MIL INST OF STAND & TECH NI8T

PUBLICATIONS

AlllOb flb5b70

NIST Technical Note 1462

A Four-Terminal Current Shunt with

Calculable AC Response

O. B. Laug

T. M. Souders

B. C. Waltrip

NISTNational Institute of Standards and Technology • Technology Administration • U.S. Department of Commerce

0,575 3

NIST Technical Note 1462

A Four-Terminal Current Shunt with

Calculable AC Response

O. B. Laug

T. M. Souders

B. C. Waltrip

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg. MD 20899-81 1

1

August 2004

^

U.S. Department of Commerce

Donald L. Evans. Secretary

Technology Administration

Phillip J. Bond. Under Secretary for Technology

National Institute of Standards and Technology Arden L. Bement, Jr., Director
Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such

identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Technical Note 1462

Natl. Inst. Stand. Technol. Tech. Note 1462, 48 pages (August 2004)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2002

For sale by the Superintendent of Documents, U.S. Government Printing Office

Internet: bookstore.gpo.gov — Phone: (202) 512-1800 — Fax: (202) 512-2250

Mail: Stop SSOP, Washington, DC 20402-0001
Table of Contents

ABSTRACT 1

1. INTRODUCTION 2

2. THE CALCULABLE AC RESPONSE 4

2.1 Inductance 4

2.2 Capacitance and Dissipation 5

2.3 Skin Effect ' 9

2.4 Eddy Current Losses 10

2.5 Thermoelectric Effect 11

3. EXPERIMENTAL AC MEASUREMENTS 11

3.1 Phase Comparisons 14

3.2 Magnitude Comparisons 14

4. FINAL MAGNITUDE AND PHASE RESULTS 21

5. CONSTRUCTION DETAILS 23

5.1 Preparing the Bifilar Resistance Element 23

5.2 Tinning the Strip for the Current Terminals 23

5.3 Locating the Potential Terminal Target Points 23

5.4 Attaching the Potential Leads 25

5.5 Attaching the Current Terminals 27

5.6 Final Assembly 27

5.7 Troubleshooting Assembly Problems 28

6. MEASUREMENTS 29

6.1 Common Measurement Problems 29

6.2 Power Coefficient of Resistance 31

7. ACKNOWLEDGMENT 32

8. REFERENCES 32

APPENDIX A-- Mechanical Assembly Drawings 33

111
List of Figures

Figure 1

.

Basic diagram of the bifilar configuration 3

Figure 2. Model of distributed capacitances and associated

dissipation factor 5

Figure 3 Basic comparator system 12

Figure 4. Measured phase difference

between arrangements M1_M2 and M1_R15 15

Figure 5. Measured phase difference

between arrangements M2_M2 and M1_M2 15

Figure 6. Measured phase difference

between arrangements M2_M2 and M1_R15 16

Figure 7. Measured phase difference

between arrangements M2_M2 and M2_R15 16

Figure 8. Measured phase difference

between arrangements M2_R15 and M1_M2 17

Figure 9. Measured phase difference

between arrangements M2_R15 and M1_R15 17

Figure 10. Measured resistance difference

between arrangements M1_M2 and M1_R15 18

Figure 1 1 . Measured resistance difference

between arrangements M2_M2 and M1_M2 18

Figure 12. Measured resistance difference

between arrangements M2_M2 and M1_R15 19

Figure 13. Measured resistance difference

between arrangements M2_M2 and M2_R15 19

Figure 14. Measured resistance difference

between arrangements M2_R15 and M1_M2 20

Figure 15. Measured resistance difference

between arrangements M2_R15 and M1_R15 20

Figure 16. Calculated resistance vs. frequency for the

selected arrangement M1_R15 with uncertainty bounds (k=2) 22

Figure 17. Calculated phase vs. frequency for the

selected arrangement M1_R15 with uncertainty bounds (k=2) 22

Figure 18. Photograph of jig used to locate target

points for potential terminals 24

Figure 19. Photograph of set up used to hold and position

potential wire prior to spot welding 26

Figure 20. Photograph of potential lead attached

and dressed against resistance sheet 26

Figure 2 1 . Diagram of voltages and loop currents involved

in comparing two four-terminal shunts 30

Figure 22. Plot of current shunt dc resistance

change at 1 A and 10 A versus time 32

IV
List of Tables

Table I Measured Capacitances 6

Table II Calculated Capacitive Time Constants

and Resistance Change due to Dielectric Loss 8

Table III Skin Effect vs. Frequency 10

Table IV Resistance Change relative to DC Due to Eddy Current Losses in Heat Sinks 10

Table V Bridge Comparison Data: Resistor

Configuration vs. Transformer Scaled Resistor 13

A FOUR-TERMINAL CURRENT SHUNT WITH CALCULABLE AC RESPONSE

O. B. Laug, T. M. Souders, and B. C. Waltrip

National Institute of Standards and Technology, Gaithersburg, MD 20899

ABSTRACT

The design of a 0. 1 Q., four-terminal current shunt with calculable frequency dependence

up to 1 MHz is described. It is intended for use as a standard for current measurements up

to 10 A rms with the primary purpose of being able to tie alternating-current measurements

to direct-current measurements. The shunt is of the bifilar flat-strip configuration where

the effects of self-inductance, skin effect, capacitance, dissipation factor, and eddy-current

losses are considered. Contributions of the individual effects, where applicable, are determined by calculation based on geometry and corroborated by differential

measurements and finite-element field simulations. The uncertainties due to dimensional

and electrical measurement tolerances are computed as well.

In addition to the calculable aspects of the shunt this technical note provides assembly

details of the shunt based on the mechanical drawings made available in the appendix. The

practical issues of measuring 4-terminal shunts with emphasis on dealing with commonmode potentials are discussed. The thermal properties of the current shunt are presented

together with some suggestions on reducing the power coefficient of resistance.

KEY WORDS: 0.1 ohm shunt, 4-terminal shunt, ac resistor, bifilar shunt, calculable shunt,

current shunt
1. INTRODUCTION

The measurement or sensing of current is traditionally made using a low resistance current

shunt, current transformer (CT), mutual inductor (Rogowski coil), or Hall Effect device.

Each of these sensors has certain attributes which makes them useful for a given

application. In support of the NIST calibration service which provides AC-DC Difference

calibrations of thermal current converters and ac shunts up to 20 A and 100 kHz, our

current shunt with calculable frequency response, is intended to be used as a working

standard. Moreover, it can help serve in the buildup process from lower currents to establish uncertainties at higher levels of current. Another important electrical metrology

application for accurate current determinations is the measurement of real and reactive

power including higher order harmonics of current where the effects of phase angle

become important.

Current Transformers (CTs) are widely used to scale a high-level primary current to a lower level secondary current. The secondary current can be measured directly with a

calibrated thermal converter or as a voltage across a burden resistor. While CTs are limited

in bandwidth and do not operate at dc (except for zero-flux designs), they offer superior

isolation. Current shunts do not have the same inherent isolation properties. Thus, when

measuring the characteristics of a four terminal current shunt special attention must be

given to the rejection of common-mode voltages and loading at the potential terminals.

These become critical measurement issues when a 4-terminal current shunt is compared

against other current measuring devices.

Current shunts used for measuring ac currents require conductor configurations that are as noninductive as possible. The presence of inductance is the primary nemesis of a shunt

resulting in appreciable phase angle errors, and to second order, magnitude errors. Cylindrical and bifilar flat strip designs can both give low inductance. However, the

practical physical limitations of each of these configurations do not allow the design to go

to the limit of zero inductance. The small but finite inductance of each design can be

calculated, and the coaxial configuration has a closed-form solution. The usual

arrangement for a coaxial design is to employ an inner tube of a given resistance material

enclosed by an outer tube acting as the return path for the current that is launched at the end

of the center tube. Coaxial designs tend to be difficult to fabricate in that the inner tube of

resistance material must be as thin as possible to minimize skin-effect errors yet be self

supporting. Some designs substitute a cage of fine parallel wires that serve as the inner

tube. Another disadvantage of the coaxial design is the difficulty of transporting heat from

the resistance element to the ambient. An air dielectric between the inner and outer tube is a poor conductor of heat. Some designs partially overcome the thermal problem by

employing a liquid or paste dielectric with desirable thermal properties to fill the air space.

