Predicting the effect of variations in ambient temperature and operating power on the response of a microwave filter

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Predicting the effect of variations in ambient
temperature and operating power on the response of
a microwave filter
L. M. de la Torre Rodrı´guez *
L. L. Bravo Roger
Jose Pissolato Filho
Yuso Iano
H. E. Herna´ndez Figueroa
School of Electrical and
Computer Engineering
University of Campinas
Campinas - SP, Brazil 13083-852
Email: lisandro@decom.fee.unicamp.com
leobravo@ft.unicamp.br
pisso@dsce.fee.unicamp
yuzo@decom.fee.unicamp.br
hugo@decom.fee.unicamp.br
* Fellow of the Students-Agreement
Postgraduate Program - PEC-PG
CAPES/CNPq - Brazil
Miguel A. Sanchez-Soriano
Polytechnic University College
University of Alicante
Alicante - Alicante, Spain
Email: m.sanchez.soriano@ieee.org
A. A. C. Alves
Institute of Electrical Systems and Energy
Federal University of Itajuba´
Itajuba´ - MG, Brazil 37500-903
Email: andreia.alves@mtel.inatel.br
Abstract—A multiphysics study of the electromagnetic behav-
ior of a filter designed for use in high-power microwave systems
is presented. In the past, the methodology used to design filters
generally assumed ideal working conditions for these devices.
However, when such filters are used in a real environment,
factors such as temperature and working power affect their
performance. Here, we use modern simulation tools to evaluate
the electromagnetic response of a filter at different temperatures
and under different operating conditions.
I. INTRODUCTION
Filter designs generally do not take into account the en-
vironment in which the filter will be working. This is an
important shortcoming as the environmental conditions and
applied RF power can cause the electromagnetic behavior of
the device to differ significantly from the intended behavior.
Analysis of the influence of temperature—a function of ther-
mal dissipation and ambient conditions—on the performance
of RF devices is of particular importance and of considerable
interest to researchers. This has led to the development of high-
performance electromagnetic simulation software packages
with computational tools such as ANSYS [1] and COMSOL
[2] that allow multiphysics simulations to be performed. As a
result, the design of RF devices can now take into account the
influence of temperature and the structural design variations.
An important factor that should be analyzed when designing
RF devices on printed circuit boards (PCBs) is the variation
in the dielectric constant of the substrate, which is caused
by two main factors, namely the ambient temperature and
the temperature distribution in the device, which in turn is
determined by the applied RF power. There are some papers
about the power handling capability in microwave filters [3]
[4], however, few papers on the influence of variations in
dielectric constant on the performance of RF devices have been
published to date [5] [6]. It is hoped that this study will go
some way to addressing this lacuna by showing how variations
in the dielectric constant of the substrate used in an RF filter
designed for operation at different power levels under a range
of environmental conditions can affect the performance of the
filter.
II. MATERIALS AND METHODS
A third-order Chebyshev band-pass filter was designed
for operation in a variety of high-power radar systems. Its
physical structure is shown in Fig.1. Fig.1(a) shows the filter
encapsulated in a copper box, and Fig.1(b) shows the internal
structure of the filter with the two different PCBs visible.
HFSS 15.0 electromagnetic simulation software from ANSYS
was used in the design process.
The materials used to make the filter are shown in Table I
[7]. The response of the electromagnetic filter when used in a
200 W 50 Ω radar system operating at an ambient temperature
of 22◦C (standard operating conditions) is analyzed in terms
of impedance match (S11) and insertion loss (S21), as shown
in Fig.2. Note the excellent performance of the filter over a
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(a) Filter encapsulated in a copper box.
(b) Internal structure of the filter.
Fig. 1. Physical structure of the filter.
TABLE I
MATERIALS USED IN THE FILTER.
Materials Materials Properties
Dielectric
Constant
Loss
Tangent
Thermal
Coefficient of
εr ( ppm/◦C)
Thermal
Conductivity
( W/mK)
Arlon
AD1000 10.2 0.0023 -380 0.81
Arlon
DiClad 880 2.2 0.0009 -160 0.261
Teflon 2.1 0.001 - 0.00091
Silver - - - 1.565
Cooper - - - 1.459
wide range of frequencies in the GHz scale. Frequencies were
normalized to the working frequency. This response served as
a reference for the analyzes in section III. The radar system
operate at pulse regime with duty cycle of 33.3%, so, average
power levels are considered in this work.
Fig. 2. Electromagnetic response of the filter for an operating power of 200W
and ambient temperature of 22◦C.
