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The Voltage Standard

February 25, 2016

Having done much electronic circuit design and construction in my career, I have several multimeters in my home workshop. The multimeters can be configured as voltmeters, I have a few analog voltmeters on my shelves, and my oscilloscope will also function as a crude analog voltmeter. When wired to a voltage source, these will read nearly the same value of voltage, but not the same value. Fortunately, my work doesn't require too precise values of voltage, so I'm not that concerned.

One of my digital multimeters will read voltage values to four-and-a-half digits; which, in electrical engineering parlance, means that it will read from 0 to 1.9999 volts. Seeing such a nice array of digits makes you think that your knowledge of voltage is very good. This reminds me of a psychology experiment done many decades ago on how people think that pocket calculators are infallible.

A team of psychologists modified calculators to give the wrong answers. As I remember, nearly all the test subjects believed that the calculator answers were right, even though a moment's reflection or a back-of-the-envelope calculation would have indicated that something was amiss. When your laboratory voltmeter shows many digits, how many of these can you believe?

Although manufacturers take care to ensure that their computer chips give the right answers, errors will occur. One famous error was the Intel Pentium P5 floating point division bug. This was a subtle error, since it would occur in just one in nine billion divisions. Even then, the error was at the few tens of parts-per-million level. Intel recalled all the faulty chips at a cost of nearly half a billion dollars. I recall that in the interim there was a software patch for the Excel spreadsheet that corrected this error.

Figure caption
(Webcomic xkcd no. 217 by Randall Munroe, licensed under a Creative Commons Attribution-NonCommercial 2.5 License. Click for original on his xkcd web site.)

Accurate laboratory measurements require calibration of instruments to standards. Most large corporations have a policy of calibrating their laboratory instruments at intervals. In my laboratory, calibration was done for our balances and digital thermometers, but rarely for voltmeters. I had an antique instrument, a Leeds & Northrup Millivolt Potentiometer, that I used to compare voltage readings against a standard cell. A standard cell is nothing more than a specially constructed battery, and a potentiometer has the unique property of not drawing any current from the standard cell when it's compared against another voltage source.

The Weston cell, invented in 1893 by the chemist, Edward Weston, was the voltage standard in common use through 1990. The cell cathode is an amalgam of cadmium and mercury, the cell anode is pure mercury, and the electrolyte is an aqueous solution of cadmium sulfate. At the anode, cadmium goes into solution as cadmium sulfate. At the cathode, mercuric sulfate becomes liquid mercury. The cell potential is 1.018638 volts. More information than you'll ever need about the Weston cell can be found in ref. 1.[1]

Fig. 1 of US Patent No. 494,827, 'Voltaic Cell,' by E. Weston, April 4, 1893Fig. 1 of US Patent No. 494,827, "Voltaic Cell," by Edward Weston, April 4, 1893.

This cell served as a voltage standard as late as 1990, but it had the disadvantage that it contained the toxic elements, mercury and cadmium.

The voltage of a carefully maintained Weston cell is 1.018638 volts, and the temperature coefficient of the voltage is very small.

(Via Google Patents.)[2]

Semiconductor devices started to replace such electrochemical voltage reference cells in the 1960s. The first practical semiconductor voltage reference was the Zener diode, based on a particular reverse voltage breakdown effect in highly doped semiconductor diodes discovered by Clarence Zener. While silicon diodes, both Zener and ordinary, have a voltage temperature coefficient of about 2 mV/°C, you can connect a reverse-biased Zener diode and a forward-biased ordinary diode in series to effectively cancel the temperature effect (see figure). I've done this trick many times in my own circuits.
Zener diode voltage reference circuitIn the days before bandgap voltage reference circuits, analog designers would combine a Zener diode with an ordinary silicon diode to create a temperature-compensated voltage reference.

(Created with Inkscape.)
Other semiconductor voltage references are based on the bandgap of silicon, which is about 1.22 electronvolts at absolute zero. The first of these, the Brokaw bandgap reference, was invented by Paul Brokaw in 1974. The Brokaw bandgap reference has a temperature coefficient of just a few tens of ppm/°C.[3] A more recent bandgap voltage reference is shown in the figure.

Fig. 1 of US Patent No. 4,447,784, 'Temperature compensated bandgap voltage reference circuit' by Robert C. Dobkin.Fig. 1 of US Patent No. 4,447,784, "Temperature compensated bandgap voltage reference circuit" by Robert C. Dobkin.

Dobkin, co-founder of Linear Technology Corporation, has more than a hundred patents.

(Via Google Patents.)[3]

While these simple semiconductor voltage standards are good for most laboratory work, the world demands much more from its primary standards. That's why a device that operates at liquid helium temperatures, the Josephson junction array, is used as today's voltage reference. Such arrays will give a voltage value that's accurate at the parts per billion level.

The principal behind this device is the Josephson effect, a property of superconducting materials separated by a thin insulating gap discovered by Brian Josephson. This is a quantum mechanical effect in which electrons can tunnel through the insulator to allow a current flow. If a superconductor-insulator-superconductor junction is driven at a frequency, f, then regions of constant voltage will appear in the device current-voltage curve. These voltages, Vn are given as

 AC Josephson equation

where h is Planck's constant, and e is the elementary charge. Since the voltages depend only on fundamental constants, this is a very nice standard. One such voltage standard chip is shown in the photograph. To produce a volt-level signal, the device has many junctions in series, and it's driven at microwave frequency.

NIST Josephson array voltage referenceAn array of 3020 superconducting Josephson junctions that act as a voltage reference at liquid helium temperature.

(NIST image, via Wikimedia Commons.)


  1. Walter J. Hamer, "Thermodynamics of Standard Cells of the Saturated Cadmium Sulfate Type," Journal of Research of the National Bureau of Standards A - Physics and Chemistry, vol. 76A, no.3 (May- June, 1972).
  2. E. Weston, "Voltaic Cell," US Patent No. 494,827, April 4, 1893.
  3. P. Brokaw, "A simple three-terminal IC bandgap reference," IEEE Journal of Solid-State Circuits, vol. 9, no. 6 (December 1974), pp. 388–393.
  4. Robert C. Dobkin, "Temperature compensated bandgap voltage reference circuit," US Patent No. 4,447,784, May 8, 1984.

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