Any significant power generated in the resistance element will cause a temperature rise

depending on the thermal resistance to the ambient. Temperature changes in the resistance

element will cause the shunt to display a power coefficient of resistance if the resistance

material exhibits a non-zero temperature coefficient of resistance.
A bifilar strip configuration can also have low and calculable inductance provided that a high width-to-thickness aspect ratio of the resistance material is maintained. The bifilar

configuration that we have chosen is shown in Fig. 1 . The design has two main attributes;

it is relatively simple to fabricate, and the thermal issues are easier to accommodate. A thin

dielectric placed between the folded strip insulates the two halves preventing a short circuit

along the intended path. Adding a thin dielectric between the strips increases the

inductance slightly but its effects are still calculable. By clamping the folded element

together with flat blocks insures mechanical stability of the structure. The blocks are made

of aluminum with integral fins to provide a low thermal resistance path from the resistance

element to the ambient. In our model a fan attached to the shunt provides forced cooling

across the fins to further lower the thermal resistance from the aluminum blocks to the

ambient.

POTEr^JTIAL

CONNECTION

TOP

HEAT SINK

PLATE

X"

Jk. X COPPER

^ -I

RESISTANCE

STRIP

W

"X"

COPPER

BOTTOM

HEAT SINK

PLATE X r^

Figure 1. Basic diagram of the bifilar configuration
2. THE CALCULABLE AC RESPONSE

Calculations were performed to derive the complex frequency response of the bifilar shunt

configuration of Fig. 1 based on applicable formulae and nominal dimensions taken from

the prototype model designed for a nominal 0.1 Q. resistance. Contributions from

equivalent inductance, inductive coupling to the aluminum heat sinks, shunt capacitance

and dissipation factor, skin effect, and electro-thermal effects were all considered.

Uncertainties due to dimensional and electrical measurement tolerances are computed as

well. Four different configurations were studied, differing by the dielectric materials that were used to separate the halves of the resistance strip, and the dielectric used to separate

the resistance strip from the heat sinks.

2.1 Inductance

Formulas for the inductance of 4-terminal bifilar strip resistors in terms of their dimensions were long ago derived by Silsbee [1]. These are presented as an expanded series in EQ (28)

of that document. The relevant dimensions are expressed in cm. Using this formula, the

equivalent series inductance of the resistor being fabricated has been calculated, and by

differentiating with respect to the dimensional variables, the tolerances have been

calculated as well. Ignoring the higher order terms (although second order terms were

included in the actual calculations, reducing the value by about 0.5 %), the inductance is given by

_47re_ 2d

t + —

3

lO'*" =0.1460/2// (1)

w

where,

w = width of strip = 5.08 cm (2.00") nominal

d = thickness of strip = 0.00508 cm (0.002") nominal

t = thickness of insulator = 0.00254 cm (0.001") nominal

€ = length of circuit = 10.008 cm (3.94")

(Here the thickness, t, is given for the configuration finally chosen.)

The deviation in inductance resulting from dimensional deviations from nominal is given

by

AL = 1 6.5 AJ- 0.0289 Ah- + 0.0147 A^ + 24.8 Ar (2)

Since the width and length of the strip are relatively large (approximately 5 cm and 10 cm

respectively), measurements of w and / can easily be made with 1 % uncertainty. The

small dimensions (0.005 cm and 0.0025 cm) of d and t however have estimated 2 a

measurement uncertainties of about 15%. Taking the root-sum-of-squares of the four terms

in (2), assuming 1 % tolerances for w and / and 15% for d and t, gives an 1 1 % uncertainty

in L. The corresponding inductive time constant (L/R) and associated uncertainty are given

by T= 1.460 ns ±0.16 ns.
2.2 Capacitance and Dielectric Loss

There are six components of shunt capacitance (and associated dielectric loss) that affect

the frequency response of the resistor (see fig. 2): (C|) the distributed capacitance between

the two halves of the strip from the fold to the potential terminals; (Co) the distributed

capacitance between the two halves of the strip from the potential terminals to the

termination with the current terminals; (C3) the lumped capacitance between the current

terminals; (C4) the distributed capacitance between the strip and the lower heat sink from

the fold to the lower potential terminal; (C5) the distributed capacitance between the strip

and the upper heat sink from the fold to the upper potential terminal; and (C6) the

distributed capacitance between the strip and the upper heat sink from the upper potential

terminal to the end of the strip. Note that the aluminum heat sinks are connected to the

lower current terminal. The values of each of these capacitances (and associated

conductances) have been estimated from direct capacitance (and dissipation factor)

measurements and knowledge of the dimensions of the structure.

POTENTIAL

TERMINALS

Figure 2. Model of distributed capacitances and associated dissipation factor
Table I Measured Capacitances in nF, and (Conductances in |liS) at 100 kHz

Dielectric

Used M2_M2 M2_R15 M1_M2 M1_R15

Capacitance

measured T

Ce-e_X

Between

Elements

2.30

(13.6)

2.30

(13.6)

4.34

(25.0)

4.34

(25.0)

Ce-a _Y

Elements to Heat Sinks

4.67

(55.3)

0.98

(1.6)

4.67

(55.3)

0.98

(1.6)

Cc, Between I Terminals

0.49

(14.1)

0.49

(14.1)

0.49

(14.1)

0.49

(14.1)

Capacitance

derived T

Cj 0.63(18.1) 0.63(18.1) 0.63(18.1) 0.63(18.1)

Ci M2 0.67 (4.0) 0.67 (4.0)

C2_M2 0.31 (1.8) 0.31 (1.8)

C(4+5)_M2 1.51 (17.9) 1.51(17.9)

C6^M2 0.31 (3.6) 0.31 (3.6)

C(4+5)_R15 0.32 (0.5) 0.32 (0.5)

C6_R15 0.064(0.1) 0.064(0.1)

C] Ml 1.27(7.3) 1.27(7.3)

C2 MI 0.58 (3.3) 0.58 (3.3)

For each shunt configuration studied, measurements were made of the total capacitance,

Ce.e_Xr between two equivalent resistor elements (strips) with the designated separation but

not connected where the fold would normally occur, the total capacitance, Ce.a_Y, between

the resistance elements connected together and the two heat sinks connected together, and

the total capacitance, Cc, between the two current terminals by themselves with no

resistance elements connected. These measurements are reported in bold font in Table I, and the corresponding conductances are reported beneath them in parentheses, for four

different dielectric configurations. At the top of each column is the configuration code for

the dielectrics used. The left part of the configuration code designates the dielectric used

between the resistance strips, with Ml and M2 designating 25.4 |im ( 1 mil) and 50.8 )Lim (2

mil) Mylar, respectively. The right part of the code designates the dielectric separating the

heat sinks from the resistance strips, with M2 designating 50.8 fxm (2 mil) Mylar, and R15

designating 381 |xm (15 mil) thermally conductive rubber.
The equivalent effect of each of the six identified capacitances (and the associated

conductances) is modeled by a lumped equivalent capacitance (or conductance) connected

across the potential terminals, i.e., in parallel with the defined resistance. The lumped

equivalent capacitances (and conductances) are computed in two steps, and the final values

are listed in Table I in normal font. In the first step, the proportional amounts of the

measured capacitances that contribute to each of the six components are computed as intermediate values, based on the dimensions of the strip from the fold to the potential

terminals, and from the fold to the end of the strip. From these intermediate values, the

equivalent lumped values are computed from integral equations that are based on the

assumption that the capacitances, conductances and strip resistance are all uniformly

distributed over the length of the resistance strip.

The lumped equivalent capacitances are computed from the following formulas, where £t is the total length of the resistance strip from fold to current terminal (1 1.43 cm), ip is the

length of the strip from the fold to the potential terminal (10.01 cm), AC is the difference

between £j and {p, X refers to the dielectric between resistance strips, and Y refers to the

dielectric between resistor and heat sinks.

