Electronics > Metrology

I'm building an ultra-precision high resistance bridge(now: panel finished)

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Current status: power supply and the main board finished. Panel just finished. 

 - Commercial high ohmmeters/bridges are not very good in accuracy and precision
 - Metrology grade bridges such as used in NIST or MI 6600A are unobtainium
 - Absolute necessary when DIY high resistance standards
 - There are many high resistance resistors need testing
 - High ohm-nutting.
 - The knowledge and learning curve of high resistance bridge is also related to weak current measurement.

These are my ultimate goals.
 - Comparison decade resistors of 1M, 10M, 100M, 1G, 10G, 100G and 1T
   (It is the limitation of test range makes the the low uncertainty possible. If a resistor box instead of a dummy is used, any intermediate value can be measured but with increased uncertainty)
 - Test voltage: 100V, 50V and 10V for Rs and Rx, 10V for dummy.
 - Dummy resistors can either be internal(from 100k to 1G) or external.
 - 10:1 ratio allow easy step up.
 - Noise and linearity: 0.1ppm (1M), 1ppm(100M)
 - Resolution, same or better than above
 - Range +-2% and 0.2%(+-2000ppm)
 - Comparison uncertainty 0.3ppm (10M. much depending on the value of resistors to be compared, degrade for high resistance)
 - Measurement method: substitution, 1:1 and 10:1 comparison, direct measurement
 - Output: 4 digits LED readout and Voltage output(-2V to 2V, 1ppm/mV)


 - Dark blue for sockets, light blue for display, green for operation
 - Double circle for triaxial BNC sockets, single circle for normal BNC sockets
 - Rs and Rx can be selected by switch.
 - Rd can be either external or internal of 100k, 1M, 10M and possible 100M
 - There is a coarse and a fine adjustment knob for offset
 - The range of the LED display is -19999ppm to +19999ppm
   A switch provide fine display mode for -1999.9ppm to +1999.9ppm
 - There are two Voltage input sockets, one for 126V external power(also for charging), and 21V for another battery charging

Calibration is necessary for comparison or direct measurement(not necessary for substitution)
Calibration is done for every Rd involved(one calibration for one Rd, including internal Rd)
Calibration procedures:
 - Connect a Standard resistor Rs and switch the 'Source' to Rs
 - Switch the dummy select to one of the internal dummy resistors or switch to external position and connect a dummy resistor Rd.
 - Switch power on, wait for stable.
 - Turn the fine adjustment knob to left most, adjust coarse knobs to display the deviation of Rs
 - Record the knob reading on paper, this is the calibration value for the corresponding Rd.

Operation procedures for substitution methord:
 - Connect a Standard resistor Rs and a test resistor Rx to be compared
 - Switch to one of the internal dummy resistors or switch to external position and connect a dummy resistor Rd.
 - Switch the 'Source' to Rs and switch power on
 - Adjust two knobs to display the deviation of Rs
   For example, if Rs is calibrated as -28.9ppm, adjust so that the LED reads -28.9ppm
 - Switch the 'Source' to Rx, the deviation of Rx will be displayed in ppm on the LED or can be read/recorded from the 'Rec Out'.

Operation procedures for comparison or direct measurement:
In these cases, Rs is not to be used, Rd may or may not be used.
 - First of all, the bridge and the Rd has to be calibrated before.
 - Switch Rd select to external and connect a Rd(for comparison) or switch to an internal Rd(for direct measurement).
 - Connect Rx, Switch the source select to Rx and switch the power on
 - Turn the fine adjustment knob to left most position and adjust the coarse to the calibrated value.
 - The offset of Rx is displayed on the LED or from 'Rec Out'.

High resistance buildup system

 - Higher resistances are step up on lower resistances, forming a calibration chain
 - Many of my intended high resistances are Hamon style as well.
 - The first link in the chain is the 100k Hamon which will be compared with my SR104 when connected as 10k and used as 1 Meg standard when connected in series.
 - The second link in the chain is SR1050 10Meg Hamon, configurable from 1M to 100M, will be compared with the 100k Hamon at 1M level and used as a temporary 100 Meg standard.
 - Similarly, the third link is 1G Hamon, and the fourth, 100G Hamon. There will be Hamons of other value or repeated Hamon such as 100M and 10G as drawn by dashed line.

