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AC-DC Voltage Transfer Difference due to Seebeck Effect
in Thermal Converters
Kunihiko Takahashi, Hitoshi Sasaki*, Barry D. Inglis **, and Manfred Klonz***
Japan Electric Meters Inspection Corp., 4-15-7 Shibaura, Minato-Ku, Tokyo 108, Japan
*
Electrotechnical Laboratory, 1-1-4 Umezono, Tsukuba-shi, Ibaraki 305, Japan
**
National Measurement Laboratory/ CSIRO, Bradfield Road, West Lindfield, NSW 2070, Australia
***
Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
Abstract -- The thermoelectric transfer difference of Thermal
Converters (TCs) can be evaluated in both current mode and
voltage mode, using a fast-reversed dc (FRDC) source. Some
types of TCs show differences in the thermoelectric transfer
difference between voltage and current mode as large as some
parts in 106. In order to investigate the origin of the discrepancy,
the change of the thermoelectric transfer difference with the
value of a resistor in series to the thermal converter has been
measured. The result was in good agreement with an assumption
that the Seebeck effect in the heater/heater support junction is
the main source of the voltage transfer difference.
Index Terms -- AC-DC difference, ac-dc transfer, thermoelectric
effects, thermal converter, Seebeck effect.
I. INTRODUCTION
A fast-reversed dc (FRDC) source transforms a steady-state
dc voltage or current to a square-waveform by reversing the
polarity of the dc in such a way that the rms value of the
square-wave is equivalent to the dc [1,2]. When the dc current
passes through the heater of a single-junction thermal converter
(SJTC), non-Joule heating/cooling takes place along the heater
due to thermoelectric effects such as Thomson or Peltier effects,
which changes the temperature distribution along the heater. On
increasing the reversing frequency of the current, the
thermoelectric effects do not have enough time to develop before
the reversal of the current-polarity. Hence, the FRDC source
can be used to evaluate the influence of thermoelectric effects on
the ac-dc transfer difference of thermal converters.
With the FRDC sources, we have evaluated the thermoelectric
effect of different types of TCs, including the SJTCs and
multijunction thermal converters (MJTCs). The results
obtained by the FRDC measurement were generally in good
agreement with conventional ac-dc transfer standards based on
theoretical evaluations of the thermoelectric transfer difference.
However, in the measurements of some types of MJTCs, a
discrepancy as large as some parts in 106 was observed in the
thermoelectric transfer differences, depending on whether the
measurements were performed in the voltage mode or in the
current mode ( "mode-dependence" of the thermoelectric
transfer difference). The mode-dependence may be explained by
thermoelectric voltages in the input circuit due to the Seebeck
effect in the case of SJTC elements[3,4]. However, the modedependence was much larger than we anticipated for MJTCs. In
most of the ac-dc transfer difference measurements, the TCs are
used in combination with range-resistors. In these cases, the
measurement conditions are neither pure voltage mode nor pure
current mode. The effect of the mode-dependence may become
significant in the voltage step-up procedure, where TCs are
combined with range-resistors of different values, and the
accumulation of systematic errors may be possible in the stepup procedure.
In this paper, we present the result of FRDC-DC difference
measurements on a SJTC and two MJTCs. The measurement
was performed on different configurations of range resistor/ TC
combinations, changing the value of the range resistor from zero
(TC only) to infinity (current mode). The results were
compared with a theoretical evaluation based on an assumption
that the Seebeck effect is the main source of the voltage transfer
difference.
II. ORIGINS OF AC-DC TRANSFER DIFFERENCES
The origin of the ac-dc voltage transfer difference of a thermal
converter results from the following three main sources:
1) Frequency-independent transfer differences caused by
non-Joule components due to Thomson and Peltier effects
at dc mode (thermoelectric transfer difference)[3,4].
2) Frequency-dependent transfer differences caused by
skin-effect in the leads and the stray inductance and
capacitance as well as dielectric losses in the heater circuit
(high-frequency effect)[5].
3) Frequency-dependent transfer differences due to
insufficient thermal inertia of the heater/ thermocouple
system (low-frequency effect)[6,7].
The high-frequency effect and the low-frequency effect may be
evaluated using the methods as described in references [5-7]. In
the middle frequency range around 1 kHz, the ac-dc transfer
difference is dominated by the thermoelectric transfer difference.