C, ^2 and ^\ M\ l^ 1 X /' -^ (3)

^2 Ml a^^ ^2 Ml ^2 X

1 + - M

li p J

(4)

1 + — (5)

^(4+5)_A/2 ^^^ ^{4+5)_Rl5 ~V-4_y '^^5_y \ ^

"*" 1 Ai

3 4^

(6)

p J

^6_M2 ^^^ ^6_R\5 ~ ^6_Y 1 +

3A(?

i p J

(7)

As noted above, these formulae were derived by determining the capacitances per unit

length and then integrating the effects of the differential shunting currents over the length

of the structure. It is assumed that in use the two heat sink plates are electrically connected

together and are both connected to one of the current terminals. The intermediate

capacitances Ci * through C6_* are defined as follows, based on the measured values in the

table:

(8) Between the resistance strips from the fold to

the potential terminals, for X dielectric
Q_;,=—xC__, (9)

C4_y+Q_, =^XC__, (10)

Q.^fx£^ (H)

Between the resistance strips from the

potential terminals to the end, for X dielectric

Between one resistance strip and heat sink,

from the fold to the potential terminals, for Y

dielectric

Between one resistance strip and heat sink,

from the potential terminals to the end, for Y

dielectric

The capacitive contributions to the phase angle of the respective shunt geometries are computed from the values in Table I as:

Oc=-2;r/{(C,_;,,) + (C3_^) + (C3) + (C„,„_^) + (Q_^))7? (12)

where/is frequency, R is resistance (0. 1 Q.) and XX and YY refer to the appropriate

dielectric (between resistance strips and between strips and heat sinks, respectively) for the

geometry in question. Using the average values from Table I in (12), we get the capacitive

time constants given in Table II for the four configurations.

Table II Calculated Capacitive Time Constants and Resistance Change due to Dielectric Loss

M2_M2 M2_R15 M1_M2 M1_R15

Time Constant

(ns)

0.342 0.199 0.429 0.285

Uncertainty

(ns)

0.032 0.018 0.040 0.030

(Rac -Rdc)/Rdc

(liQ/Q/kHz)

-0.045 -0.024 -0.050 -0.029

Uncertainty

(|n^Q/kHz) 0.007 0.005 0.007 0.005

Assuming that the uncertainties in the five capacitances of (12) are within 15% (2 a) and

recognizing that the uncertainties of the first two terms are directly correlated as are the last two terms, we obtain the expanded uncertainties in the values of time constants shown in the table. Here the sum of the first two terms is root-sum-squared with third term and the

sum of the last two terms to give the expanded uncertainties.
The equivalent shunt conductances were computed from the components of measured

conductance using equations (3) through (11), substituting "G" for "C". The total proportional change in resistance with frequency caused by the shunting conductances is given by:

' ^' --Q-Ql/((fi_.VA) + «^2..V.v) + «^3) + «^.4.5,_>T) + «^6_>T))^

^.. (13)

where/is the operating frequency in kHz (since the conductances of Table I are for

100 kHz). Using the average values from Table I in (13), we get the proportional changes

in resistance given in Table II for the four configurations. The expanded uncertainties (2 o)

for these values are computed as for the time constant case, assuming the uncertainties in

the conductance measurements to be ±25 %. The resulting uncertainties are less than

1 i^Q/Q for each of the configurations at frequencies up to 100 kHz.

2.3 Skin Effect

The change in resistance due to skin effect is estimated to be less than 1 |iQ/Q at 100 kHz.

In [2], Silsbee gives two equations for the skin effect of parallel plate resistors. The first (EQ20, p. 86) assumes the strips are so wide that edge effects are negligible. For the shunt

in question (with d = 0.00508 cm, w = 5.08 cm, p = 1.295 x 10" |LiQ-cm for Evanohm, and a

relative permeability of 1 for Evanohm), this gives a ratio of ac resistance (R') to dc

resistance (R) of

/?' — = 1+5.5x10"" at/ = 100 kHz (14)

R

The second equation (EQ21, p. 86) assumes the plates are so far apart that they exert no

effect on each other and therefore current crowding at the edges is appreciable. This gives

/?' — = 1 + 2.17x10"' at/ = 100 kHz (15)

R

While one can easily conclude from the subsequent discussion in Silsbee that our case is closer to the first result, it is hard to quantify by how much. It is clear however, that the

skin effect at the frequencies of interest here (e.g., below 10 MHz) should be directly

proportional to/" and inversely proportional to p

~. To get a better estimate of the skin

effect for our case, the structure was modeled using a finite element field modeling

software program [3]. The results for configurations with 25.4 \im (1 mil) separation

between the resistance strips are given in Table III where Rf - Rik is the resistance change

from 1 kHz to frequency/ The resistance change for the 50.8 jxm (2 mil) separation is essentially the same. Higher frequencies were chosen for the simulation to improve

resolution and accuracy. These results indicate a skin effect about 10 times larger than that

given in ( 14) (although much less than that given in ( 15)), and show a nearly square-law

dependence on frequency, both of which are consistent with Silsbee's observations.
Table III Skin Effect vs. Frequency

f(MHz) 0.001 0.1 1.0 2.0 5.0 10

(Rf-Rik)/Rf

5 22 138 554

2.4 Eddy Current Losses

To quantify the effective resistance change caused by eddy current losses in the aluminum

heat sinks, additional simulations were performed using the field modeling software [3]

noted previously. Simulations were run for the four different combinations of separation

between strips, t, and separation, k, between the resistance strip and heat sink plates. These

results are summarized in Table IV. As before, in the configuration designations at the

tops of the columns, the first number designates the separation between the resistance strips

(x 25.4 }xm, i.e., in mils) and the second number designates the separation between the

resistance strip and the heat sink (x 25.4 \im). The letters designate the dielectric materials

used, although for these simulations that information was not needed since the separation

was assumed to be free space. Note that the frequency range used for these simulations is ten times higher than that used for the measurements discussed in the next section.

Table IV

Resistance Change relative to DC Due to Eddy Current Losses in Heat Sinks

FREQ.

kHz

M2_M2 M2_R15 M1_M2 M1_R15

1 0.071 0.055 0.018 0.014

2 0.198 0.139 0.049 0.035

5 0.752 0.437 0.190 0.111

10 2.02 0.972 0.518 0.250

20 5.31 2.02 1.384 0.523

50 18.2 4.78 4.86 1.250

100 43.8 8.48 11.21 2.232

200 100.0 14.23 28.29 3.79

500 271 26.6 80.16 7.09

1000 533 40.8 163.0 11.06

For the two configurations with separation k of 50.8 |Lim (2 mils) designated M2, the

resistance change is approximately proportional to/' over the frequency range considered.

10
However, for the configurations using Ri5 {k of 381 |im (15 rnils)), the dependence on

frequency decreases to approximately/^'^^. As seen in the table, the resistance change is quite small for the M1_R15 configuration that we have chosen to use, giving 2 \iQ./Q. at 100 kHz and only 1 1 iiQ/Q at 1 MHz.

2.5 Thermoelectric Effects

The thermoelectric properties of resistive alloys can give rise to an apparent change in the

dc resistance of resistors made from them [4]. This takes place as follows: The current

passing through junctions of dissimilar metals in the resistor (e.g., at the current terminals)

gives rise to a difference in temperatures at the two junctions due to the Peltier effect. The

temperature difference in turn creates opposing thermoelectric voltages in the junctions via

the Seebeck effect and the net result is an increase in the apparent resistance. If the current

is reversed, the temperature difference reverses so the thermoelectric voltage reverses also

with the consequence that averaging with reversals is unable to eliminate the effect. However, as the rate of reversal exceeds the reciprocal of the thermal time constants of the

structure, the effect disappears because there is no opportunity for a temperature difference

to be established between the junctions. This effect is mitigated in the resistor design in

question as follows: The Seebeck coefficient for Evanohm is relatively close to that of

copper, so that the thermoelectric potential is less than 2.5 |j.V/°C. Since the Peltier

coefficient is directly proportional to the Seebeck coefficient, the rate of heat

generation/absorption at the junctions is also very small. The two copper plates that form

the current terminals have relatively low thermal resistance between them since they are separated by only 0.08 cm of Bakelite sheet and the communicating area of the plates is approximately 39 cm'; consequently the temperature difference between the two plates

should be very small, especially since the rate of heat production is low. In our fourterminal design however, the salient thermoelectric voltages are those at the junctions of

the resistance strip with the potential leads, rather than those at the current terminals. The

temperature difference at these junctions caused by the Peltier heating/cooling of the

current terminals should be much smaller still. These junctions are each separated from the

heat-producing junctions by approximately 1.4 cm of Evanohm strip that has a crosssectional area of only 0.026 cm, allowing only very slow heat conduction. Furthermore, the

two strips (at either ends of the resistor) are in very close thermal contact over the full 1.4 cm path of thermal conduction, being separated by only 0.0025 cm of Mylar insulation.

