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  • 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 aMobile Multimedia Broadcasting ) system and method to deflect the end walls of a cavity using aDTTB(Digital Television Terrestrial broadcasting) thermally stable external structure (usually Invar) [12].system resulted in increasing demand on efficient Another approach for temperatureutilization of the frequency spectrum. The UHF adjacent compensation in cavities is to insert a thermally actuatedchannels transmitting technology imposed stringent structure into the cavity, providing temperaturerequirements on the high performance filters with sharp dependent field perturbation at the side wall, or varyingselectivity 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 thatresonators. The properties and performance of an actuates a tuning rod inserted through the side wall of aresonators 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 andsome extent dependent on temperature. The performance Raafat R. Mansour ,produced a temperatureof any RF device will therefore exhibit a certain amount compensation instrument (TCI) using SMA (shapeof 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 oftemperature variation. Heating and cooling is caused by convection heat transfer. In which heat load and heat 43 All Rights Reserved © 2012 IJARCSEE
  • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 4, June 2012exchange has been measured according to which the mass 1flow 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 l0resonant cavity without the temperature compensation is Here n=1, m=1, p=1 and Pnm = 1.841, 1both analyzed and measured. The effect by introducing a 2 2 2chiller 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 ismodel 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 9.86resonators(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, theWhere, 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 2of half sine wave variations in the X,Y,Z direction 𝑓 = + ..………(9) 2𝜋 Rc 0 𝑙0respectively. 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 BehaviorThe resonant frequency, for TE111 (dominant mode) attemperature t0 is In this arrangement, we use a chiller (water tank), cooling pipe, pumps, valves, temperature 44 All Rights Reserved © 2012 IJARCSEE
  • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 4, June 2012sensors and copper coils. The temperature of the chiller is Assumptionsmaintained at 20℃. Cooling pipe is grooved on cavity (1) Lc = 1 meter (length of the cavity),(2) R c = 0.1meterresonator 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 99.4Heat Load t3 45 124.25 The Heat load between a surface and an adjacent fluid is t4 50 149.1presented by Newton’s law of cooling t5 55 173.95 Qc = UA t c − t w …………..(10) t6 60 198.8Where, 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] 45 All Rights Reserved © 2012 IJARCSEE
  • 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 compensationheat exchange before and after chilling, This table showsthat heat exchange increases after chilling. The followinggraph is according to the values which is given in table 3. 6. ConclusionThe dark line shows the heat exchange after compensationand doted line shoes the heat exchange before This paper, studied the temperaturecompensation. This graph shows that heat exchange compensation in resonant cavities. Both analytical andincreases after compensation. Increases heat exchange will simulation result have been presented. An analytically derived model for the temperature drift of circular cavity 46 All Rights Reserved © 2012 IJARCSEE
  • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 4, June 2012 resonator for dominant mode[𝑇𝐸111 ] used for analysis. Techniques Symposium., vol. 82, issue 9, pp. 1311-1316, Chiller arrangement is used in circular waveguide September 1982. cavity. By maintaining the mass flow rate we can reduce [7] S. B. Lundquist, ―Temperature compensated microwave filter,‖, Feb. 2,1999. the heat load. It is concluded that, if a proper [8] C. Wang and K. Zaki, ―Temperature compensation of relationship is built between the heat load, heat combine resonators and filters,‖ in IEEE MTT-S Int. Microwave exchange and mass flow rate, the frequency drift of the Symp. Dig., 1999,Paper WE2C-6, pp. 1041–1044. cavity can be controlled. This temperature compensated [9] D. Kajfez, S. Chebolu, A. A. Kishk, and M. R. Abdul- cavity design is feasible and can substantially reduces Gaffoor, ―Temperature dependence of composite microwave the temperature drift of circular cavity resonator. cavities,‖ IEEE Trans. Microwave Theory Tech., vol. 49, pp. 80–85, Jan. 2001. References [10] P. Piironen, J. Mallat, and A. V. Räisänen, ―Cryogenic millimeter-wave ring filter for space application,‖ IEEE Trans. Microwave Theory Tech., vol. 46, pp. 1257–1262, Sept. 1998. [1] C. Wang and K. A. Zaki, ―Temperature compensation of [11] Jilong Ju, ―A Novel Configuration of Temperaturecombline resonators and filters,‖ in IEEE MTT-S Int. Compensation in the Resonant avities‖, IEEE Trans.Microwave Symp. Dig., vol. 3,1999, pp. 1041–1044. Microwave Theory Tech., vol 52,pp. 139-143, Jan. 2004 [2] Y. Hui-Wen and A. E. Atia, ―Temperature characteristics of [12] D. J. Small and J. A. Lunn, "Temperature compensatedcombline resonators and filters,‖ in IEEE MTT-S Int. high power bandpass filter," nited States Patent 6,232,852,Microwave Symp. Dig., vol.3, 2001, pp. 1475–1478. March 2003. [3] S.-W. Chen, K. A. Zaki, and R. F.West, ―Tunable, [13] B. F. Keats, R. R. Mansour, and R. B. Gorbet, "Designtemperature-compensated dielectric resonators and filters,‖ and testing of SMA temperature-compensated cavityIEEE Trans. Microwave Theory Tech., vol. 38, pp. 1046–1052, resonators,"IEEE Transactions on Microwave Theory andAug. 1990. Techniques., vol.2, pp. 8-13, June 2003. [4] N. McN. Alford, J. Breeze, S. J. Penn, and M. Poole, [15] Y. Wang, and Qiang Sui, "A New Temperature―Temperature compensated high Q and high thermal Compensation Method of Rectangular Waveguide Cavities,"conductivity dielectrics for Ku and Ka band communications,‖ Asia-Pacific Microwave Conference Proceedings, vol. 5,in IEEE icrowave Filters and Multiplexers Colloq., Ref. December 2005.2000/117, 2000, pp. 6/1–6/4. [16]Brain F. Keats, Rob B. Gorbet and Raafat R. Mansour, [5] A. Atia, "A 14-GHz high-power filter," IEEE Digest on ―Design and Testing of SMA Temperature-Compensated CavityMicrowave Theory and Techniques Symposium., vol. 79, issue Resonators‖, IEEE Trans. Microwave Theory Tech., vol. 51,1, pp. 261-261, April 1979.s pp. 2284-2289, Dec. 2003. [6] S. J. Fiedziusko, "Dual-mode dielectric resonator loaded [17] R.K. Rajput, "Heat And Mass Transfer".cavity filters," IEEE Digest on Microwave Theory and [18] The engineering toolbox, ― overall heat transfer coefficients for some common fluids and heat exchangers‖. 47 All Rights Reserved © 2012 IJARCSEE