Thermoelectric voltages in the heater/heater-support junction
due to Seebeck effect may also contribute to the ac-dc voltage
transfer difference, as will be described in section IV. In the case
of a SJTC with standard design, an ac-dc difference of a few
parts in 106 is observed due to the thermoelectric effects. Since
the thermoelectric effect occurs in the dc-mode, the effect
contributes a frequency-independent offset to the ac-dc transfer
difference.
Since there is no significant difference in the temperature
distribution between slow-reversing DC and steady-state DC,
the measured FRDC-DC difference approaches zero as the
reversing-frequency is decreased. While at sufficiently high
reversing frequencies, the thermoelectric effects are suppressed
in the FRDC mode, and the FRDC-DC difference approaches
the thermoelectric transfer difference contributed from the dc
mode.
Fig. 1(a) shows the result for an SJTC(SN#TCJ94014C) used
for the main working standard of JEMIC. The SJTC consists of
four units of 10 mA, 25 Ω type-SS283 SJTC elements from
Best-Technology Co. The thermoelectric transfer differences of
the SJTC are measured to be -0.3 × 10-6 in current mode and 2.4 × 10-6 in voltage mode. This SJTC has two time-constants
(2.5 s, 0.14 s) as shown by the fitted curve. Fig. 1(b) represents
the results for an MJTC(SN#32465) with 460 Ω input
resistance, Guildline Instruments Type-7000.
The
thermoelectric transfer differences are measured to be < 10-7 in
the current mode and -2.2 × 10-6 in the voltage mode. Fig. 1(c)
represents the results for a type 'T3m-6' MJTC(SN#477)
developed at the D. I. Mendeleyev Research Institute of
Metrology (VNIIM). The thermoelectric transfer differences
are measured to be < 10-7 in the current mode and -0.7 × 10-6 in
the voltage mode.
III. MODE -DEPENDENT T RANSFER DIFFERENCE
The mode-dependence of the thermoelectric transfer difference
was measured for an SJTC and two MJTCs. The FRDC-DC
difference measurement was performed both in the voltage and
current mode, changing the reversing frequency from 0.05 Hz to
5 kHz. The results of the FRDC-DC difference measurement
are shown in Fig. 1. The FRDC-DC transfer difference δFRDCDC of a thermal converter is defined in the same way as the acdc transfer difference, except that a sine-wave is replaced by a
square-wave.
1
FRDC-DC Difference
10 -6
SJTC (#TCJ94014C)
0
I-mode (10 mA)
-1
V-mode (1 V)
-2
Rh =100 Ω
-3
10-2
10-1
10-0
101
102
Reversing Frequency
103 104
Hz
IV. T HERMOELECTRIC T RANSFER DIFFERENCE
SEEBECK EFFECT
1
FRDC-DC Difference
10 -6
TO
I-mode (10 mA)
0
A) Mathematical Model
When the dc current I passes through the heater/heater support
junctions of an SJTC, Peltier heating and cooling takes place at
the junctions, as illustrated in Fig. 2.
MJTC (#32465)
-1
V-mode (4.6 V)
-2
Rh =460 Ω
-3
10-2
I
10-1
10-0
101
102
Reversing Frequency
1
103 104
Hz
T'+∆T/2
2
R hI+ε12
1
10 -6
FRDC-DC Difference
DUE
T0
1
I-mode (10 mA)
T'-∆T/2
0
Fig. 2 Model for an SJTC with heater '2' and support leads '1'. The
temperature difference ∆T is produced by Peltier effect across the
heater, which generates a thermoelectric voltage ε 12 due to the
Seebeck effect.
-1
V-mode (1 V)
-2
Rh =100 Ω
-3
10-2
10-1
MJTC (#477)
10-0
101
Reversing Frequency
102
This effect results in a difference in temperature ∆T between
the two junctions, which can be calculated as
103 104
Hz
∆T =
Fig. 1.Frequency characteristic of the FRDC-DC difference of thermal
converters at voltage and current mode. (a) Result for an SJTC
[SN#TCJ94014C] with four type-SS283 elements from Best
Technology. (b) Result for an MJTC [SN#32465] from Guildline.
(c) Result for a MJTC [SN#477] from VNIIM. The bars represent
type-A uncertainties (3σ) of the measurement.
2π 12
⋅I ,
K1 + 2Kh
(1)
where
π 12 relative Peltier coefficient between the support lead 1
and the heater 2,
K1 thermal conductance of the support lead from the
heater end to the cold junction region,
-2-
80 %, and 60 % of the rated currents. In the case of
SJTC(SN#TCJ94014C), a small current-level dependence of a
few parts in 106 is observed. However, the dependence of the
thermoelectric transfer difference on the total resistance was not
affected by changing the current level, which is also in agreement
with (3).