Based on these considerations, we believe the temperature difference at the junctions of the

potential terminals (caused by Peltier heat/cooling at the junctions of the current terminals)

will be less than 0.01°C for currents up to 10 A. This temperature difference will cause a thermoelectric potential of less than 0.025 ^xV in each junction, changing the apparent

resistance by no more than 0.05 |iQ/Q. The effect is thus considered negligibly small.

4. EXPERIMENTAL AC MEASUREMENTS

In an attempt to corroborate the above calculations and simulation results, we have made a

series of measurements. While there are currently no impedance standards or methods of

intercomparison available at NIST that can be used to independently verify the calculations

11
mentioned above, the calculations can be corroborated or bounded using differential

measurements in which the dimensions and materials of construction are changed. Thus, a

series of experiments was performed in which the calculable shunts were intercompared

with transformer-scaled shunts having the same nominal (0. 1 Q.) value, in a bridge circuit

with dual sampling channels. A circuit originally developed for testing phase angle

generators was used as a magnitude and phase comparator and is diagramed in Fig. 3. Data

from the samplers is used to compute the magnitude and phase (relative to the synchronous

trigger) of the two channels. From this information, the relative magnitude and phase

differences between the two channels are calculated. Although not important for

differential measurements, the two channels are repeatedly swapped and the results

averaged to eliminate channel-to-channel differences in the sampler. The transformerscaled shunt acts as a dummy standard, and is only required to have stable frequency

response from test to test. The primary-to-secondary circuit isolation provided by the

transformer allows the two devices to be connected in series (i.e., primary of transformer in

series with resistive shunt) while simultaneously grounding one potential terminal of each

device. Errors caused by shunt capacitance from primary circuit to secondary and primary

circuit to ground must be considered if this method is relied upon for accurate

intercomparison data, but for the differential measurements of interest here, such errors are inconsequential.

CONTROLLER

IEEE-488 BUS

i^

PHASE GENERATOR

VAR REF

JV

CHANNEL

REVERSING

SWITCH

NIST 20A-2 TRANSCONDUCTANCE

AMPLIFIER

V-IN OUT

OUT

WAVEFORM ANALYZER

/^

CHI CH2 TRIG V

AAAATRANSFORMER-SCALED RESISTOR

RESISTOR UNDER

(DUMMY) TEST

Figure 3. Basic comparator system

12
Table V

Bridge Comparison Data: Resistor Configuration vs. Transformer Scaled Resistor

Proportional Magnitude and Phase Differences

FREQ.

kHz

M2_

X

10"' _M2

^iRad

M2_

X

10"' R15

^iRad

Ml_

X 10'

M2

^Rad

Ml_

X

10"' R15

(iRad

0.1 1050 55.8 1038 59.3 1089 61.1 1003 6J.1

0.2 1059 29.7 1037 26.2 1088 33.2 1009 31.4

0.5 1066 12.2 1036 10.5 1085 14.0 1012 12.2

1.0 1066 7.0 1036 3.5 1082 8.7 1016 10.5

2.0 1066 1030 -5.2 1078 7.0 1013 5.2

5.0 1064 -19.2 1028 -20.9 1074 5.2 1013

10 1068 -45.4 1027 -54.1 1075 1010 -8.7

20 1067 -96.0 1022 -110 1073 -10.5 1008 -27.9

50 1059 -251.3 1010 -296.7 1057 -36.7 997 -87.3

100 1331 -649.3 1272 -754.0 1321 -233.9 1253 -347.3

Data acquired using this measurement system are presented in Table V for the four

different shunt configurations involving 25.4 |xm (1 mil) or 50.8 |xm (2 mil) Mylar

dielectric between the resistance strips, and 50.8 |xm (2 mil) Mylar or 381 |iim (15 mil)

thermally conductive rubber between the resistance strips and heat sink plates.

Because the uncertainties in the reference transformer-scaled shunt are much larger than

the uncertainties we are seeking for the calculable shunts, we are only able to use measurement differences between configurations as a meaningful basis for comparison

with calculations. Such comparisons are given in figs. 4-9 for phase angle differences, and

in figs. 10-15 for resistance changes. These are further described below.

The major source of uncertainty in the differential responses derived from this data is the

temperature coefficient of resistance of the shunt itself, which is approximately

20\xQ,/QJ°C. We estimate that self-heating and room temperature changes contribute errors of up to 15 \iQ./Q. (k=2) in the differential magnitude responses that were derived from the

data. In addition, we observed that the dc resistance of the shunt shifted each time the

configuration was changed. We attribute this to stress-induced changes, and ignored

resulting global offsets in the differential responses, as noted below. On the other hand, the

differential phase angles are unaffected by temperature and stress to first order, and the

errors in differential phase are dominated by type A uncertainties which are estimated to be

5 ^rad for this data (for k=2), at all frequencies. Although data was obtained at frequencies

down to 100 Hz, any differential changes in magnitude and phase below 1 kHz are totally

overwhelmed by the measurement uncertainties. Therefore the results at frequencies below

1 kHz are ignored in the following sections.

13
3.1 Phase Comparisons

The measured phase differences between configuration pairs are presented in figs. 4-9 for

the six unique pairs, along with the corresponding calculated phase differences based on

the inductive and capacitive phase contributions discussed in sections 2.1 and 2.2 above.

The error (meas. - calc.) is also given. "Calc." refers to the combined inductive and

capacitive components. The largest error among these six plots is -54 ^irad, occurring at 100 kHz for the (M2_M2)-(M1_R15) pair. In comparison, the absolute phase angle

computed for the (M2_M2) condition is 1094 |irad, and that computed for the (M1_R15)

condition is 738 |irad. Note that the level of agreement is well within the uncertainties

expected for the calculations (q.v., 101 [xrad for M1_R15) based on the root-sum-squares

of the uncertainties in L and C, as discussed in previous sections. These results also show

that the phase differences are linear with frequency to well within the uncertainties of the

measurement data.

3.2 Magnitude Comparisons

The measured resistance differences between configuration pairs are presented in figs. 10-

15, along with the calculated resistance differences based on the dissipation errors given in

Table II and the field simulations presented in Table IV for eddy current losses in the heat

sinks. (At the frequencies for which measurement data are available, the calculated changes

due to skin effect are negligible, per Table III.) To account for the dc offsets noted above,

the measured differences are always normalized to the 1 kHz values. The difference

(Meas. - Calc.) is also given.

Among all six configuration pairs, the largest difference between measured and calculated

differences was 12 • 10'^, which is less than the 15 • 10'^ estimated uncertainty for the

measurements. In the three cases where the calculated differences are greater than the

estimated measurement uncertainty (i.e., the pairs involving the M2_M2 configuration), the

agreement is relatively good between the measured and calculated values

14
(M1_M2)-(M1_R15)

20

(0 -20

c

<

-40

-60

o

Q.

-80

-100

-120

1 000 10000

Frequency (Hz)

100000

Figure 4. Measured phase difference between arrangements M1_M2 and M1_R15

500

D

(0 400

^

3r 300

o

O)

c 200

<

0) 100

(0

(B £ n

Q.

