A flat mounting unit with electronically variable thermal resistance [1] has
been presented in the last year [2]. The design was based on a Peltier cell and
the appropriate control electronics and software. The device is devoted
especially to the thermal characterization of packages, e.g. in dual cold plate
arrangements. Although this design meets the requirements of the static
measurement we are intended to improve its parameters as the settling time and
dynamic thermal impedance and the range of realized thermal resistance. The new
design applies the heat flux sensor developed by our team as well [3], making
easier the control of the device. This development allows even the realization
of negative thermal resistances.Comment: Submitted on behalf of TIMA Editions
  (http://irevues.inist.fr/tima-editions

Kollar, E.

Szekely, V.

Torok, S.

English

arXiv

A flat mounting unit with electronically variable thermal resistance [1] has been presented in the last year [2]. The design was based on a Peltier cell and the appropriate control electronics and software. The device is devoted especially to the thermal characterization of packages, e.g. in dual cold plate arrangements. Although this design meets the requirements of the static measurement we are intended to improve its parameters as the settling time and dynamic thermal impedance and the range of realized thermal resistance. The new design applies the heat flux sensor developed by our team as well [3], making easier the control of the device. This development allows even the realization of negative thermal resistances

Török, S.

I-Revues

 Budapest, Hungary, 17-19 September 2007 
©TIMA Editions/THERMINIC 2007 -page- ISBN:  
 
IMPROVEMENTS OF THE VARIABLE THERMAL RESISTANCE 
 
V. Székely1,2, S. Török1, E. Kollár1 
 
1Budapest University of Technology & Economics 
Department of Electron Devices 
szekely|torok|kollar@eet.bme.hu 
2MicReD Microelectronics Research and Development Ltd. 
 
 
 
ABSTRACT 
 
A flat mounting unit with electronically variable thermal 
resistance [1] has been presented in the last year [2]. The 
design was based on a Peltier cell and the appropriate 
control electronics and software. The device is devoted 
especially to the thermal characterization of packages, 
e.g. in dual cold plate arrangements. 
Although this design meets the requirements of the static 
measurement we are intended to improve its parameters 
as the settling time and dynamic thermal impedance and 
the range of realized thermal resistance. The new design 
applies the heat flux sensor developed by our team as well 
[3], making easier the control of the device. This 
development allows even the realization of negative 
thermal resistances.  
 
Keywords:    variable thermal resistance,   Peltier cell, 
heat-flux sensor, DCP measurements 
 
1. INTRODUCTION 
 
Let us briefly summarize the operating principle of 
the first version of the device. The electronically variable 
thermal resistance (VTR) mount is a sandwich structure, 
consisting of a Peltier cell, with a heat spreading plate in 
both sides. Temperature sensors are placed in both sides 
of the structure; the temperature data are forwarded to the 
control unit. This unit provides the driving current for the 
Peltier cell. The Peltier current is controlled by the two 
temperatures T1 and T2 in such a way that the Rthv virtual 
thermal resistance "seen" on the top of the structure has to 
be the prescribed value. 
The above realization has some drawbacks. Due to 
the control based on the T1 and T2 temperatures the 
settling times are high. The realized Rth value is very 
sensitive to the exact values of Peltier cell parameters. 
Moreover, the stability of the control is problematic if we 
try to realize negative Rth values. 
In order to overcome these weaknesses we 
completed the mount by a heat-flux sensor. This paper is 
dealt with the experiences gained by this new structure. 
 
2. THE NEW MOUNT STRUCTURE 
 
The new mount structure is shown in Fig. 1. Two 
heat spreader metal layer and a Peltier cell constitute a 
sandwich structure (similarly to the former version). The 
temperatures of both metal layers are measured by diode 
temperature sensors. The improvement is that a heat flux 
sensor is placed on the top of the structure. Using this 
sensor the total heat flux penetrated at the top surface can 
be measured and used in the control algorithm. The heat 
flow sensor is a full-silicon, gradient type sensor, 
characterized by a very small thermal insertion resistance 
and good sensitivity. Design of this sensor is described in 
our earlier paper [3].  
 
3. CONTROL HARDWARE AND ALGORITHM 
 
The voltage of the temperature sensor diodes is amplified 
and converted to digital data. The measured range is 
0…100 oC, the resolution (LSB) is 0.0015 oC. The output 
voltage of the heat flux sensor is very small (~10 µV/W) 
requiring an amplifier stage with voltage gain of about 
20000. Due to the noise considerations the bandwidth of 
this amplifier is limited in only 10 Hz. The heat flux data 
is converted into digital one as well. 
The control of the variable thermal resistance unit 
is realized by software. The T1 and T2 temperature data 
converted to digital are read in into the control program 
that runs on a PC. The program controls the current of the 
Peltier cell via an AD converter and a power 
voltage/current converter. 
 
 
 
V. Székely, S. Török, E. Kollár 
Improvements of the variable thermal resistance 
©TIMA Editions/THERMINIC 2007 -page- ISBN:   
  
 
Fig.1. The mount completed with a heat flux sensor 
 
The user has to declare two data for the control program: 
 
? The required virtual thermal resistance Rthv 
? The nominal ambient temperature Tamb 
(practical but not obligatory if this latter is 
equal to the temperature of the cold plate). 
 
