微带线损耗的理论研究及工程应用
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摘要
无线通信技术的飞速发展,促使了微波射频电路朝着平面化、小型化、集成化等方向发展。微带线作为单片微波集成电路中信号传输的主要载体,因此受到研究人员的广泛关注。众所周知,微带线的损耗主要有介质损耗,导体损耗和辐射损耗。近年来,我们对微带线损耗问题也开展了一定的研究。在低频小规模微带电路中,微带的损耗可忽略不计。但是随着频率的升高和电路规模的增大,电路中单个器件损耗叠加起来的总损耗会越来越大,对电路性能造成了一定影响,特别在毫米波段,更是不容忽视。目前对微带传输线损耗的计算一般是采用查表近似估算的方法,其具体的分析过程比较繁琐而且计算的结果精度不够高,而不能为设计提供较为精确的数据。本论文分别对微带线的导体损耗和介质损耗做了比较深入的研究,从微带导体损耗和介质损耗的产生机理出发,推导出微带导体损耗和介质损耗的计算公式,对这些公式进行了验证,并总结出降低微带损耗的有关结论,对工程上设计低耗微带电路具有一定的指导意义。最后论文还对微带电路的紧凑性做了一定的研究,设计了一个结构紧凑的一分四的Wilkinson功分网络。
The rapid development of wireless communication technology has excited the developing tendency of compactness, miniaturization and integration for the microwave radio frequency circuits. As one of the main transmission lines of MMIC, the microstrip lines have received a lot of attentions. The researches of microstrip lines are mainly focused on engineering design and losses. As we all know, the losses of microstrip lines mainly include dielectric loss, conductor loss and radiation loss.
In the low frequency miniature microstrip circuits, the loss may be negligible. However, as frequency and circuit scale increase, the total loss accumulated in the large-scale circuits becomes bigger, which will affect the performance of the microstrip circuits, especially in millimeter wave. In this way, it is thus impossible to neglect the losses. Currently, looking-up table and approximate estimation are the main methods to calculate the losses of microstrip, however, they are a little complicated and the accuracy is not high enough. In this paper, some researches have been carried out, including the formula derivation and verification for conductor loss and dielectric loss in microstrip lines. The comparisons between theoretical calculation and software simulations indicate the high accuracy of our formulas. These will provide some useful guides for engineering design of low-loss microstrip circuits. In addition, a compact four-way Wilkinson power divider is designed to demonstrate the compact design of microstrip circuits.
The rapid development of wireless communication technology has excited the developing tendency of compactness, miniaturization and integration for the microwave radio frequency circuits. As one of the main transmission lines of MMIC, the microstrip lines have received a lot of attentions. The researches of microstrip lines are mainly focused on engineering design and losses. As we all know, the losses of microstrip lines mainly include dielectric loss, conductor loss and radiation loss.
In the low frequency miniature microstrip circuits, the loss may be negligible. However, as frequency and circuit scale increase, the total loss accumulated in the large-scale circuits becomes bigger, which will affect the performance of the microstrip circuits, especially in millimeter wave. In this way, it is thus impossible to neglect the losses. Currently, looking-up table and approximate estimation are the main methods to calculate the losses of microstrip, however, they are a little complicated and the accuracy is not high enough. In this paper, some researches have been carried out, including the formula derivation and verification for conductor loss and dielectric loss in microstrip lines. The comparisons between theoretical calculation and software simulations indicate the high accuracy of our formulas. These will provide some useful guides for engineering design of low-loss microstrip circuits. In addition, a compact four-way Wilkinson power divider is designed to demonstrate the compact design of microstrip circuits.
引文
[1]廖承恩.微波技术基础.第1版.西安:西安电子科技大学出版社.1994
[2]刘学观,郭辉萍.微波技术与天线.西安:西安电子科技大学出版社.2004
[3]赵克玉,许福永.微波原理与技术.第1版.北京:高等教育出版社.2006
[4]牛忠霞,雷雪,张德伟.第1版.北京:微波技术及应用.国防工业出版社.2005
[5]李晓蓉,陈章友,吴正娴.微波技术.第1版.北京:科技出版社.2005
[6]梁昌洪,谢拥军,官伯然.简明微波.第1版.北京:高等教育出版社.2006
[7]David K.Cheng.Field and Wave Electromagnetics.Addison-Wiley Publishing,1989
[8]R.Collin.Foundations for Microwave Engineering.McGraw-Hill Book Company.1966:178-179
[9]Y.L.Chow,W.C.Tang.Development of CAD formulas of integrated circuit components - fuzzy EM formulation followed by rigorous derivation.J.of EM Waves and Appl.Vol.15,No.8,August 2001:1097-1119.