-100

1000

(M2_M2)-(M1_M2)

10000

Frequency (Hz)

100000

Figure 5. Measured phase difference between arrangements M2_M2 and M1_M2

15
400

1000

(M2_M2)-(M1_R15)

10000

Frequency (Hz)

100000

Figure 6. Measured phase difference between arrangements M2_M2 and M1_R15

(M2_M2)-(M2_R15)

•a

(0

c

<

V

<0

(0 Q.

000 10000

Frequency (Hz)

100000

Figure 7. Measured phase difference between arrangements M2_M2 and M2_R15

16
(M2_R15)-(M1_M2)

(0

o

O)

c

<

0)

(A

600

500

400

300

200

100

-100

i ——Meas. /

--Calc. -•- Error

' y/

-^

B- -• "

1 T

1000 10000

Frequency (Hz)

100000

Figure 8. Measured phase difference between arrangements M2_R15 and M1_M2

500

1000

(M2_R15)-(M1_R15)

10000

Frequency (Hz)

100000

Figure 9. Measured phase difference between arrangements M2_R15 and M1_R15

17
(M1_M2)-(M1_R15)

o

o

o

CC

u

a

a.

1000 10000

Frequency (Hz)

1 00000

Figure 10. Measured resistance difference between arrangements M1_M2 and M1_R15

(M2_M2)-(M1_M2)

b

o

"D

oc

'cT a

tr6

CO cc

40

30

20

10

—-Meas.

--Calc.

-•-Diff.

)

>

^^=*'"^~~K.

T

-10

1000 10000

Frequency (Hz)

100000

Figure 11. Measured resistance difference between arrangements M2_M2 and M1_M2

18
(M2_M2)-(M1_R15)

50

'9O 40 y~X^ 30

o

"D 'A) cc'o 10

TJ

CCu

(0 -10

-20

1000 10000

Frequency (HZ)

100000

Figure 12. Measured resistance difference between arrangements M2_M2 and M1_R15

40

O

30

X^«—

u

a 20

tro 10

•a

cco n «

CE 10

1000

(M2_M2)-(I\/I2_R15)

1 ——Meas.

--Calc.

--Diff.

J / ^/

.^:^-r-—

10000

Frequency (Hz)

1 00000

Figure 13. Measured resistance difference between arrangements M2_M2 and M2_R15

19
(M2_R15)-(M1_M2)

"o

u

a

cc

cc

I u

(0 QC

15

10

5

——Meas.

--Calc.

V**^'^''^^^^*^ -•-Diff. ^^^ ^Vvk. Ak. ^f_.^^1^=V

1000 10000

Frequency (Hz)

100000

Figure 14. Measured resistance difference between arrangements M2_R15 and M1_M2

10

O

oD

QC'oo

cc

I o

(0 cc 10

1000

(M2_R15)-(M1_R15)

^^^

J

r^^•""^Tl-.^^Kr^ H —-IVieas.

--Calc.

--Diff.

10000

Frequency (Hz)

100000

Figure 15. Measured resistance difference between arrangements M2_R15 and M1_R15

20
4. FINAL MAGNITUDE AND PHASE RESULTS

In summary, the experimental measurement results presented in the previous section are

fully consistent with the calculated magnitude and phase responses, to within the estimated

uncertainties of the measurement process.

The differential phase measurements agree with calculations to well within the estimated

uncertainties of the calculations. Although there is likely a phase angle component caused

by the eddy currents in the heat sink, it should be of the same order as the in-phase

component (see Table IV) and consequently should be negligible compared to the

uncertainties in the phase angle calculations.

Therefore, with a coverage factor of 2, the time constant of the M1_R15 configuration is assumed to be essentially constant up to 1 MHz, and is given by:

r = r^-rc±[(ArJ' +(Arc)-f " = 1.17 ns ± 0.16 ns. (16)

Over the frequency range of interest (0 - 1 MHz), the proportional change in resistance due

to dielectric losses is given by

AR^ -- -2.9x10'' f . (17)

The calculated change in resistance due to skin effect for the Ml _R 15 configuration is closely approximated by

r f \

ARs -5.5x10" /

vlO^

(18)

and the proportional change in resistance due to the calculated eddy current losses is approximated (to better than 0.27 [xQ/Q.) by:

A7?^ =10-'x/"'"* (19)

where in each case/ is the frequency in Hz. Based on the agreement between calculations

and measurements for the resistive component, an uncertainty (with coverage factor of 2) can be assigned given by:

^/, -10"' +1.5x10"' x^ . (20)

Therefore, over the frequency range of - 1 MHz, the resistance of the Ml _R 15

configuration is given by :

21
R = R. 1 + 5.5-10"

r fV

vlO%

/

+ 10"'x/"^''*-2.9xl0~'7± 10"' + 1.5- 10 'x

V (21)

where Rdc is the dc resistance and/is the frequency in Hz.

The predicted resistance change (21) and phase angle, cot, (16) are plotted in figs. 16 and

1 7 over the frequency range from 1 kHz to 1 MHz, along with the corresponding

uncertainty bounds.

Resistance Change: (M1_R15)

^ 200

150

(OO

o

"D

IT

"Du

100

50

-50

-100

-150

-200

Delta R

Pos. Bound

Neg. Bound

1.E+03 1.E-I-04 1.E+05 1.E-H06

Frequency (Hz)

Figure 16. Calculated resistance vs. frequency for the selected arrangement M1_R15 with

uncertainty bounds (k=2)

10000

(0

Ui

c

<

(0

(0

1000

100

10

11.E-H03

Phase Angle: (M1_R15)

—•— Phase Angle

Pos. Bound

Neg. Bound.

'"

1.E+04 1.E+05

Frequency (Hz)

1.E+06

Figure 17. Calculated phase vs. frequency for the selected arrangement M1_R15 with

uncertainty bounds (k=2)

22
5. CONSTRUCTION DETAILS

The following construction details are intended as a recipe for those readers interested in

replicating the shunt from the mechanical drawings provided in Appendix A. The details were developed from numerous trial and error procedures and are coupled with an emphasis of important particulars that should be adhered to for those desiring to employ the

basic design with modifications.

5.1 Preparing the bifllar resistance element

The material selected for the resistance element is from a metallic resistance alloy called

Evanohm which is available on a roll as a thin strip 0.00508 cm thick and 5.08 cm wide

having a nominal sheet resistivity, 0.025Q/square of surface area. Thus, a nominal

resistance of 0.1 Q will require a length to width ratio of 4 which in this case results in a

circuit length of about 20 cm. Note that the actual physical length of the circuit is twice the

value defined in (1).

Cut a length of resistance strip equal to about 30 cm to provide for additional length from

the potential terminals and the attachment edge of the current terminals. Place the sample

in a brake and form a 90^ bend at about 1 5 cm from one end. An alternate to using a brake

is to form the initial bend by bending the material over the edge of a block of aluminum.

Make sure that the bend is exactly orthogonal to the edge of the strip. Remove the strip

from the brake and fold by hand the material back on itself while insuring that the edges of

the folded strip are parallel. Flatten the fold as much as possible by rubbing stiff paper

back and forth across the fold by hand while insuring the fold appears uniform across the

width of the material. The material is malleable enough so that a tight fold can be formed

entirely by hand without resorting to additional mechanical force. The objective in forming

the shape of the fold is that it be reasonably compressed but still allow for a thin dielectric

material to be positioned between the sheets up to and against the inside of the fold.

5.2 Tinning the strip for the current terminals

The next step is to trim the ends of the folded sample to a total length of 12.7 cm from the

fold using a shear. An ordinary paper shear works well in this case. Place a tape mask

across the width of the strip to expose 0.8 cm of resistance material from both sheared ends on the outsides of the folded strip. Use a high temperature masking tape such as Teflon to withstand soft-solder melting temperatures. Tin the unmasked ends across the width of the

strip on each side using a flux intended for stainless steel. The most controlled process of

tinning was done by heating each end of the strip on a hot plate while scrubbing the surface

with flux and solder. Once the Evanohm material is wetted wipe off the excess leaving

only a thin coating of solder.

