A Self-Balancing Nanovolt Potentiometric System for Thermometry and Calorimetry

The principle of a self-balancing potentiometric system is described. The principle is applied to the modification of an existing manually operated thermo-free, low voltage potentiometer consisting of Diesselhorst ring elements. The modification involves the addition of reed relays which enable the potentiometer voltage to be set by digital signals. By incorporating a digital voltmeter, or an analog-to-digital converter, and a nanovolt amplifier with the modified potentiometer, self-balancing of the potentiometer may be achieved through either hardware logic implementation or direct digital control from a minicomputer. The resolution of this self-balancing potentiometric system for a full scale input of 100 mV is about one to 10 parts in 108. With real-time digital processing of the data, resolution of about 1 nV or better has been achieved for slowly changing input signals. The overall accuracy of the system is better than 10 ppm for voltage measurements and about 1 ppm for voltage ratio or resistance measurements.


. Introduction
In high preCISlOn low temperature calorimetrv cov~ring the .temperature r ange from 4 to 400 re, ' a platmum resIstance thermometer is often used as the temperature indicating instrument. The r esistance .of th e thermometer n?ay be measured either by a bndge or by a potentlOm eter. Automated high resol~tion dc and ac bridges have been developed and used l~ ther~om e try and calorim etry [1 -4]l. In the potentlOmetnc m ethod th e resistance of a four terminal resistor is obtain ed from the ratio of the p.otential drop developed across Lhe unknown re-SIstance to that across a seri es-conn ected standard resisto~' of l~nown value. The advantage of the potentIOmetn c m ethod over the bridge method is that with th e former th e measurement is independent of the lead wire r esistance. This is especially important at low temperatures where the lead wire resistan ce may be a couple of orders of mag ni t ude greater than t he r esistance of the th ermometer to be m easured. An add ed ad vantage in calorimetry is that the poten.tiometer may be used also to measure the energy supphed to the calorimeter. The present work describes the principle and an example of an automated potentiometri c system with high r esolution and high sensitivity suitable for platinum r esistance thermom etry and calorimetry work, by t he modification 1 Fi gures in brac kets indi cate the lite rature re ferences at the end of this paper of an existing manually operated t herillo-free poLe ntiom eter in to a progranlll1 able potentiometer.

Principle
The prin ciple of this present app roach to a high resolution au tom atic po tentiometric measurement is outlined in figure 1 and is described by t he following sequence of operations.
(1) With the gan ged swi tch at position 1, th e galvanometer or detector outpu t of the programmable potentiometer, POT, is open and the input to the nanovolt amplifier, NV A, is shorted.
(2) A digital voltmeter , DVM , or an analog-todigital converter is used to sample the unknown voltage, Ex . The first few most significant figures of the DVM are then transferred digitally to the POT to generate a voltage E p- The ganged switch changes to position 2. This connects the NVA input to the output of th e POT. The NVA amplifies the POT imbalance signal, Ex -E p, by an amplification fac tor A. The DVM input is now connected to read the output of the NVA, E n=A (E x -E,,).
The combination of the two DVM readings, Ep and E n, yields a potential readng of Ex= Ep +E~/A to a high degree of resolution. In the followmg example an automated potentiometric system with a resolution of the order of one to 10 parts in 10 8 and a sensitivity of about 1 nV is demonstra ted .