The control software measures continuously the incoming 
heat flux P and calculates the *1T  “required” temperature 
of the upper heat spreader sheet in the following way: 
 
thvamb RPTT ⋅+=
*
1    (1) 
 
In order to calculate the current of the Peltier cell we 
apply proportional control, by using the equation: 
 
( )1*1 TTGIPeltier −=    (2) 
 
where the value of G has to be determined considering the 
stability limit of the system. Visibly the T2 temperature 
does not participate now the control algorithm but may 
serve the monitoring of the cold plate temperature.  
 
4. EXPERIMENTAL RESULTS 
 
In order to measure the parameters of the VTR unit, a 
bipolar transistor has been mounted on the top of the 
device, serving as a thermal impedance probe. This 
transistor was driven and measured by the T3Ster thermal 
transient tester equipment [4].  
First the static behavior of the VTR unit has been 
examined. Some of the results are plotted in Fig. 2.  
 
Fig. 2. Measured vs. prescribed thermal resistance values 
 
This diagram shows the measured static Rth values as the 
function of the declared (prescribed) Rth data. The solid 
squares have been measured directly on the top of the 
device using T1 while the crosses mark the data measured 
by the transistor probe. The latter involves the thermal 
resistance of the probe transistor and the upward direction 
heat loss. By taking into account these effects with 2.5 
K/W and 35 K/W thermal resistance respectively, the 
solid line can be calculated.  
The static behavior is well represented by the curves of 
Fig. 3 where the change of T1 temperature is plotted as the 
function of the injected power. The different curves 
belong to different virtual thermal resistance values, 
between –2 K/W and 6 K/W. Linear behavior corresponds 
to straight lines in this diagram. Slight curvature of the 
diagrams indicates slight nonlinearity. The slope of the 
lines gives the realized thermal resistance values. These 
values are referred to the plain interface just below the 
heat flow sensor. 
V. Székely, S. Török, E. Kollár 
Improvements of the variable thermal resistance 
©TIMA Editions/THERMINIC 2007 -page- ISBN:   
 
Fig.3. Measured characteristics of the VTR unit, 
programmed to six different Rthv values. 
 
The quasi-linear region of the VTR characteristics is 
limited by the finite cooling or heating capability of the  
 
Fig. 4. Peltier current vs. injected power for a negative 
(−3 K/W) Rthv value 
 
Peltier cell. This limitation is stronger in case of negative 
Rth values. Fig. 4 shows the steep increase of the current 
of Peltier cell, in case of Rthv = -3 K/W. If the current of 
the Peltier cell is limited in e.g. 2 A, the –3 K/W can be 
realized up to 7.5 W injected power. For positive virtual 
thermal resistance values this limitation is much less 
severe.   
In order to investigate the dynamic behavior of the unit 
thermal transients have been measured. The heating 
curves are plotted in Fig. 5 for five different values of the 
prescribed thermal resistance. It is obvious that the 
beginning parts of the curves are the same for all cases 
since this part corresponds to the thermal structure of the 
transistor probe. It should to draw the attention to the –1 
K/W and –2 K/W curves where the temperature reaching 
a maximum value falls finally. This phenomenon can be 
explained as the effect of the realized negative thermal 
resistance. 
 
Fig. 5. Heating curves for five programmed values of the 
virtual thermal resistance 
The heating curves can be transformed into Nyquist plots 
in the frequency domain. Such a plot is presented in Fig.6 
for five prescribed Rth values. 
 Fig. 6. Loci of the complex thermal impedance (Nyquist 
plots) for five Rthv values 
Again the beginning parts of the diagrams are coincident. 
This region corresponds to the internal thermal structure 
of the transistor probe. The remaining region of the 
curves is more or less a semi-circle suggesting that the 
V. Székely, S. Török, E. Kollár 
Improvements of the variable thermal resistance 
©TIMA Editions/THERMINIC 2007 -page- ISBN:   
VTR device can be characterized by a single RC stage. 
The τ time constants are about 5 s for 0 K/W and 19 s for 
4 K/W.1 
Finally the cumulative structure functions are presented 
(Fig.7). This diagram shows very clearly that the thermal 
resistance of one section of the heat flow path is variable, 
programmable by the control program of the VTR device.   
 
 
Fig.7. Cumulative structure functions for five prescribed 
Rth values 
 
5. CONCLUSIONS 
By using a built-in heat-flux sensor the properties of the 
variable thermal resistance unit can be improved. The 
range of the realized Rth values is broadened, even 
negative thermal resistance can be realized. 
The time-dependent properties of the VTR unit can be 
described by a single thermal RC stage (by a single time 
constant). 
 
6. ACKNOWLEDGMENTS  
The authors wish to express their gratitude to M. Ádám 
for her contribution in the production of heat/flow 
sensors. The support of this work by the Hungarian grant 
“INNOCHECK” KM-CHECK-2005-00043 is acknowledged 
as well. 
 
 
REFERENCES 
 
[1] V. Székely, A. Nagy, S. Török, G. Hajas, M. Rencz: 
“Realization of an electronically controlled thermal 
                                                
1 The settling time for 99% of the final value is 4.6⋅τ. 
resistance”, Microelectronics Journal, Vol.31, pp. 811-
814 (2000) 
 
[2] V. Székely, G. Mezősi: “Design issues of a variable 
thermal resistance”, 12th Therminic International 
Workshop, Nice, Côte d'Azur, France, 27-29 Sept 2006, 
pp.186-190 
 
[3] M. Rencz, E. Kollár, V. Székely: Heat flux sensor to 
support transient thermal characterization of  IC packages, 
Sensors and Actuators, A. Physical, Vol. 116/2 pp. 284-
292, 2004 
 
[4] www.micred.com/t3ster 
 
 
 
 
 
 
 


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