Kh thermal conductance of the heater,
I
dc current applied to the thermal converter.
The temperature difference ∆T generates the thermoelectric
voltage ε12 due to the Seebeck effect [3,4]. The thermoelectric
voltage ε12 between the input leads of the SJTC may be
expressed approximately as
2Sc π 12
⋅I .
K1 + 2K h
1
(2)
10 -6
Here Sc represents the Seebeck or thermoelectric coefficient of
the heater/heater-support junctions. Since the thermoelectric
voltage ε12 is proportional to current I and changes its polarity
with current direction, we can define an effective resistance as
∆Reff ≡ ε12 I . The contribution of the thermoelectric voltage to
2Sc π12
.
K1 + 2Kh
Rh =100 Ω
-3
0
2
4
6
8
10
×10-3 Ω-1
1 / (Rh +Rr )
1
10 -6
(3)
FRDC-DC Difference
∆Reff =
SJTC (#TCJ94014C)
-2
−∆Reff
−ε12
=
=
( Rh + Rr ) I (Rh + Rr )
where
10 mA
8 mA
6 mA
-1
the ac-dc transfer difference δEMF depends on the total voltage
drop across the range resistor/ SJTC combination
δ EMF
fSW=1 kHz
0
FRDC-DC Difference
ε 12 = Sc ⋅∆ T =
The resistance Rh and Rr represent the heater and the range
resistor, respectively. The thermoelectric transfer difference
δEMF due to the Seebeck effect is expected to decrease with the
total resistance Rh+Rr and to be independent of the current.
In the case of a typical SJTC element, the thermal conductance
K1 and the Seebeck coefficient are of the order of 0.3 mW/K and
(5 ± 6) µV/K respectively [4]. The thermal conductance of the
heater Kh is assumed to be small compared with that of the
support lead K1. The effective resistance ∆Reff is estimated to be
≤ 300 µΩ, resulting in a thermoelectric transfer difference of a
few parts in 106 in voltage mode.
fSW=1 kHz
10 mA
8 mA
6 mA
0
-1
MJTC (#32465)
-2
Rh =460 Ω
-3
0
0.5
1
1.5
2
×10-3
1 / (Rh +Rr )
2.5
Ω-1
1
FRDC-DC Difference
10 -6
B) Experimental Results
To test the adequacy of the mathematical model described
above, the dependence of FRDC-DC voltage transfer differences
δFRDC-DC on the value of range resistors Rr was measured for the
three TCs described in the previous section. The results are
shown in Fig. 3. The horizontal axis represents the inverse of
the total resistance [1/(Rh+Rr)] in Ω-1.
Fig. 3(a) shows the result of the FRDC-DC difference
measurement for the SJTC(SN#TCJ94014C). The total
resistance Rh+Rr was varied from 100 Ω to 1000 Ω. The data on
the y-axis represent the data for current-mode measurements.
Fig. 3(b) shows measurements for the MJTC(SN#32465) from
Guildline. The total resistance Rh+Rr was varied from 460 Ω to
960 Ω. Fig. 3(c) shows measurements for the type 'T3m-6'
MJTC(SN#477) from VNIIM. The total resistance Rh+Rr was
varied from 100 Ω to 300 Ω.
For all three TCs measured, the FRDC-DC voltage transfer
differences showed linear dependence on the inverse of the total
resistance [1/(Rh+Rr)], as expected from (3). The FRDC-DC
transfer difference was measured at current levels of 100 %,
fSW=1 kHz
0
-1
MJTC (#477)
Rh =100 Ω
10 mA
8 mA
6 mA
-2
-3
0
2
4
1 / (Rh +Rr )
6
8
×10-3
10
Ω-1
Fig. 3.Variation of the FRDC-DC voltage transfer difference versus
resistance of the range resistor/TC combination measured at different
current levels (a) Result for a SJTC [SN#TCJ94014C] with four
type-SS283 elements from Best Technology. (b) Result for an
MJTC [SN#32465] from Guildline. (c) Result for an MJTC
[SN#477] from VNIIM. The x-axis represents the inverse of the total
resistance in Ω -1
V. CONCLUSION
The ac-dc voltage transfer differences of thermal converters
were characterized using a FRDC source. The FRDC-DC
difference measurement was performed for different values of
-3-
the range resistor in series with the thermal converters. The
experimental results were in good agreement with a theoretical
formula based on the assumption that the ac-dc voltage transfer
difference originates from thermoelectric voltage due to the
Seebeck effect.
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