1. ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 4, June 2012
A New Temperature Compensation Method
For Circular Cavity Resonator Using Low Conductivity Cooling Water
System Based On Convection Heat Transfer
Nidhi Verma Dr. Bhavana Jharia
M.E.-Student, Associate Professor,Dept. of EC
Jabalpur Engg. College, Jabalpur Jabalpur Engg. College,Jabalpur
er.nidhiverma@gmail.com bhavanajharia@yahoo.co.in
Abstract factors such as resistive power dissipation, ambient
temperature changes, and thermal radiation. These factors
A novel temperature compensation are common to nearly any RF design. Therefore,
method is presented, in which we used the Low minimizing or eliminating temperature drift is a major
Conductivity Water Cooling System. This paper, studied concern for the RF designer.
the temperature compensation in resonant cavities In Over the past five years, efforts have
this method, heat load and heat exchange has been been reported for temperature compensation of cavity
measured and according to this, the mass flow rate has resonator [1]-[4].Most of these efforts focus on using
been maintained. Temperature compensation depends combination of materials in constructing the resonators.
on the three major parameters- cooling area, mass flow The most common way to design
rate, temperature of the chiller . By using these temperature compensated cavity resonators is to use
parameters, we can calculate the heat transfer from thermally stable materials such as invar material [5]-
cavity to water . If we want to remove all the heat, heat [6].Invar materials have low coefficient of thermal
load should be equal to heat transfer. expansions (CTE), and the temperature stability of the
In this method, by maintaining mass invar material cavities can reach 10 times of that of
flow rate, we can simply reduce the heat load. This ordinary materials cavities.
paper gives an expression for the temperature drift of To overcome the problems of the invar
resonant frequency. Simulation results confirms the cavity, several methods for TC of the resonator have been
feasibility of the proposed design approach. This presented in [7]–[10].In [7], S. B. Lundquist proposed
temperature compensated cavity design is feasible and the idea, is to use different CTE materials to keep the size
can substantially reduces the temperature drift of of the cavity as unchanged as possible when the
circular cavity resonator. temperature varies.
Jilong Ju,develop developed a method of
introducing a dielectric puck in to a resonant cavity, and
1. Introduction changing the position of the dielectric puck can change
the resonant frequency efficiently [11].
Rapid development of CMMB (China D. J. Small and J. A. Lunn, proposed a
Mobile Multimedia Broadcasting ) system and method to deflect the end walls of a cavity using a
DTTB(Digital Television Terrestrial broadcasting) thermally stable external structure (usually Invar) [12].
system resulted in increasing demand on efficient Another approach for temperature
utilization of the frequency spectrum. The UHF adjacent compensation in cavities is to insert a thermally actuated
channels transmitting technology imposed stringent structure into the cavity, providing temperature
requirements on the high performance filters with sharp dependent field perturbation at the side wall, or varying
selectivity and temperature stable frequency responses the electric length at the end wall [13]-[15].
especially for the high power transmitting systems. More recently in [15] Y. Wang, and
RF filters can be realized by coupling Qiang Sui, proposes an external bimetal structure that
resonators. The properties and performance of an actuates a tuning rod inserted through the side wall of a
resonators are highly dependent on its dimensions. Due to rectangular cavity..
thermal expansion, the dimensions of any device are to Brain F. Keats, Rob B. Gorbet and
some extent dependent on temperature. The performance Raafat R. Mansour ,produced a temperature
of any RF device will therefore exhibit a certain amount compensation instrument (TCI) using SMA (shape
of temperature dependence, or temperature drift. memory alloy), and the result is acceptable [16].