[10]E.H.Fooks,R.A.Zarkarevicius.Microwave Engineering Using Microstrip Circuits.Prentice-Hall,1990:177
[11]Y.L.Chow,N.N.Feng,D.G.Fang.A simple method for ohmic loss in conductors with cross-section dimensions on the order of skin depth.Microwave and optical technology letters.Vol.20,Issue 5,March 1999:304-306
[12]G.B.Stracca.A simple evaluation of loss in thin microstrips.Microwave and optical technology letters.Vol.20,Issue5,March 1999:304-306
[13]许福永,赵克玉.电磁场与电磁波.第1版.北京:科技出版社.2005
[14]黄玉兰.电磁场与微波技术.第1版.北京:人民邮电出版社.2007
[15]李绪益.微波技术与微波电路.第1版.广州:华南理工大学出版社.2007
[16]David Pozar.Microwave Engineering,2nd Edition.New York:John Wiley & Sons.1998
[17]G.Marrocco.Gain-optimized self-resonant meander line antennas for RFID applications.IEEE Antennas Wireless Propagate.Lett,2003,2:302-305
[18]T.J.Wamagiris,T.J.Minardo.Performance of a meandered line as electrically small transmitting antenna.IEEE Trans.Antennas Propagat,1998,46:1797-1806
[19]Keren Li,Kazuhiko Atsuki.Low Conductor Loss Microstrip Lines With Side-Grooves.1996 IEEE MTT-S Digest:311-314
[20]Wenquan Che,Yufang Tang,Larissa Vietzorreck,Y.Leonard Chow.Resistance and Attenuation Formulas of Microstripline Constructed by Inspection and Compared to Results from Different Softwares. 2008 Asia Pacific Microwave Conference, Dec. 16-20, 2008, Hong Kong, China: F3-04.
[21] Wenquan Che, Yufang Tang, Y. Leonard Chow. Attenuation Formula of Microstrip Line Constructed by Inspection Its Validation and the Possibility of Lower Loss with Lower Characteristic Impedance. Submitted to MTT.
[22] Robert A. Pucel, Daniel J. Masse, Curtis P. Hartwig. Losses in microstrip. IEEE Trans Microwave Theory Tech.Vol.16, No. 6, June 1968: 342-350
[23] H. Y. Lee, T. Itoh. Phenomenological loss equivalence method for planar quasi-TEM transmission lines with a thin normal conductor or superconductor. IEEE Trans Microwave Theory Tech.Vol.37, No. 12,Dec. 1989: 1904-1909
[24] P. Waldow, I. Wolff. The skin-effect at high frequencies. IEEE Trans Microwave Theory Tech.Vol.33,No.l0,Oct. 1985:1076-1082.
[25] S. K. Kwok, K. F. Tsang, Y. L. Chow. A novel capacitance formula of the microstrip using synthetic asymptote. Microwave and Optical Letters.Vol.36, No.5, March 2003: 327-33
[26] W. Tang, Y. L. Chow, K. F. Tsang. Different microstrip line discontinuities on a single field-based equivalent circuit model. IEE Proc.-Microw.Antennas No.3, Propag.Vol. 151,June 2004: 256-262
[27] Albert Sabban, Kuldip C. Gupta. Characterization of Radiation Loss from Microstrip Discontinuities Using a Multiport Network Modeling Approach. IEEE Transactions On Microwave Theory And Techniques.Vol.39, No.4: 705
[28] Wanchun Tang, Qi Cui, Guang Xu. CAD Modeling of square spiral.Microwave And Optical Technology Letters.Vol.50, No.2, February 2008: 281-284
[29] Y. L. Chow, K. L. Wan. A transformer of one-third wavelength in two sections - For a frequency and its first harmonic. IEEE Microwave Wireless Comp. Lett.Vol.12,2002: 22-25
[30] C. Monzon. Analytical derivation of a two-section impedance transformer for a frequency and its first harmonic. IEEE Microwave Wireless Comp. Lett.Vol.12,2002:381-385
[31] James C. Rautio. An Investigation of Microstrip Conductor Loss.Microwave, December 2000: 60
[32] Keren Li, Kazuhiko Atsuki. Low Conductor Loss Microstrip Lines With Side-Grooves.1996 IEEE MTT-S Digest: 311-314
[33] A. Gopinath, R. Horton, B. Easter. Microstrip Loss Calculations.Electronics Letters 22nd January 1970.Vol. 6, No.2: 40-41