Making considerations
 - Thermal EMF, not important, 1uV = 0.01ppm for 100V. Therefore, not low thermal EMF or power reversal used.
 - Contact resistance, not important, 0.1 Ohm = 0.1ppm for 1M, 0.1 Ohm = 0.001ppm for 10M
 - Interference, use metal box, screened connections, battery powered.
 - Leakage, guarded. The guard will keep the voltage of the outer screen very close to the inner conductor thus minimize the leakage. Also, PTFE materials are used whenever possible.
 - Guarding current: 1uA to 10uA. That is to say, 1/10 Meg guarding resistor for 10V, 10/100 Meg guard resistor for 100V
 - Humidity, sealed box, with moisture absorbent inside
 - Dust, plastic bag covers the box when not in use
 - Battery life, bridge, 600mAh type, 0.3mA consumption, 2000 hours in one charge.
 - Battery life, others(LED display and opamp), 3400mAh*5, 20mA consumption, >150 hours per charge.
 - Power supply circuit, linear, low-power type.
 - Temperature drift, use foil type for critical internal resistors
 - Shock, firm fix of batteries and board.


The principle is simple, just another modified Wheatstone  bridge. Detector U1 together with Left two arms plus and an photocoupler form a feedback amplifier. Because this electo-meter grade U1 draws very tiny current(max 25fA), and also because voltage at point B and D are fixed, voltage at point A is proportional to Rsx. In theory, this point A can be used as the output owing to it is a low internal resistance, but in practice, the voltage is high, and need a long scale DMM to resolve the small relative change of this voltage.
Then the right two arms(R1 and R2) will step down this high voltage, and make the output earth referenced. That is to say, if the bridge is balanced, voltage at point C will be zero. However, this step down lost some magnitude, so I use another opamp U2 to magnify the signal to it's original value or even higher. This U2 isolates the relatively high resistance bridge arms from output, and also the magnification can be adjusted by R3. Because the current of R1 and R2 is 250uA, Ib of U2(<0.1nA ) contribute to less than 0.25ppm offset.

There are many advantages in this circuit:
 - The bridge balancing is automatic
 - Balancing is very fast compared to dual active arm method.
 - Only one critical point(point D), and the potential of this point is very close to ground(it is the virtual ground of U1), making the guarding very easy(no guard drive is necessary).
 - The output is linear (be noted that the output of a normal Wheatstone bridge is none-linear, this  none-linearity play an insignificant role in normal value resistors where deviation is very small, but become troublesome for high resistance bridges where the deviation of resistors may be very large )
 - Sensitivity of the bridge is precisely known(100uV/ppm or 1mV/ppm) and does not vary with battery voltage.
 - Batteries are all ground referenced! This avoid so many troubles as encountered in float batteries design. It's also possible to implement a mains power supply or external power supply.
 - The output is the deviation of Rx (or Rs), making it easy to use a very cheap meter to distinguish sub-ppm level.
 - The bridge is simple in design, small in size, easy to construct, cheap to make.
 - Potable, stand-alone use, no other expensive or bulky equipment necessary such as programmable calibrators or electrometer.
 - Most of all, ultra-precision. Common error sources have been identified and handled accordingly.

Sensitivity analysis
This refereed to the determination of how every components affect the output, thus used for components selection.
Step one, formula the output equation
The voltage at point A, Va=Rsx*Isx=Rsx*(Id-Ik1)=Rsx*(-Vb/Rd-Ik1)
where Vb and Id is the voltage and current of the dummy resistor, Ik1 is the leakage convert to point D.
The voltage at point C, Vc=R2*(Rsx*(-Vb/Rd-Ik1)-Vb)/(R1+R2)+Vb+R2*Ik2
where  Ik2 is the leakage convert to point C
The output voltage Vout=(R4/R3+1)*(Vc-Vos)

Step two, analyse how each component affect the output.
This can be done by one of the following three ways
 - partial differential, and calculate
 - calculate in Excel
 - simulation
I've done all three and the results are exactly the same as follow:

Column 1 is the component name, column 2 is the amount of output change by certain change in the component. As can be seen that 1fA change of Ib of U1 will make the output change by 1uV, 1pA of Ib of U2 changes output by 4.4uV.
Column 4 is similar to 2 except the output unit changed to ppm.
Column 5 is similar to 4 but on condition that deviation of Rsx at 10000ppm(0.1%)

Step three, select components according to the above results and the requirements.
As can be seen that R1, R2 and Rd are very important, choose the best you have.
Although Ik1 affect the output very little, it is for Rsx=100 Meg, will be 1000 times worse if Rsx=100G. In order to measure 100G, a good electro-meter type opamp is necessary.
Similarly, a chopper-stabilized opamp is used for U2.