Most, RF devices are subjected to In this method we use the concept of
temperature variation. Heating and cooling is caused by convection heat transfer. In which heat load and heat
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All Rights Reserved © 2012 IJARCSEE

2. ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 4, June 2012
exchange has been measured according to which the mass 1
flow rate has been maintained. This approach is tested c Pnm 2 pπ 2 2
f0 = +
using a circular cavity resonator. Frequency drift of the 2π R c0 l0
resonant cavity without the temperature compensation is Here n=1, m=1, p=1 and Pnm = 1.841,
1
both analyzed and measured. The effect by introducing a 2 2 2
chiller arrangement in to cavity is then analyzed. c 1.841 π
f0 = +
The second portion of this paper describes 2π R c0 l0
the temperature characteristics of the circular cavity c 1.841 2 π 2
resonator. These results were use to understand the f0 = + …(2)
2π Rc 0 l0
behavior of uncompensated resonator in third portion of When the resonant cavity is heated from t0 to t1, the new
the paper(section 3).The next step in this design is to radius and length of the resonant cavity is
develop a model for the compensated temperature R c1 = R c0 1 + 𝛼∆𝑡 …..(3)
response of a circular cavity resonator (Section 4). l1 = l0 1 + α∆t . …..……(4)
The measured results of the compensated Where 𝛼 is the CTE of the cavity material, and ∆𝑡 is
model include temperature stability are explain in section change in temperature, and, the new resonant frequency
(5).Finally, these results are used to draw conclusions 𝑓1 , at temperature 𝑡1 is given by,
about the general behavior of compensated c 3.39 9.86
resonators(section 6). f1 = + …..(5)
2π R c 0 1+α∆t l 0 1+α∆t
Under the temperature change of 𝑡1 − 𝑡0 , the resonant
2. Modeling Of Resonant Frequency And frequency change is
Temperature Drift ∆ft = f1 − f0
For nth degree change in temperature, the length and
radius of cavity is given by
The resonant frequency is one of the
important parameters of the resonator cavity. The
resonant frequency is determined by the shape, the R cn = R c 𝑛−1 1 + 𝛼∆𝑡 . ………….(6)
make-up, the material, the dimension, the mod etc. ln = ln−1 1 + α∆t . …………..(7)
To derive a relationship between the
resonant frequency of a cavity and temperature, a And resonant frequency at 𝑛 𝑡ℎ degree change in
relationship between temperature and geometry must be temperature is given as,
established. For metals, which are allowed to expand c 3.39 9.86
fn = + ….…….(8)
freely, linear expansion can be assumed. The geometry 2π R cn 1+α∆t l n 1+α∆t
of the circular resonator is given in figure 1.
We know the resonant frequency of the 3. Uncompensated Resonator Behavior
cavity is given by-
1
c P nm 2 pπ 2 2 In order to derive the compensated
f = + ……..(1)
2π Rc l temperature response of the resonator, the
Where, uncompensated temperature model of the resonator must
R c -radius, l-length, c—speed of light 3 × 1010 be analyzed .By using equation (2)
The integer m, n, p represents the number 𝑐 1.841 2 𝜋 2
of half sine wave variations in the X,Y,Z direction 𝑓 = + ..………(9)
2𝜋 Rc 0 𝑙0
respectively.
In this equation. the base frequency 𝑓
refers to the resonant frequency of the uncompensated
cavity. If the cavity is subject to temperature change, this
frequency will change according to (8).
The term 𝑎 and 𝑙 refers to the radius and
length respectively of the uncompensated cavity. These
will change as the resonator is subject to temperature
change in accordance with (6) and (7).
Figure 1 Circular Cavity Resonator
4. Compensated Resonator Behavior
The resonant frequency, for TE111 (dominant mode) at
temperature t0 is
In this arrangement, we use a chiller
(water tank), cooling pipe, pumps, valves, temperature
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All Rights Reserved © 2012 IJARCSEE

3. ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 4, June 2012
sensors and copper coils. The temperature of the chiller is Assumptions
maintained at 20℃. Cooling pipe is grooved on cavity (1) Lc = 1 meter (length of the cavity),(2) R c = 0.1meter
resonator in the form of channels as shown in figure 2. (Radius of the cavity), (3) R p = 0.01meter( Radius of the
The water flows through the cooling pipe cooling pipe), (4) N = 35 (Number of turns of cooling
over the surface of resonator. when the water flows pipe), (5) t c = 25℃(intial temperature of cavity), (6) t w =
through the pipe, the heat of cavity is transfer to water. 20℃ (Temperature of water), (7) Thickness of the cavity,
In this process the temperature of cavity will decrease Tc ≪ R c , therefore it can be neglected.
and temperature of water will increase. Here, we used
the temperature sensor to measure the cavity Cooling area A is given as
temperature. A=πR p L
A = π2 R p N(R c + R p )
Where,
L = 2πN(R c + R p ) and
Rp
R p = + T…………………….(11)
2
Here, we considered only contact area of cooling pipe,
Rp
that is
2
Here, T≪ R p
Rp
Rp =
2
R c = Radius of the cavity
R p = Radius of the cooling pipe
N = Number of turns of cooling pipe
T = Thickness
Let,
Figure 2-Chiller Arrangement
A = 0.3795m2
If these values are substituted in to equation (10),the heat
load of a cavity can be calculated. The heat load at
When the temperature of the cavity is 25℃
different temperatures are listed in table 2.