5.3 Locating the potential terminal target points

The target points for the potential terminals are located midway across the width on each

side of the bifilar strip at a determined distance from the fold to set the nominal resistance

23
at O.in. A special jig was designed to locate the target points (see Fig. 18). The jig

basically consists of a slot in a Bakelite material that can accept and clamp the folded strip

of Evanohm material. Two pointed-tip screws threaded in the Bakelite can be turned to protrude against each side of the folded resistance element. A thin dielectric material such

as 0.002" Mylar is placed between the folded sheet. A four-terminal resistance

measurement is made by attaching current leads to the previously tinned ends of the strip,

and connecting the sense leads to the threaded screws. It is important that the current leads

are attached in a manner such that the current is applied across the entire width of the strip.

A simple modification to an alligator clip can accomplish this by soldering two wide

copper strips equal to the width of the strip to each jaw.

Fig. 1 8. Photograph ofjig used to locate target points for potential terminals

Use a four-wire resistance-measuring instrument that has at least a 100 |j.Q/Q resolution

with a provision for compensating the effects of thermally generated offset voltages.

Monitor the resistance while lightly turning each screw to make contact to the strip.

Through an iterative process of loosening the screws and sliding the strip to a new position

and then retightening the screws again, it is possible to locate the point that provides the

desired resistance. Once the desired position has been obtained, lightly tighten each of the screws to create a small dimple on each side of the resistance strip. Do not over tighten, as the objective is to create only very small visible indentions that become the two target

locations where the potential leads will be attached.

24
5.4 Attaching the potential leads

Attaching the potential leads to the target points on the Evanohm strip is perhaps the most

difficult and tedious part of the assembly process. Failure in the attachment process may

ruin the bifilar strip, requiring another prepared strip. The method chosen is to spot-weld

the end of # 30 copper Formvar-coated wire directly to the element. A commercially

available capacitive discharge welder was chosen for this application having a 5 to 50

Watt-Second stored energy capacity. This type of welder commonly uses the capacitor

discharge technique where the voltage stored on a capacitor is discharged through the

circuit creating enough heat at the junction to fuse the metals together. A variable control

sets the voltage on the capacitor, which establishes the potential energy at the weld site. Experimentation is required to determine the correct amount of energy. Too high a level

will bum a hole through the resistance sheet while too little results in an incomplete

attachment. The most reliable visible indicator of a good weld is a small ring of

discoloration on the resistance sheet where the weld is formed. If the weld is sound the

wire should be able to be moved back and forth at a slight angle without becoming

detached.

It is necessary to first prepare the ends of the wires that will be welded to the resistance

strip. Shear the end of the wire to form a flat surface that is at a right angle to the wire

length. Depending on the type of shear it is usually necessary to dress the end of the wire

with an abrasive to create a flat end. Experience has shown that the most reliable welds are formed if the end of the wire is held against the resistance strip with a jig that holds the

wire and exerts downward pressure against the strip. The setup used to accomplish this

was to employ a circuit probe micromanipulator with a 3 -axis variable adjustment. The

manipulator was adapted with a syringe needle to contain the wire. The beveled point of

the needle was cut off. Fig. 19 shows the setup used to hold the wire and position it over

the target point. The wire is positioned and locked about 1mm beyond the tip of the syringe

needle. Note that an aluminum plate is placed under the sheet where the weld is performed. Having a back-up plate that acts as a heat sink was found to produce the most

consistent results. The manipulator is spring-loaded in the Z direction so that once the X-Y

position has been set above the target point the Z-axis control is moved until the spring in

the manipulator is engaged and the butt end of the wire is forced against the Evanohm

material with constant pressure. One connection of the welder is made to the wire and the

other to the resistance strip. A discharge switch on the welder produces the one-shot pulse

of energy. If the weld results in improper attachment of the lead it may be possible to try

again, but if a hole is burned through the material it will be necessary to start over with

another sample of material. It is advisable to first practice the technique on scrap material

until the correct amount of energy has been determined. If a successful weld is achieved a small spot of fast-curing epoxy is applied around the weld area. Once the epoxy has cured

the wire is bent down against the strip and held in place with epoxy. Fig. 20 shows the

completed potential lead attachment and lead dressing. The same process is repeated on

the other side of the strip while providing support under the strip with an aluminum plate

suspended high enough to protect the cormection on the other side.

25
Figure 19. Photograph of set up used to hold and position potential wire prior to spot

welding

Figure 20. Photograph of potential lead attached and dressed against resistance sheet

26
5.5 Attaching the current terminals

The last step in fabricating the resistance element is attaching copper end plates to each end

of the strip. Refer to the Right and Left current plates in appendix A. Each copper plate is predrilled to accept a modified female/male type LC connector. Pre-tin the ends of the

copper plates on the ends away from the holes using the same technique and dimensions

described in tinning the resistance strip ends. Spread open the folded resistance strip and

place the tinned end up on a hot plate. Place the tinned side of the copper plate down

against the pre-tinned side of the resistance element overlapping only the tinned portion.

Carefully align the copper plate with respect to the folded strip so that it is centered across

the width and parallel to the long edge of the strip. Press the copper plate against the sheet

and hot plate while checking again the alignment. Heat the joint and add a bit of extra

solder until a smooth fillet is formed at the transition of the two metals. Align the second

plate with pins through the predrilled holes with the first plate that has been soldered to one end of the strip. While maintaining the aligned position of the second plate on the strip,

repeat the soldering process previously described. After soldering both current plates to the

bifilar strip inspect the assembly to insure that the four mounting holes of each plate are in

alignment.

5.6 Final Assembly

Select the pre-machined Left Side Heat Sink Block and lay the block on a surface with fins

down. The two slots machined on the flat surface serve to provide a channel for the

potential lead and a relief for the fold at the end of the strip. Cut two strips of elastomeric

thermally conductive insulation material, Sil-Pad 2000, with a width slightly greater than

the resistance strip and a length of 10.7 cm. Lay the insulation on the surface of the heat

sink with one end flush with the inside edge of the slot near the end. The other end should

be flush with the cutout relief end provided for the copper plates. Mark the position of the

slot for the potential wire and cut a slot in the rubber equal to the width of the slot to about

the center of the width. The slot in the rubber is intended to provide a relief for the

potential connection and wire as can be seen in Fig. 20. Lay the Left Current Plate Backup

insulator in the recess provided for the current terminals in the Left Side Heat Sink Block

so that the holes align with the holes in the block. Lay the previously assembled bifilar

strip with attached potential wires and current plates on top of the elastomer rubber with

the Left Current Plate against the Left Side Backup insulator. Slide the Current Plate

Separator Insulator between the Left and Right current plates.

Cut a strip of 0.025 mm (0.001") Mylar insulator approximately 2 mm wider than the

resistance strip and a length extending up to the first set of mounting holes in the current

plates. Slip the dielectric insulator between the folded sheet and pull the end up as far as possible against the inside of the fold. Align the insulator so that an equal amount extends

beyond both edges of the strip.

Lift up the Right current plate and insert four insulator bushings in the four holes of the

Left current plate. Place at least two Va-IO screws through the holes in the current plates

and lightly tighten them against the Left Side Heat Sink Block with nuts. This insures that

27
the resistance assembly becomes anchored and ahgned in the Heat Sink Block. Check that

the fold protrudes over the fold relief slot and that the potential wire against the element

lies with the potential wire relief slot.

Before attaching the Right Side Heat Sink Block the potential wires should be attached to the potential connector. Screw into the Potential Connector Housing a type BNC connector

with an insulated outer shell. Attach with one screw the Housing Block to the Left Side

Heat Sink Block in the threaded hole provided on the edge. Cut, strip and solder the

potential wires to the terminals on the BNC connector. Make sure that the potential wire

attached on the left side (i.e. the potential connection closest to the Left Current Plate) is connected to the center pin of the BNC connector. This will insure that the polarity of the

potential terminal is aligned with the polarity of the current terminal.

Lay the second precut elastomer rubber over the element aligned with the previously

placed rubber that was placed on the Left Side Heat Sink Block. Position the Right Side

Heat Sink Block over the assembly and align the ten clamping screw holes around the two

edges of the heat sink blocks. Insert the clamping screws through the holes and four fan

mounting brackets. Tighten the ten clamping screws with nuts using a torque wrench.