[34] Fei-Ran Yang, Yongxi Qian, Roberto Coccioli, Tatsuo Itoh. A Novel Low-Loss Slow-Wave Microstrip Structure. IEEE Microwave And Guided Wave Letters.Vol.8, No.11,November 1998: 372-374
[35] Nor Ayu Zalina Zakaria and Charles Free. An Investigation of Losses in Microstrip Lines. 2004 RF And Microwave Conference, October 5-6, Subang, Selangor, Malaysia:93-98
[36] Hai-Young Lee, Tatsuo Itoh. Wideband Conductor Loss Calculation Of Planar Quasi-TEM Transmission Lines With Thin Conductors Using A Phenomenological Loss Equivalence Method. 1989 IEEE MTT-S Digest: 751-760
[37] Edgar J. Denlinger. Losses of Microstrip Lines. IEEE Transactions On Microwave Theory And Techniques. Vol.28, No.6, Nov. 1980: 513-522
[38] J. H. C. Van Heuven. Conduction and Radiation Losses in Microstrip. IEEE Transactions On Microwave Theory And Techniques. September 1974: 841-844
[39] B. Rama Rao. Effect of Loss and Frequency Dispersion on the Performance of Microstrip Directional Couplers and Coupled Line Filters. IEEE Transactions On Microwave Theory And Techniques. July 1974: 747-750
[40] R. Horton. Loss Calculations of Coupled Microstrip Lines. IEEE Transactions On Microwave Theory And Techniques. May 1973: 359-360
[41] Christopher, L. Holloway, George A. Hufford. Internal Inductance and Conductor Loss Associate with the Ground Plane of a Microstrip Line. IEEE Transactions On Electromagnetic Compatibility.Vol.39, No.2, May 1997: 73-78
[42] R. Horton, B. Easter, A. Gopinath. Variation Of Microstrip Losses With Thickness Of Strip. Electronics 26th August 1971.Vol.7, No.17: 490-491
[43] V. K. Tripathi. Loss Calculations for Coupled Transmission-Line Structures. IEEE Transactions On Microwave Theory And Techniques. February 1972:178-180
[44] Giovanni B. Stracca. A Simple Evaluation of Losses in Thin Microstrips. IEEE Transactions On Microwave Theory And Techniques.Vol.45, No.2, February 1997: 281-283
[45] Andreas Cangellark. A Note on the Calculation of the Current Distribution in Lossy Microstrip Structures. IEEE Microwave And Guided Wave Letters.Vol.1, No.4, April 1991:81-83
[46] A. Tugulea, I. R. Ciric. Analysis Of lossy Microstrips Using Two-Dimensional Equations For Planar circuits. 1995IEEE MTT-S Digest: 226-229
[47] Xiaoming Chen. EM Modeling of Microstrip Conductor Losses Including Surface Roughness Effect. IEEE Microwave And Wireless Components letters.Vol.17,No.2,February2007: 94-96
[48]T.E.van Deventer,P.B.Katehi,A.C.Cangellaris.High Frequency Conductor And Dielectric Lossess In Shielded Microstrip.1989 IEEE MTT-S Digest:919-922
[49]C.K.C.Tzuang,W.K.Wang.Rigorous Dispersive Analysis Of Skin effects On A printed Microstrp Line Containing Finite Conductor Losses.Electronics Letters.16th August 1990.Vol.26,No.17:1334-1336
[50]秦廷楷.微带和鳍线导体损耗的全波分析.南京邮电学院学报.Vol.14,No.3Sept.1994:17-21
[51]Tunner,E.Neikirk,D.P.Highly Accurate Quasi-Static Modelling of Microstrip Lines Over Lossy Substrate.IEE Microwave and Guided Wave Lett.1992.Vol.2:409-411
[2]刘学观,郭辉萍.微波技术与天线.西安:西安电子科技大学出版社.2004
[3]赵克玉,许福永.微波原理与技术.第1版.北京:高等教育出版社.2006
[4]牛忠霞,雷雪,张德伟.第1版.北京:微波技术及应用.国防工业出版社.2005
[5]李晓蓉,陈章友,吴正娴.微波技术.第1版.北京:科技出版社.2005
[6]梁昌洪,谢拥军,官伯然.简明微波.第1版.北京:高等教育出版社.2006
[7]David K.Cheng.Field and Wave Electromagnetics.Addison-Wiley Publishing,1989
[8]R.Collin.Foundations for Microwave Engineering.McGraw-Hill Book Company.1966:178-179
[9]Y.L.Chow,W.C.Tang.Development of CAD formulas of integrated circuit components - fuzzy EM formulation followed by rigorous derivation.J.of EM Waves and Appl.Vol.15,No.8,August 2001:1097-1119.