then water will flow with a constant mass flow rate, but
At t 0 (starting time) , 𝑡 𝑐1 = 30℃ , U=
if the temperature of cavity is greater than 25℃, the
13.1w/m2 ℃ and t f = 20(h and t f are constant) then
temperature sensor will send a signal to PC. Which will
Qc1 can be calculated according to equation (7)
calculate new mass flow rate according to current
Qc1 = 13.1 × 0.3795 × 30 − 20
temperature of cavity. After that, water will flow with
= 49.71w
new mass flow rate through mass flow controller. In this
way we can remove all the heat which is generated Similarly, we can calculate Qc2, Qc3 , Qc4 , Qc5 , Qc6 ,
through the cavity. Qc7 , Qc8 , Qc9 and Qc10
Temperature compensation depends on the
three major parameters- cooling area, mass flow rate, Table1
temperature of the chiller. By using these parameters, Time Cavity Heat Load
we can calculate the heat transfer from cavity to water . Temperature (watts)
If we want to remove all the heat, heat load should be (.c)
equal to heat transfer. In this method, by maintaining t0 30 49.71
mass flow rate, we can simply reduce the heat load. t1 35 74.55
t2 40 99.4
Heat Load t3 45 124.25
The Heat load between a surface and an adjacent fluid is t4 50 149.1
presented by Newton’s law of cooling t5 55 173.95
Qc = UA t c − t w …………..(10) t6 60 198.8
Where, t7 65 223.65
Qc – Heat load of the cavity (joule)
t8 70 248.5
A – aera exposed to heat transfer
t c – cavity temperature t9 75 273.35
t w – water temperature
Table-1 shows that, Heat load increases with cavity
U - convective heat coefficient (13.1w/m2 ℃,
temperature.
)[18]
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All Rights Reserved © 2012 IJARCSEE

4. ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 4, June 2012
decrease heat load and stable resonant frequency will
Heat load presently through chiller is, achieve.
Qc = UA t c − t w ……………(12)
Required mass flow rate can be calculated as
dQ
= mcp t wo − t wi ……………. .(13)
dt
Where, m- mass flow rate, cp - specific heat of water,
t wo - Outlet temperature of water, t wi - inlet temperature
of water
dQ
Now, we equate the equation (12 ) and (13) Qc =
dt
UA t c − t w = mcp t wo − t wi
hA t c −t w
m= ..….(14)
c p t co −t wi
From equation (14), we can calculate mass flow rate for
different temperature of cavity. In this Case we assume
outlet temperature is 2℃.
Figure 3-Plot of Temperature Versus Heat Exchange Before And
5. Simulation Results After compensation
The exchange load before temperature
Figure-4 shows that, the cavity is heated
compensation and after compensation at different
from 20.c to 70.c , and the result is shown in Figure. The
temperatures are listed in table 2. Table-2 Shows the
dark line shows the resonant frequency without
comparison between heat load and heat exchange before
compensation and dotted line shoes the resonant
and after compensation, This table shows that heat
frequency after compensation. It can be seen that without
exchange increases after compensation.
temperature compensation, an cavity has a frequency drift
and when the Temperature compensation is used on the
Table-2
cavity, the frequency drift is less than 1KHz/.c , which
can almost be neglected.
After Compensation After Compensation
Constant MFR Variable MFR
HLBC HEBC RMFR HEAC
(watts) (watts) (kg/s) (watts)
49.71 24.85 5.9 49.71
74.55 24.85 8.9 74.55
99.4 24.85 11.8 99.4
124.25 24.85 14.8 124.25
149.1 24.85 17.8 149.1
173.95 24.85 20.8 173.95
198.8 24.85 23 198.8
223.65 24.85 26.7 223.65
248.5 24.85 29 248.5
Figure 4- Plot of temperature versus Resonant frequency(RF)
Table-2 Shows the comparison between before and after compensation
heat exchange before and after chilling, This table shows
that heat exchange increases after chilling. The following
graph is according to the values which is given in table 3. 6. Conclusion
The dark line shows the heat exchange after compensation
and doted line shoes the heat exchange before This paper, studied the temperature
compensation. This graph shows that heat exchange compensation in resonant cavities. Both analytical and
increases after compensation. Increases heat exchange will simulation result have been presented. An analytically
derived model for the temperature drift of circular cavity
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5. ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 4, June 2012
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