Beginning with the middle screws, establish a build-up torqueing sequence from the center

to outside screws ending with a final torque of 25 in-lbs.

Attach the modified female LC connector (see appendix A) to the current plates using

appropriate length 14-20 screws. The male LC connector is modified with a male center

pin extension soldered to the male center pin. Screw the back shell of the modified male

LC connector onto the female LC connector. Insert a V^-20 nut through the hole provided

in the Left Side Heat Sink Block and tighten onto the threaded end of the center pin

extension. This completes the assembly process for the 0.1 Q current shunt.

5.7 Troubleshooting Assembly Problems

After the unit has been assembled the shunt should be checked for functionality with a four-terminal resistance meter having a minimum resolution of 100 ^QJQ, and automatic

reversal capability to null out thermoelectric offsets. The shunt should indicate a resistance

of 0. 1 Q ± 500 ^Q/Q. Experience in constructing four shunts has shown that a 500 iiQ/Q.

uncertainty in resistance from the intended value is about the best that can be achieved

without resorting to trimming techniques. This is consistent with the uncertainties

associated with the practicalities of locating the potential lead target points, lead placement,

and welding.

Make sure that the polarity of resistance is consistent with the convention of positive

current into the center pin of the LC connector producing a positive voltage at the center of

the BNC potential terminal. If this is not the case it will be necessary to reverse the

potential lead connections.

If the resistance measurement indicates a very high value it is likely that there is an open

circuit somewhere in the potential circuit. Check for continuity at the BNC potential

28
terminal and continuity through the weld joints. If the resistance measurement indicates a very low value of resistance it is likely that a short circuit has developed during the

assembly process. If this is the case there is no alternative but to disassemble the shunt. A

clue of where the problem might be is to monitor the resistance while loosening the

clamping screws. If the resistance returns to normal either during loosening or removing

the Right Side Heat Sink it is usually an indication that a short has developed across the

dielectric material separating the sheets. It is advisable at this point to make sure that the

potential wires are not shorted together at some point and that the resistance element is not

making contact with the heat sink plates other than at the "low" side of the current

terminal.

Experience has shown that shorts are most likely caused by foreign particles puncturing the

thin dielectric material. Since it is practically impossible to locate the failure it is easiest to replace the existing dielectric material with a new sheet. Also, it is advisable to check the

edges of the resistance sheet for possible sharp or ragged edges. The edges can be

smoothed by using a fine abrasive. Before replacing the dielectric, swab the insides of the

sheets with alcohol to rid any foreign material. Monitor the resistance after a new

dielectric has been installed and continue to monitor the resistance while torquing the heat

sink clamping screws.

6 MEASUREMENTS

6.1 Common measurement problems

The diagram shown in Fig 3, offers a generalized scheme of how differential measurements

were made between the current shunt in question and a reference standard current

triansformer. It does not convey all of the nuances that may affect the absolute accuracy of

a comparison measurement. The diagram assumes that the current circulating in the

measurement loop is not detoured through ground loops or other unintended paths, and that

the loading caused by the input impedance of the waveform measuring instrumentation is negligible. We know from practical experience that this is not always the case and may

require extraordinary means to approach the best possible configuration.

In order to appreciate the possible pitfalls of comparing the performance of say, two 4-

terminal current shunts against each other, consider the schematic in Fig. 21. This

configuration represents possibly the worst condition where the measuring instrumentation

must deal with differing and substantial common-mode voltages. Here the non-idealities of

two identical measuring instruments are represented by input impedance Zin and a lowterminal impedance to ground, Ziow. Also, included are finite potential lead resistances, Rg.

Because of the common mode voltage across Z|ow. a fraction the main current is diverted

through a ground path. The result is that the current through the two shunts is not the same. Thus, the potential across shunt 2 will be in error by the amount of diverted current. Furthermore, an error is produced by any current in the potential terminals creating

additional voltage drops that differ in the two shunts by the different common-mode

voltages of each shunt.

29
©

CURRENT

SOURCE

HI

Z|N

<?L0

S1

nrVWV

Rs

SHUNT 1 IX

-LOW

I '^

'CM

I-I1-I2

VcM-Vsi

/77

/TV

Figure 21. Diagram of voltages and loop currents involved in comparing two

four-terminal shunts

If the measuring instruments are of a high quality differential input type so that the

impedances Zin and Ziow are essentially infinite, there is still one more error source to contend with and that is the common-mode rejection properties of the differential

amplifiers. Common-mode rejection ratio (CMRR) is a measure of the capability of the

measuring instrument to reject the common-mode signal. CMRR is important because it indicates the fraction of the common mode signal that is indicated or translated as a normal-mode signal. While the standard test methods for CMRR of differential amplifiers

often specify a 1 kQ resistance in the LO input, for this application it is more meaningful to connect one potential terminal to both differential inputs in the presence of the actual

common mode voltage and observe the reading. CMRR of a differential amplifier is sensitive to frequency and tends to deteriorate with increased frequency. CMRR should be

checked at all frequencies of interest.

Refer again to Fig. 3 where a four-terminal shunt is being compared against a CT. Note

with respect to the common mode issues just described the advantage of placing the CT in

the "high side" of the current loop. The voltage developed as a result of the drop across the

shunt is the common mode voltage of the CT. Because of the inherent isolation properties

30
of a CT the common mode voltage presented to the measuring instrument is greatly

reduced and thus reducing the requirement for instruments with very high CMMR.

Furthermore, leakage currents through the instrumentation to ground tend to be lower.

However, at high frequencies even a small primary to secondary capacitance can allow

significant leakage currents to ground. A test to insure that there are no sneak-paths of

current is to monitor the outgoing and return currents of the source. A convenient way to do this is to place the outgoing and return current conductors from the source through the

window of a wide band current transformer. If all of the outgoing current equals the return current then the secondary current should be zero. Any measured amount in the secondary

is an indication that there are leakage current paths around the intend paths.

Thermal converters can be used to monitor the potential terminals of a shunt under test. They have the advantage of having excellent isolation properties in addition to well known

characterized ac-dc differences. Their isolation properties are limited only by the small

capacitance between the heater element and thermocouple. However, thermal converters

are limited to measuring the ac-dc differences and are unable to provide any phase angle

information. Shunts can be characterized either by direct comparison against a current

thermal converter or a shunt thermal converter combination. Future work is anticipated

which will be designed to compare the ac-dc difference of the calculable shunt against

various thermal converter standards.

6.2 Power coefficient of resistance

The Evanohm resistance material selected for this application has a positive temperature

coefficient of resistance of about 25 \iQ./Q./°C. This will affect the absolute accuracy of the

shunt in two ways: changes in resistance due to ambient temperature changes and changes

due to self heating effects. The latter is usually referred to as the power coefficient of

resistance and is affected by the thermal resistance between the resistance element and the

ambient. Fig. 22 shows the result of resistance changes that take place when the shunt is operated at 1 A and 10 A. The vertical axis indicates the deviation from 0. 1 Q.m fiQ/Q.

The temperature of the heat sink was monitored throughout the test indicating about a

1 .5 C rise and a change in resistance of 58 [iQ/Q.. A time constant of about 10 minutes is indicated with over 30 minutes required to reach an equilibrium value of resistance.

For some metrology applications where the absolute value of resistance must be known to within a few jxi^/Q over normal laboratory ambient temperature changes and different

currents, it is possible to improve the performance by several different methods. The first

is to choose or modify by annealing the resistance material for a lower temperature

coefficient of resistance. Recent work has shown that greater resistance accuracy can be

achieved by a thermal error correction model using the temperature of the heat sink as the

variable that predicts the change in resistance. A more recent work has shown that thermal

errors due both to ambient and power dissipation can be significantly reduced by using

thermal-electric heater/coolers attached to the heat sinks in a control system that maintains

the heat sink at a constant set-point temperature.