Step four, characterize the performance of the bridge according to the components used for different operation mode.
For substitution, because the swap time usually short ranging from several seconds to not more than one minutes, the value change of components will be very small compared to noise and interference.
For comparison or direct measurement, if the calibration gap is longer than hours, the tempco of components will play important roles for errors. There will be aging effects as well.

Detailed schematics and more explanation

Guarding and switching circuit added. Red path is the high voltage output(point A in simplified), permanently connected to inner conductors and middle shields of the two triax sockets of Rs and Rx. Outer shields are connected to ground(not drawn). Middle shields provide the guarding and the potential are exact the same as inner conductors. Rsg is the internal guarding resistor of Rs(may or may not present, won't affect the guarding in both cases), Rxg is similar. The lower part of the guarding resistors are connected to ground.  The inner conductor of lower part of Rs and Rx will be either connect to ground or connected to point D(as in simplified diagram). In both cases, the potentials are all at ground level, making the these resistors power-up through out the test period except in very small transit gaps where Rs and Rx are switched. These power-up-all-the-time conditions are very important for high resistors where capacitor charge time and dielectric absorption time cannot be ignored.
Dummy resistors can be externally connected just like Rs or Rx, or can be selected internally from a group of seven resistors.
Purple line is the critical path which any leakage should be controlled to 1E-15 level if a 1T resistor is to be tested. The switch is well tested to have insulation resistance of greater than 1E13, and all the terminals and outer metal shield are all zero or very near to zero potential, forming a natural guarding. Rp protected U1 during Rs and Rx switching and there is a guarding ring on both sides of the PCB.   
Cf is the feedback capacitor to obtain stability in the presence of input capacitor, which should be carefully selected for ultra-low leakage(less than Ib is preferred at 2V). Four possible types should be considered: polystyrene, NP0/C0G, PTFE and air.
R2 is the starting current provider for this high voltage PS2513, and R11 increase the loop gain above 1 to avoid oscillation.
The value of the upper-right arm of the bridge is 400k, making use of my available ten 40k AE foil resistors. It is also switchable to 200k and 40k making the test voltage 50V and 10V.
The value of the lower-right arm of the bridge is 40k, consisting of a 40k//7.5M plus an adjustable string of 500 Ohm 10-turn pot etc.
Battery two(Batt2) is charged thru connector V_In2 and a reverse protection diode D2, but is still measurable thru the same socket because R7 is present. Similarly, Batt1 can be charged and monitored by V_In1, D1, and R6.

There are some weak points though, mainly concern the leakage:
 - Ib of U1, typical 10fA, max 25fA for LTC6001A, may further reduced of better opamp is used such as ADA4530-1.
 - Leakage of Cf. The requirement for Cf may change for different external resistors. It is very difficult to make a low leakage switchable Cf.
 - leakage of the dummy resistor switch.

Test Range

Low voltage power supply

Five 18650 cells inside the case provide the power. By use of HT Low power LDOs to achieve +4.2V, -3.0V and -12.8V.
+4.2V is used for LED display and is simulated by dummy load RL1.
+4.2V and -3.0V are used by opamp U1 and U2, and is simulated by dummy load RL2.
A 10V precision shuntable reference LT1021-10 is power by a constant current source of 2mA(by 2SK170 JFET and a 100 Ohm resistor) providing -10V necessary for low-side of the bridge(simulated by dummy load RL3).

Internal dummy resistor and switch
It's convenient to use internal dummies. The requirement for dummy resistors are short-time stability and not too much deviation.

It's peculiar to place 1M at the end because I want a dummy of 2Meg in order to test my 20Meg resistors to assemble my 100Meg standard, which is the starting point of this high resistance bridge any way.  I may add more dummy resistors than charted such as 1G, 10G if the test shows good results.

Output and Adjustment

The output is split into three part:
 - Record out.
 - LED display(not drown)
 - An analog meter. This is for the quick adjustment.

I modified the coarse adjustment pot to a multi-turn so that to extend the applicable Rs. Ideally it should be a 330 Ohm but I only have 1k, has to parallel another 500 ohm.

Mini survey of existing high precision high resistance measurement

1. Guarded Wheatstone Bridge
This is the fundamental way, adopted by NBS/NIST long time ago.

Detector D is a commercial electrometer, it must be ground referenced, therefore the V must be floated.