Programmable Potentiometer With Diesselhorst Rings
One commercially available manual potentiometer is easily adaptable to the principle outlined above. It is a double six-dial potentiometer Z of thermo-free design [5]. The four most significant decades are composed of Diesselhorst rings [6]. These four decades are divided into two sections, each with its own power supply. The least significant two decades are composed of Lindeck elements. The maximum potentiometer voltage is 0.1 V.
A Diesselhorst ring consists of N resistors, each of resistance R, connected in series. In figure 2, a ring of 10 resistors is shown. The junctions between the resistors are labeled from n=O to N-1 starting from the fixed current lead. The ring current, l, flows between position 0 and a position n on the ring, selectable by a movable pointer. The potential drop E, developed across the resistor between positions 0 and N-1 is then given as lR n jN, In general one decade of potential values is generated by one such ring. Several rings of successive , Commercial materials are identified in this paper to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsemcnt by the National Bureau of Standards. decades may be connected in series to form a potentiometer. A schematic diagram of one of the sections of the potentiometer with modifications is shown in figure 3. The values of the ring elements Rl and R2 are related such that R1=10 Rz, where Rl is in the most significant decade.
The potential, E p , of the potentiometer is connected in series with but opposing the unknown voltage, Ex, to be measured. A galvanometer or a nanovolt amplifier may be connected in series with Ex and Ep as a null detector or as an unbalanced signal indicator. There are no sliding contacts involved in this (Ex-Ep)-detector-potentiometric circuit. Any change in the switch resistance and thermal emf is restricted mainly to the potentiometer current, I p, circuit.
If a highly regulated constant current supply, CCS, is used to supply I p , it minimizes the effects from the irreproducibility of the switch resistance and from the thermal emf generated in the switches. Therefore, the quality of the switches to be used in conjunction with a CCS is not critical, and ordinary reed relays in dual-in-line packages may be used in place of the massive rotary switches in the original potentiometer. The schematic diagram of the logic circuit to control one of the Diesselhorst rings is shown in figure 4. Identical control circuits are used for other decades. The clock pulse, Cp , is activated when a change of potentiometer setting, E p , is desired. During the clock pulse, the incoming binary coded decimal, BCD, signal passes through the latch to the decoder which activates one of the ten relays (0 to 9). The potentiometer setting will remain latched at the value when the clock pulse is deactivated.
Position 10 and its associated circuit is not required for ordinary potentiometric operation. However, the presence of the 10th position and the abilit~T to reverse the polarities of the individual power supplies of the potentiometer make the auto-calibration or dial-to-dial comparison of the potentiometer easier.
The relays at position 10, activated by any signal designated from 10 to 15, also avoids the open condition to the CCS, even in case the decoder receives a random or noisy signal other than for 0 to 9. To further prevent the CCS from experiencing an open circuit, normally closed relays are placed between positions 3 and 1 or 3 and 2 of ganged switch 8 1 -8z• These relays are activated directly by the 5 V power supply of the potentiometer relay controller. Therefore the CCS will not seen an open circuit even if the power to the controller is off.  The resistors between the ring clemen ts and the decade switches (see fig. 3) are used Lo provide a constant resistive load to a potentiometer power supply (usually a battery 01' a constant voltage supply) and thus provide a constant I p at different E/I settings. However, in exactness or the adjustmen t in Lhe values or these resistors may require readjustment or I ii for every change or Ep-' With the CCS, these resistors become unimportant and may be eliminated entirely. The lise or CCS also eliminates the need for I'requent 1/1 standardization when batteries 01' constant voltage suppli es are used to supply the ] p' The potentiometer Cllr rent, ]/1 may be monitored by the voltage drop, E" developed across the current sensing rcsistor, R s·

Constant Current Supply
Highly stable constant currents required by the potentiometer may be supplied by either commercially available CCS's with photogalvanometer feedback control or CCS's built around a highly stable, low noise operational amplifier.
The schematic of a simple constant current supply is shown in figure 5A. By properly choosing the com- In a different configmation than shown in figure  5A, the resistive load HL may be placed between the ground and the common point of Er and R S) whil e the output of the amplifier is connected directly to the negative input. However, this configuration works well only if the voltage developed across the load is much less than 1 V, otherwise the performance of the amplifier deteriorates because of the high common mode voltage applied to both inputs.
In order to protect the standard cell Er from excessive discharge in case of electrical power failure, a low thermal emf « 1 !J. V) bistable magnetic latching relay is installed in series in the standard cell circuit. The relay control circuit is shown in figure 5B . When the ac power to the ± 15 V power supply is turned off, the normally closed reed relay K 2 causes the energy stored in capacitor C to be discharged through the "off" coil of the latching relay, K 1 , and thus dis-connects the stand ard cell. The standard cell connection may be restored manually by the momentary switch S a, when the ac power is on. Switch S~ may be used to disconnect the stand ard cell manually. The diodes or zener diodes across the relay coils are used to protect the relays, especially the latching relay.

. Low Level Signal Multiplexers
The relays used in the sys tem to selec t different inputs to the DVM generate less than 0.5 p.V of offse t thermal emf, and that used for the input to the nanovolt amplifier Jess th an 50 nV. Under normal operational conditions these offset voltages are relatively stable. Both types of relays are of bistable m agnetic latching construction. A pulse duration of 1 ms is sufficient to ch ange the s tate of the relay. Th e very low duty cycle with such a short pulse keeps the energy dissipation in the relay coil to a minimum and produces negligible temperature differ ential between the relay contacts. These relays h ave copper leads which furth er reduce the thermal emf at the relay connections. Although the two types of relays used in this system and several other types of latching-type relays tested have satisfactory th ermo-electrical characteristics, their mechanical reliability seems to be low. The biasing magnets in the relays are susceptible to damages due to overdrive. This may cause failures of the relays to latch onto one of the states without constant coil current. A low thermal emf silver-silver alloy rotary switch used in the manually operated potentiometric system is retained as the selector for low level signals (Ex) to the potentiometer. A rotary solenoid h as been added to this rotary switch so that its position may be selected by digital signals.
When the potentiometer is used for resistance measurements, s uch as in the case of resistance thermometry, the stray and thermal emf in the potentiometer-Ex-detector circuit may be obtained by reversing the polarities of all the CCS's used for the potentiometer and thermometer. This may be accomplished with DPDT relays with common open periods. The connections associated directly with the Ex measurement path , such as the potentiometer inpu t selector and the nanovolt amplifier input relay, should remain undisturbed during the reversal measurement.