31
NIST AC/DC Shunt 603X

0.1 Q 1-10 Amps

220

210

200

9 190 + a

c 180

.oo

oO

170 -

160

150 +

140

206 /vQ/0

25.2 °C

1A

148)L/Q/Q

23.7 °C

20 40 60 80 100 120 140 160 180 200 220 240 260 280

Time (minutes)

Figure 22. Plot of current shunt dc resistance change at 1 A and 10 A versus time

7. ACKNOWLEDGEMENT

The authors gratefully acknowledge the efforts of Nicholas Paulter who performed the

finite element field modeling.

8. REFERENCES

[1] F. B. Silsbee, A Study of the Inductance of Four-Terminal Resistance Standards,

NBS Scientific Paper No. 281, July 1916.

[2] F. B. Silsbee, Notes on the Design of Four-Terminal Resistance Standards for

Alternating Current, NBS Journal of Research Paper No. 133, Vol. 4, January 1930.

[3] Ansoft, Maxwell® version 10

[4] F. J. Wilkins and M. L. Swan, "Precision AC/DC Resistance Standards," Proc.

ffiEE, Vol. 1 17, No. 4, April 1970, pp. 841-849.

32
APPENDIX A

Detailed Mechanical Drawings

A complete set of mechanical drawings suitable for replication of the Current Shunt

described in this note are provided in this appendix.

33
Is i

!L

ii ^

4

' i

I

i

i

i -----rr^ ^

gs ^"Vmmnnnmi

o

o

o

:::

o

o

o

o

-It :

a i

A

34
m^

L-'- :^—^-

o\

\1 a

^==7^

I

'—

innnmf

^j^

-5-

-^--.

s-l 4.

rt

i

i

I i

I

I 4-^

X

IK

I ^--^-b I X- .J

T

- ^

-

10;

ii

lul

35
^

L/l

'i 1 Q

^ \r -J- < OJ " o

ruo b ^ _S_ 1- CD

OJ

i tu;;i < ^

« § m t ^

f E

_i < o

<

<:

T

E

2 ^OQ

i 3

_J

1

<

ru5

uM i

o

-I

!t!

in

LJ

cr- o

aj S a-

>-

i^ R

t- U

::?! = ^ —1 M 13 < _1 <. UJ —1 <c AV S re Qi CL /\ 1— (A B^ oi /O G 1- u. a

s

G 1 / /

o S

/ // / // - / '^ '^ \

_l f

X ^

fU *

o

i5

10 X o \V i I Xj1 ^1_

"—

s

^ * yS !

, : t n>^ in

1

a\

c5

tM \\

in

1 CO V,

>-

,

cD

rD

Ifc

f^ j

H

o

;^ ^

36
4^

i 1

[/I \D 5 <

j CO X 00

s

LO tD i —1

a LL O '? O -1 n

1- 1

r_) Ld

ru

pq

P 1 ^D..: u S ± 2 ;:: _i ^ -I < <: i

' < 1—

1

1— 1

z:u1-

-z. Cl l^ i

M

g %s CO

. a u z 3 _l

-1 Cl /\ \

fB f

- \C)\

\ }

y

ALUMINUM

ACK

ANDDIZE

(=1

c> o

4-

_i

_l CO

1—

)

Q.

1- S - LiJ LJ

ui 2 X Qi \A

IJ M ^^ CI T

« t^ g

r,i <: " 1— lO

ai

1 s ^ ^ es f^n

00

-1 U" U X

1x1=^ wd ^* ct: UJp, Q —1 1—

^i^lD 3CD

fij Dl^ in

^

o

o

in \ \ 1 ^y^ \ 1

^ \

^^^^ _ o --N \l M::

-^--^-ef3 i

1

1

U) (3

"A o " ID Q ^ —h- —

o

^

37
^ > 6 [/I Z

i^ 1 Q s

-z.

m

— UJ

1—

CZ) OJ

X h--. i W CD ;: LJ CD

b

u.

O ? z o O -J rl ^

lu

O i- Q- ru I m[/3 [~ ,

LJ

1—u

PQ 3 2 Q ;;; o ± 2 ;;; z _i < u 1 <o

_l< D

1- o 1 <r 1 " 2

l^ \ « '* A S o g

a. ^ —

OJ I I I 2 117 c* =j !j

<i: <

_i £L f 1 <\ §S

r\ yi-* \ \ ¥"^ \ \ Irt \^^^ 1-* IT) - (A 1 " +

YCx o ^ — fo

^-\(^ lO \x^ OJ -^ o f —'-I o 1 _ 1 eysa^ p

UIM>fi i c_> CL Cj \D

;.

0.208

SI

FIT

TDL

:r

pin

pri 1

CENTER )

BE

SIZE I

0^o U

PRO NUG ENT IDTE DUL 0.00^3: 1 sm ^ d o 1 in ^

38
39
4.

i g

2

s s

T

IT< u

hCO

CO

i

z.3= u. O ?

<: CD 1 —

1-

(Ow

UJ

-J

1—

-z.

Or:

O

OJ

W

s

a: 2Q :::

=1 — -i^:- 1" s

_i <

<

1—

g H s -z. IJ3 g X W \

O

1-< s

In

T

u <n LJ S

Q. _1 o K

CL L- (=1 D LJ o

O o o — 1- LU

ITP _) ^ u-1 i

1 o UJ X

n

UJ S^ CO o LU ^ -j w _j S M a UJ i^

UJ lu fl_ -a:

UJ

LD s (- 1- CU UJ >- _l

-a q; t~ 1 <

z 3; o m G5 D

lO - o

\ f

UJ-Io / / ' ia> if/ sji < i £3> / '1 / / lD s

i

C^ in

nj

UJ 1-1 IJCI a ._

fU UJ" , -TO !jO

^d

in ' ^ 10 ,/^' J

V^ ^(Sf-

^_^^^

p> / \.

X^^'^ r y^ 1

1 X/ ,1 >:

^

40
4^

^

1 s

cs

Q

DC

<r — Q DJ

1 +

-z. cn ^> |---.. m Z S tD 4 (—

i LL O L^ O -J rl LlI 1—

<!_l

^

I o

cuW

i

s

ER

SHEET

ATNESS

EQUAL

TD

DR

ES

1/64

NATIONAL

INSTI

AND

TE 1—

-z. UJ

q:

h-L.

UJ

_J

1

0- L_ O

UJ o ,= O _l

1 0,065 HEET L

HDL 5=' 3^ H

2

SjJ j W _1 =) g -So: u

UJ u cu <s: z

(- H Cl_ UJ >- ^ -I o <c ci: 1— 1 I

Z S O CQ a

B

i

E3

0.

1

lO > c5 ^ A /

1 UJ

i <^ 4^/ CO

/-^

UJ

_lo 1=1 M

ft I CD OJ 2

D

, a^ y^

d" S^.

incu _CiJ ^

^Pl

__,! K W -^ o

c5 / \. / -< o

' V /i^-^^ \ Qari '^ /^

^^w/^'

M...^ >

- ^r^ - ^

41
m

O

<

a

u. O ?

uj § r m

_i <

"' <z

O

u

r-- o

c

ru

53

/ / / /

1 /i> <?/ /^/ LJ /<S» tf»/ _1Ow

M - uj3

kJ <C _l ds SS^

=^in — ^

42
^

s a

g

COQ

d;

cc < c

^D^ I-- 1

>- O "88 i 2

LJ

1—

1

Lu 2: e IJ o

aj

<E

v

1 Z) H T ^

1—

1

<[ a 20 t3 X Q

s 1—

1

LJ I— UJ 1^ i/) s a: Q£ H 1- "^ ZJ

u

S LJ <^ Q si pq

h- ?- 2 ^ S] i <E h- _i <

£ X a <

o z S

a T

OJ

o

-z. l< i a o CD

>- CD -

£

_J

1 1 <-

1 2O

1

1

1 1 3

<: f uo 1 <:

..-1 a _j 1 i

-^ OJ

1

C5 ^ c5 " 1,0 '- k

o

1 \

1

1

1 ^

43
LJJ O

XI-

^ _] o

S I— Q

o I I

o o

Q

<Q

_i <

<

o

1^ m

III CM

1 r— < c-j ^ m

LJ ^

u. o

n LJ CnI o

s;iQ

44