To analyze the effect of higher operating power levels and
extreme ambient temperatures on the filter, multiple multi-
physics simulations were performed using ANSYS Workbench
platform version 14.5 [1]. A simulation strategy was devised
in which the electromagnetic simulator was connected to the
thermal simulation system [6] in the multiphysics package. In
this approach, the electromagnetic solution is passed to the
thermal simulation system, which provides the temperature
distribution throughout the device. The results are then fed
back to the electromagnetic simulator for further analysis of
the electromagnetic performance of the filter. The temperature
distribution changes the values of the dielectric constants,
which are then fed back to the electromagnetic simulator to
give a new solution for the filter response. This process is
repeated as shown in Fig.3 until a convergence criterion is
met.
Fig. 3. Simulation strategy.
In the experiments, the conductive heat-transfer mechanisms
in the metal and dielectric elements of the filter as well as
heat transfer by natural convection between the flat surfaces
of the filter and the surrounding air were taken into account. A
natural convection coefficient for air of 10 W/m2◦C was used.
To study the behavior of the filter at different temperatures,
experiments with ambient temperatures of −5, 22 and 44◦C
and applied powers of 200, 400 and 600 W were performed.
Two types of analyses were carried. In the first, the ambient
temperature was kept constant and the RF power applied to
the filter was varied, while in the second the applied power
was kept constant and the ambient temperature varied. The
dielectric constants of the substrates used in the filter are given
by (1) [6].
εr(T ) = εr(T0)[1 + C1(T − T0) + C2(T − T0)2] (1)
Where εr(T ) is the dielectric constant of the substrate,
εr(T0) is the dielectric constant in ambient temperature, T0 is
the ambient temperature, T the temperature of the circuit and
C1 and C2 the coefficients of linear and square thermal expan-
sion, respectively. The coefficient of linear thermal expansion
C1 corresponds to the values for the Thermal Coefficient of
εr in Table I. If the analysis is restricted to the linear case,
then C2 = 0 in (1). Fig.4 shows the relation between input
power and dielectric constant of the substrates Arlon AD 1000
and Arlon DiClad 880, showing how the dielectric constant of
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this substrates decreeses due to the fact that, for both cases
the coefficient of linear thermal expansion C1 is negative.
Fig. 4. Relation between input power and dielectric constant of the substrates
Arlon AD 1000 and Arlon DiClad 880.
Fig.5 show the temperature distribution across the device
when a working power of 200 W is applied to the filter
in an environment whose temperature is kept constant at
22◦C (standard operating conditions). As the peaktemperature
is 24.2◦C, we have a temperature gradient of 2.2◦C. The
resolution of the temperature gradient responds to a partial
derivatives linear system (as long as the effects of infrared
radiation are negligible). After determining the thermal re-
sponse of the device at any ambient temperature for a constant
applied power, the maximum temperature reached for any
other ambient temperature can be obtained from (2).
TMAX = TAMB + TG (2)
Where TMAX and TAMB are the maximum temperature
reached and the ambient temperature, respectively, and TG is
the temperature gradient. Therefore, for a maximum tempera-
ture of the device of 100oC, the proposed filter could afford
around several kilowatts of average applied power. Probably,
other effects such as corona discharge may limit the power
handling of the device for such levels of power. Fig.5(a) shows
that the filter box has a temperature of 22.976◦C (minimum),
which is practically the ambient temperature.
III. RESULTS AND DISCUSSION
Fig.6 shows the electromagnetic response of the filter for a
constant temperature of −5◦C and radar operating power of
200, 400 and 600 W.
Fig.7 shows region 1 in Fig.6 in greater detail. Note that
there is a frequency offset in the S21 response at the beginning
of the passband that varies with the applied RF power. For a
fixed attenuation of S21 = −3 dB, the frequencies correspond-
ing to the beginning of the normalized passband are 0.8526,
0.8527 and 0.8528 for applied powers of 200, 400 and 600 W,
respectively, and a constant temperature of −5◦C.
Fig.7 shows frequency offset in the boundaries of the
working band of the filter. This is because, as shown in (3),
the wavelength is a function of the dielectric constant, which
changes with temperature. A similar situation occurs in region
2 in Fig.6.
(a) Temperature of the filter box.
(b) Temperature inside the filter.
Fig. 5. Temperature distribution across the device for standard operating
conditions.
Fig. 6. Filter response for an RF power of 200, 400 and 600W and a constant
ambient temperature of −5◦C.