Measurements
Hardware logic circuits have been constructed and tested to operate the potentiometric system according to the procedures ou tlined in the Principle section. Only a few momentary switches or a sequential switch are required to carry out the procedure. However, as a minicomputer became available, a simpler digital interface to the central processing unit has been built. This provides far more ver-satile operation of the system through software implementations. A typical software program for self-balancing procedure is illustrated by the flow chart, figure 6. The values of the controlling parameters in the diagram may be changed to suit the application. The program begins with the low level signal scanner selecting an unknown voltage source Ex, to be measured. Ex is first examined by the DVM to a resolution of 1 p.V. If Ex is greater than 0.1 V, the maximum voltage of E p , the potentiometric measuring procedure is bypassed . If Ex is less than 0.1 V and the rate of change of Ex is less than 10 -7 V S -t, potentiometer setting, Ep is set to the nearest 10 p.V of the value Ex as indicated by the DVM. The DVM is then shifted to read the output of the NVA, which amplifies the unbalanced signal, Ex -Ev, of up to ± 10 p.V by an amplification factor A. The full scale reading of the NVA is usually equal to the last digit of the programmable POT. When the NV A reading is within its range, the automated voltage

Characteristics and Applications
The accuracy and the stability of the entire potentiometric system depends upon many factors, such as the stability of the CCS's, the temperature coefficient of the ring resistors in the Diesselhorst ring, the rate of ambient temperature fluctuations, and to a lesser degree upon the gain stability of NVA and of DVM, etc.
The sensitivity of the system is limited by the noise of the NVA to about 5 nV. However, for slowly changing signals, it is possible to make average NV A readings every 30 s. A moving collection of oddnumbered equally spaced readings, for 5 to 10 min is then subjected to a simple least-squares evaluation The moving average method acts as a filter with a long time constant. Thus the short term noise of the NVA may be filtered out, and the system is capable of resolving signals to better than 1 n V from a signal of less than 100 mY. However, long term fluctuations, such as those caused by the temperature controlled oven for the standard cells and current sensing resistors in the CCS, may still be detected. For steady or monotonically changing signals, the successive change of the signs of the second derivative 'b' of the quadratic equation indicates the approach of the limit of measurement capability of the potentiometric system.
The accuracy of the voltage measurement by this system is about 10 ppm, even after the application of dial-to-dial autocalibration factors and the calibration of the main resistor HI, because the potentiometer current sensing resistor Rs in the potentiometer is adjustable in 10 ppm steps. However, for ratio or relative measurements, the accuracy is better than 1 ppm.
This potentiometric system has been used principally to measure temperatures in automated precision adiabatic calorimetry. Details of the auto-mated calorimetric procedure and the results obtained with the automated system on the heat capacity data from 5 to 380 K, for a-AI20 3 , poly-(vinyl chloride) and poly(chlorotrifluoroethylene) are reported elsewhere [7]. The sample of a-A120 3 used is a National Bureau of Standards, Standard Reference Material (SRM) 720, Synthetic Sapphire, for calorimetry. Its enthalpy and heat capacity values have been previously certified from 273 to 2250 K.
The temperature of the calorimeter is indicated by the resistance of a platinum resistance thermometer whose resistance is about 35 Q at 373 K and 0.02 Q at 4 K. A thermometer current of 1 to 2 rnA is generally used, except at liquid helium temperatures where a current of up to 10 rnA may be used to increase the sensitivity. These currents yield a thermometric signal from 200 !J. V to 80 m V. The thermometer current is also supplied by aCeS with photogalvanometer feedback control or a highly stable, low drift operational amplifier and is monitored by the potential drop across a 10 Q standard resistor. With the above-mentioned procedure to achieve a resolution of about 1 nV for the potentiometric system, temperatures may be resolved to 10-5 K at temperatures above 50 K. The overall stability of the entire calorimetric temperature measurement may be judged from the stability of the thermometer current. The current seems to change slowly within 1 ppm h -1 and cycles wi thin 10 ppm in 24 h. This cyclical behavior is probably due to the relatively high temperature coefficient of the ring resistors and the current sensing resistor, Rs, which follow a day to night ambient temperature change of 1 to 2 K.
The energy input to the calorimeter is also measured by the automated potentiometric proced ure, however, the req uiremen ts in the energy measurement are less demanding than those of the temperature measurement.

Conclusion
It was found that the principle outlined in the introduction is a practical and workable one. The resolution of the potentiometric system has actually been increased by the automation and the digital data treatment outlined. In many cases of auto·· mation, there have often been trade-offs between precision and convenience.
The NVA used in the present system is stable to about 0.1 percent. By using a unit with 10 ppm stability (now available), it should be possible to increase the range and resolution of the amplifier by means of incorporating two decades of programmable Diesselhorst rings. These rings should be made of resistors with a low temperature coefficient. A microprocessor may be incorporated together with the programmable Diesselhorst rings, CCS, and NV A as one integral instrument to yield up to an eight-digit display of the unknown potential without the use of an external computer.
The author thanks R. J. Carpenter for assistance in the design, construction, and testing of various l~gic a!ld interface cir?uits and, for many helpful dIscussIOns, F. 1. MOpSIk and P. r. Olsen for discussions on the applications of operational amplifiers and C. H. Pearson for assistance in the ftssembly of the system.