://scipp.ucsc.edu/~johnson/phys160/lecture14.pdf.

Various

 

schematics/layout/simulation

https://easyeda.com Could this be it for schematics/PCB ?

http://lushprojects.com/circuitjs/circuitjs.html. Very easy but crude simulation. Import the txt below to see a test design:

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f 96 80 128 80 1 4 0.03
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a -80 0 -32 0 0 30 -30 1000000 9.82639452006368 9.82649278400888
w 384 -48 384 -176 2
w 384 -176 -272 -176 0
w -96 -16 -80 -16 0
R 128 -144 128 -128 0 0 40 50 0 0 0.5
R 128 160 128 144 0 0 40 -50 0 0 0.5
a 624 160 672 160 0 15 -15 1000000 3.3399007600305324 3.3399009600186025
r 512 144 592 144 0 10000
r 512 176 592 176 0 10000
r 592 176 592 240 0 20000
r 592 96 672 96 0 20000
w 592 96 592 144 0
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g 592 240 592 272 0
O 720 160 768 160 1
a -432 -112 -368 -112 0 30 -30 1000000 0.019998807019305787 0.05
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g 592 16 592 32 0
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w -480 -128 -432 -128 2
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w -272 -176 -272 0 0
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R -256 32 -528 32 0 0 40 5 0 0 0.5
w -96 96 -96 16 3
w -96 16 -80 16 0
w -96 -64 0 -64 0
w -272 0 -256 0 0
r 0 -64 64 -64 0 100
a 416 224 464 224 0 15 -15 1000000 5.009851440027903 5.009901538542303
a 416 96 464 96 1 15 -15 1000000 4.9998517365547945 4.99990173507216
w 480 144 512 144 2
w 416 80 384 80 2
w 416 112 384 112 0
w 416 208 384 208 0
w 384 208 384 176 0
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w 0 0 0 -64 0
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a -432 224 -384 224 0 30 -30 1000000 0.019998807019305787 -0.03
w -480 -128 -480 208 1
w -480 208 -432 208 2
R -432 240 -512 240 0 0 40 -0.03 0 0 0.5
d -240 224 -176 224 1 0.805904783
w -384 224 -240 224 2
w -176 224 -96 224 0
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r 592 -32 592 16 0 500
w -208 16 -176 16 2
w -480 -128 -480 -224 0
O -368 -112 -336 -112 1
d -160 96 -240 96 1 0.805904783
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r 304 -48 368 -48 0 1
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S 464 -48 512 -48 0 1 false 0 2
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p -240 144 -160 144 1 0
w -160 144 -160 96 0
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R -176 -368 -176 -400 0 0 40 30 0 0 0.5
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162 -48 -320 0 -320 1 2.1024259 1 0 0 0.01
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