- Manual balancing, resulting complexity, multiple leakage points and time consuming
- Float battery, difficult to change voltage, multi-leakage path, and need guard drives(high voltage, may be separately powered)
- A detector is needed, outside the bridge box
- Measurement range only upto 10G

Ref: NIST Technical Note 1298, NIST Measurement Service for DC Standard Resistors, pp.20
(Note: this technical note is obsolete so is the Guarded Wheatstone Bridge)

2. Modified Wheatstone Bridge('active-arm' bridge)

Replacing two resistor arms of A and B from the above circuit by two programmable voltage sources.
The apparent advantage of this configuration is automatic balancing. By reading from D, the system know the status and adjust V1 and/or V2 accordingly, and read the output D again, adjust again if necessary.
Another good thing about this method is the total control of V1 and V2, making the very large arm ratio such as 1000:1 possible, and free adjustment of test voltage from very low to 1000V. 
NIST adopt this method soon it come out and still use it now. 
MI 6600A and 6650A are the commercial versions.

- Have to use bulky, expensive commercial voltage generators(programmable DC calibrators) and a electrometer as the detector.
- Linearity depends on voltage generators
- Slow to operate as the time constant is large and takes several loop cycles to reach to the final value.
- Need a dedicated software(balancing algorithm)

Ref: Automated Guarded Bridge for Calibration of Multimegohm Standard Resistors from 10M to 1T
NIST Technical Note 1458, NIST Measurement Service for DC Standard Resistors

3. Binary Voltage Divider

Adopted from Cutkosky Divider and commercialized as 6000B by MI.
Measurement is automatic.
Not very good for resistors higher than 1G as the accuracy of 1G measurement already gone up to 5ppm.

Ref: Resistance Measurements Systems w/Sub PPM Accuracy - 1u? to 1G?

4. DMM based

The advantage of this method is the ease of construction, by making use of existing equipment in a lab such as DC source and an DMM. However, it suffered from leakage of the DMM making it difficult to measure high resistance such as above 10G.

There is an articel 'North American One Gigaohm Interlaboratory Comparison 2006–2008'
Where table 7 lists the methods to test 1G resistor used by the participants.

There are 8 MI 6000B(30.4ppm),  3 Active Arm Bridges(13.5ppm), only 1 Wheatstone Bridge(67.9ppm), 1 DMM based(39ppm), 2 Teraohmmeter related(313.7ppm).
Brackets in ppm are the averaged uncertainty for that method. As can be seen that,  Active Arm Bridge has the best uncertainty, and the Teraohmmeter method is the worset.

Building materials, components, purchase/ arrivals

Ordered the case, will be arrive next week, size 260mm by 185mm by 96mm, smaller than a A4 paper, but big enough for the bridge. I'll use it in table top manner.

Ordered the LED meter as well. It is a 0.2V full scale voltmeter. I'll try modifying the decimal point when it arrives.
(the LED meter in the photo cannot display negative number)
2016-4-4 Panel meter arrived, display negative OK.
2016-4-7 Case arrived. Will keep me busy on this week end.

to be cont......

Building progress

2016-4-2, Power supply board done and tested.
2016-4-4, Main board done but not tested.
2016-4-5, Shift the decimal point 3 digits so that it display 1999.9 instead of 1.9999. Not a very easy task though because the display is multiplexed. I have to add a transistor.
2016-4-7, Main board tested together with the power supply board and the display, functionally okay.
2016-4-9, Power supply board modified: add battery protection and auto on/off for hi-voltage.
2016-4-9, Batteries finished. One is 18V of five 18650 cells, the other is 125V of 32 lithium cells. Both packs are triple plus insulated(extra for cells, external wrapping and PTFE sheet).
2016-4-10, Panel almost finished.

to be cont......


Some insulation resistance in Ohms, measured with 1V voltage.

 A. 3.9pF ceramic capacitor?5E13
 B. 20pF ceramic capacitor, >1E14, dielectric absorption
 C. Base and emitter revere current of 9014 BJT, 0.03pA
 C. Base and emitter forward 0.1V biased current, 0.6pA
(current of base and collector is larger than the above in both directions)
 D. Cat 5 twisted pair, >1E14, dielectric absorption
 E. Cat 6 twisted pair, 5E12
 F. Piece of dual wire, 5E11
 G. An very old vari-capacitor, severe dielectric absorption
 H. A potential meter/Varistor, terminal and case, 5E11
 I. Adjacent tracks of veroboard, with flux 1E11, flux cleaned 1E13, warshed with alcohol 5E14.

to be cont......

Reserved for future use.
to be cont......

(The End)


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