[10]E.H.Fooks,R.A.Zarkarevicius.Microwave Engineering Using Microstrip Circuits.Prentice-Hall,1990:177
[11]Y.L.Chow,N.N.Feng,D.G.Fang.A simple method for ohmic loss in conductors with cross-section dimensions on the order of skin depth.Microwave and optical technology letters.Vol.20,Issue 5,March 1999:304-306
[12]G.B.Stracca.A simple evaluation of loss in thin microstrips.Microwave and optical technology letters.Vol.20,Issue5,March 1999:304-306
[13]许福永,赵克玉.电磁场与电磁波.第1版.北京:科技出版社.2005
[14]黄玉兰.电磁场与微波技术.第1版.北京:人民邮电出版社.2007
[15]李绪益.微波技术与微波电路.第1版.广州:华南理工大学出版社.2007
[16]David Pozar.Microwave Engineering,2nd Edition.New York:John Wiley & Sons.1998
[17]G.Marrocco.Gain-optimized self-resonant meander line antennas for RFID applications.IEEE Antennas Wireless Propagate.Lett,2003,2:302-305
[18]T.J.Wamagiris,T.J.Minardo.Performance of a meandered line as electrically small transmitting antenna.IEEE Trans.Antennas Propagat,1998,46:1797-1806
[19]Keren Li,Kazuhiko Atsuki.Low Conductor Loss Microstrip Lines With Side-Grooves.1996 IEEE MTT-S Digest:311-314
[20]Wenquan Che,Yufang Tang,Larissa Vietzorreck,Y.Leonard Chow.Resistance and Attenuation Formulas of Microstripline Constructed by Inspection and Compared to Results from Different Softwares. 2008 Asia Pacific Microwave Conference, Dec. 16-20, 2008, Hong Kong, China: F3-04.
[21] Wenquan Che, Yufang Tang, Y. Leonard Chow. Attenuation Formula of Microstrip Line Constructed by Inspection Its Validation and the Possibility of Lower Loss with Lower Characteristic Impedance. Submitted to MTT.
[22] Robert A. Pucel, Daniel J. Masse, Curtis P. Hartwig. Losses in microstrip. IEEE Trans Microwave Theory Tech.Vol.16, No. 6, June 1968: 342-350
[23] H. Y. Lee, T. Itoh. Phenomenological loss equivalence method for planar quasi-TEM transmission lines with a thin normal conductor or superconductor. IEEE Trans Microwave Theory Tech.Vol.37, No. 12,Dec. 1989: 1904-1909
[24] P. Waldow, I. Wolff. The skin-effect at high frequencies. IEEE Trans Microwave Theory Tech.Vol.33,No.l0,Oct. 1985:1076-1082.