λg =
λ0√
εr
(3)
Where λg is the guided wave length, λ0 the wavelength
in free space and εr the dielectric constant of the substrate.
Although the results shown above are extremely interesting, in
many cases the radar operates at a predefined constant power,
in which case any variations in the dielectric constant are
mainly determined by variations in the ambient temperature.
We therefore simulated a situation in which the radar operates
with a constant power under extreme temperature conditions.
Fig.8 shows the filter response for a constant power of 600 W
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Fig. 7. Enlarged view of region 1 in Fig.6. The three dotted lines show the
S21 response of the filter for applied powers of 200, 400 and 600W at a
constant ambient temperature of −5◦C.
and ambient temperatures of −5, 22 and 44◦C. Under these
conditions the frequency shifts in the impedance-match (S11)
and insertion-loss (S21) graphs are more noticeable than in
Fig.6.
Fig. 8. Filter response at temperatures of −5, 22 and 44◦C with a constant
applied power of 600W.
Fig.9 shows region 1 in Fig.8 in greater detail. Note that
there is a frequency offset in the S21 response at the beginning
of the passband that varies with ambient temperature. For
a fixed attenuation of S21 = −3 dB and a scale in GHz,
the normalized frequencies corresponding to the beginning
of the passband are 0.8528, 0.8552 and 0.8569 for ambient
temperatures of −5, 22 and 44◦C, respectively, and a constant
applied power of 600 W. When the temperature decreases to
−5◦C, the shift in the filter response is more than 2 MHz to
the left, while for an increase in temperature to +44◦C, the
shift is to the right and of approximately the same order of
magnitude. A similar situation occurs in region 2 in Fig.8.
Table II shows the frequency shifts produced at the filter
response in MHz, in region 1 (reference marked with *) as
much as in region 2 (reference marked with **). The condition
(*) of region 1 refers to the cutoff frequency fc1 obtained for
22◦C and 200 W of applied working power and the condition
(**) of region 2 refers to the cutoff frequency fc2 obtained
Fig. 9. Enlarged view of region 1 in Fig.8. The three dotted lines show the
S21 response of the filter for ambient temperatures of −5, 22 and 44◦C and
a constant applied power of 600W.
TABLE II
FREQUENCY SHIFTS IN REGIONS 1 AND 2. *REFERENCE CONDITION FOR
REGION 1. **REFERENCE CONDITION FOR REGION 2.
Temperature (◦C) Power ( W)200 400 600
22 0* +0.3 +0.4 Shift in,
Region 1
( MHz)
-5 -3 -2.8 -2.7
44 +2.4 +2.5 +2.6
22 0** +0.2 +0.5 Shift in,
Region 2
( MHz)
-5 -5.1 -4.8 -4.6
44 +3.9 +4.0 +4.3
for the same temperature and working power. Note how,
to temperature lower than 22◦C displacements occur toward
low frequencies (negative displacement) and for temperatures
above than 22◦C displacements occur toward high frequency
(positive displacement).
In air-traffic-control, military, meteorological or other high-
power microwave systems, changes in the operating band of
the filter of the order of MHz as observed here can affect
performance and prevent proper system operation, particularly
when the radar makes use of the Doppler effect, for which
frequency stability is critical. Anticipating these effects at
the design stage is extremely important and is possible if
the approach adopted here is used. Indeed, this approach
can be used with many other types of RF applications. In
practice, a way to prevent that these effects compromise the
proper operation of the high-power microwave systems, can
be considering higher frequency limits of the working band
in magnitudes order of those provided in similar multiphysics
studies to shown here.
IV. CONCLUSION
This paper has investigated how the electromagnetic re-
sponse of a band-pass filter for use in high-power radars,
varies with temperature when the power applied to the filter is
increased and the ambient temperature changes. The filter used
in the analysis was a third-order Chebyshev band-pass filter.
Significant shifts in the frequency limits of the filter’s passband
were observed, although the thermal expansion of the materials
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was not taken into account. The importance of anticipating
these shifts at the design stage by performing multiphysics
simulations like those shown here was noted. Because these
frequency shifts can seriously affect the performance of a
range of high-power microwave devices depending on the
particular application, the findings reported here can usefully
be extended to other devices and applications.
ACKNOWLEDGMENT
This work received financial support from Coordenac¸a˜o
de Aperfeic¸oamento de Pessoal de Nı´vel Superior (CAPES)
Brazil, Bradar Indu´stria S/A belonging to the group EM-
BRAER Defense and Security and Sa˜o Paulo Research Foun-
dation (FAPESP) grant 2015/22246− 7.
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