[25] S. K. Kwok, K. F. Tsang, Y. L. Chow. A novel capacitance formula of the microstrip using synthetic asymptote. Microwave and Optical Letters.Vol.36, No.5, March 2003: 327-33
[26] W. Tang, Y. L. Chow, K. F. Tsang. Different microstrip line discontinuities on a single field-based equivalent circuit model. IEE Proc.-Microw.Antennas No.3, Propag.Vol. 151,June 2004: 256-262
[27] Albert Sabban, Kuldip C. Gupta. Characterization of Radiation Loss from Microstrip Discontinuities Using a Multiport Network Modeling Approach. IEEE Transactions On Microwave Theory And Techniques.Vol.39, No.4: 705
[28] Wanchun Tang, Qi Cui, Guang Xu. CAD Modeling of square spiral.Microwave And Optical Technology Letters.Vol.50, No.2, February 2008: 281-284
[29] Y. L. Chow, K. L. Wan. A transformer of one-third wavelength in two sections - For a frequency and its first harmonic. IEEE Microwave Wireless Comp. Lett.Vol.12,2002: 22-25
[30] C. Monzon. Analytical derivation of a two-section impedance transformer for a frequency and its first harmonic. IEEE Microwave Wireless Comp. Lett.Vol.12,2002:381-385
[31] James C. Rautio. An Investigation of Microstrip Conductor Loss.Microwave, December 2000: 60
[32] Keren Li, Kazuhiko Atsuki. Low Conductor Loss Microstrip Lines With Side-Grooves.1996 IEEE MTT-S Digest: 311-314
[33] A. Gopinath, R. Horton, B. Easter. Microstrip Loss Calculations.Electronics Letters 22nd January 1970.Vol. 6, No.2: 40-41
[34] Fei-Ran Yang, Yongxi Qian, Roberto Coccioli, Tatsuo Itoh. A Novel Low-Loss Slow-Wave Microstrip Structure. IEEE Microwave And Guided Wave Letters.Vol.8, No.11,November 1998: 372-374
[35] Nor Ayu Zalina Zakaria and Charles Free. An Investigation of Losses in Microstrip Lines. 2004 RF And Microwave Conference, October 5-6, Subang, Selangor, Malaysia:93-98
[36] Hai-Young Lee, Tatsuo Itoh. Wideband Conductor Loss Calculation Of Planar Quasi-TEM Transmission Lines With Thin Conductors Using A Phenomenological Loss Equivalence Method. 1989 IEEE MTT-S Digest: 751-760
[37] Edgar J. Denlinger. Losses of Microstrip Lines. IEEE Transactions On Microwave Theory And Techniques. Vol.28, No.6, Nov. 1980: 513-522
[38] J. H. C. Van Heuven. Conduction and Radiation Losses in Microstrip. IEEE Transactions On Microwave Theory And Techniques. September 1974: 841-844
[39] B. Rama Rao. Effect of Loss and Frequency Dispersion on the Performance of Microstrip Directional Couplers and Coupled Line Filters. IEEE Transactions On Microwave Theory And Techniques. July 1974: 747-750
[40] R. Horton. Loss Calculations of Coupled Microstrip Lines. IEEE Transactions On Microwave Theory And Techniques. May 1973: 359-360
[41] Christopher, L. Holloway, George A. Hufford. Internal Inductance and Conductor Loss Associate with the Ground Plane of a Microstrip Line. IEEE Transactions On Electromagnetic Compatibility.Vol.39, No.2, May 1997: 73-78
[42] R. Horton, B. Easter, A. Gopinath. Variation Of Microstrip Losses With Thickness Of Strip. Electronics 26th August 1971.Vol.7, No.17: 490-491
[43] V. K. Tripathi. Loss Calculations for Coupled Transmission-Line Structures. IEEE Transactions On Microwave Theory And Techniques. February 1972:178-180
[44] Giovanni B. Stracca. A Simple Evaluation of Losses in Thin Microstrips. IEEE Transactions On Microwave Theory And Techniques.Vol.45, No.2, February 1997: 281-283
[45] Andreas Cangellark. A Note on the Calculation of the Current Distribution in Lossy Microstrip Structures. IEEE Microwave And Guided Wave Letters.Vol.1, No.4, April 1991:81-83
[46] A. Tugulea, I. R. Ciric. Analysis Of lossy Microstrips Using Two-Dimensional Equations For Planar circuits. 1995IEEE MTT-S Digest: 226-229
[47] Xiaoming Chen. EM Modeling of Microstrip Conductor Losses Including Surface Roughness Effect. IEEE Microwave And Wireless Components letters.Vol.17,No.2,February2007: 94-96
[48]T.E.van Deventer,P.B.Katehi,A.C.Cangellaris.High Frequency Conductor And Dielectric Lossess In Shielded Microstrip.1989 IEEE MTT-S Digest:919-922
[49]C.K.C.Tzuang,W.K.Wang.Rigorous Dispersive Analysis Of Skin effects On A printed Microstrp Line Containing Finite Conductor Losses.Electronics Letters.16th August 1990.Vol.26,No.17:1334-1336
[50]秦廷楷.微带和鳍线导体损耗的全波分析.南京邮电学院学报.Vol.14,No.3Sept.1994:17-21
[51]Tunner,E.Neikirk,D.P.Highly Accurate Quasi-Static Modelling of Microstrip Lines Over Lossy Substrate.IEE Microwave and Guided Wave Lett.1992.Vol.2:409-411