射频电路理论与技术-Lectrue2(微带线).ppt

2019/7/20,射频电路理论与技术,2019/7/20,微带的基本概念,微带线目前是混合微波集成电路和单片微波集成电路使用最多的一种平面型传输线。它是在金属化厚度为 h 的介质基片的一面制作宽度为 W ，厚度为 t 的导体带，另一面作接地金属板构成。如图,2019/7/20,1. 一般地说，微带均有介质填充，因此电磁波在其中传播时产生波长缩短。,2. 结构上微带属于不均匀结构。,为了处理方便经常提出有效介电常数(它是全空间填充的)，注意是相对的。,3. 严格说来，微带不是 TEM 波传输线，可称之为准 TEM 模(QuasiTEM mode)，然而作为工程分析，这种概念和精度已足够满足要求。,2019/7/20,微带的特性阻抗,其中，vp 是微带中的相速：,工程上，常常认为微带线中近似传播TEM波,微带线单位长度电容；,空气微带线单位长度电容；,2019/7/20,微带的特性阻抗,2019/7/20,Synthetic asymptote,I. “Root of Area” Capacitance Formula,For a conductor of convex shape of surface area S,The shape factor: 0.9 cf 1.1 . cf =1 for sphere.,A plate of A=ab, total surface area S=2A, cf 0.9.,2019/7/20,Microstrip Parallel Plate Capacitor from Synthetic Asymptote,The near asymptote parallel plate,The far asymptote isolated plates on half space (fringe field),2019/7/20,The synthetic asymptote (sum with adjustment n),Maximum errors: 10% for n = 1, 1% for n = 1.114.,Y. Leonard Chow and Wan C. Tang, “Development of CAD formulas of integrated circuit components - fuzzy EM formulation followed by rigorous derivation,” Journal of Electromagnetic Waves and Applications, vol. 15, pp. 1097-1119, Aug. 2001.,2019/7/20,er=9.6; A=1m2.,2019/7/20,平行双线传输线的单位长度的电容,例3.1.4 平行双线传输线的结构如图所示，导线的半径为 a ，两导线轴线距离为 D ,且 D a ，设周围介质为空气。试求传输线单位长度的电容。,解：设两导线单位长度带电量分别为 +rl 和 -rl,由于 D a ，故可近似地认为电荷均匀分布在两导线的表面上。,应用高斯定律和叠加原理，可得到两导线之间的平面上任意一点 P 的电场强度为,2019/7/20,两导线之间的电位差为,故得平行双线单位长度得电容为,2019/7/20,Derivation of the microstrip formula (analysis),I. Near asymptote of h,II. Far asymptote of h,2019/7/20,III. Synthetic asymptote of h,n=1.07,Wan C. Tang and Y. Leonard Chow, “CAD formulas and their inverses for microstrip, CPW lines without and with a backing ground plane, by successive synthetic asymptotes,” Journal of Electromagnetic Waves and Applications, vol. 16, pp. 1-20, Jan. 2002.,2019/7/20,Derivation of the microstrip formula (inverse),I. Near asymptote,and,2019/7/20,II. Far asymptote,2019/7/20,III. Synthetic asymptote,2019/7/20,2019/7/20,Dispersion,The dominant mode in microstrip line is quasi-TEM mode, the longitudinal components of the electric and magnetic fields are not zero (when the frequency is very low, the longitudinal components approach zero).,It is actually the hybrid modes of E and H waves, denoted as EH modes. Therefore, obvious dispersion occurs in the microstrip lines.,When f4GHz, the dispersion effect must be considered.,2019/7/20,在前面所给出的特性阻抗以及等效介电常数eff的计算公式，均只适用于较低应用频率。 而事实上微带线上为混合模式，其传播速度随频率而变，即存在色散现象。 因此Z0和eff随频率而变，频率升高，相速vp降低，则eff增大，特性阻抗要减小。所以应该引入一些修正。 在10GHz以下，色散对Z0的影响可忽略，但对eff的影响较大。,色散效应的影响,2019/7/20,Higher modes,When microstrip operates at high frequencies, some higher modes emerge in the microstrip lines, including waveguide modes (TE and TM modes) and surface waves. 当微带工作在高频时，会出现高次模式（波导模和表面波模）,2019/7/20,Waveguide modes,The emergence of these modes lie in that the conductor strip and the ground forms a parallel-plate waveguide filled with dielectric (width is W, height is h, the dielectric constant of the dielectric is r). 微带线的导带和接地板之间构成一个平行板波导，所以会有波导模的存在。,2019/7/20,TE10 mode The lowest TE mode is TE10 mode, which is quite different with that in RW. (不同之处在哪里?) Its cutoff wavelength is found to be (t is the thickness of the conductor strip),2019/7/20,TM01 mode The lowest TM mode is TM01 mode, its field distribution is shown in the book, and its cutoff wavelength is expressed as:,2019/7/20,Condition of single mode transmission In order to ensure that only the dominant mode (quasi-TEM) propagates in the microstrip lines, the following condition should be satisfied:,2019/7/20,Surface waves,在金属波导中，所传输的TE或TM导波的相速度总是大于光速，称之为“快波”。 在介质波导或接地的介质基片这样的导波系统中，所传输的导波的相速度小于光速，称为“慢波”。 在传输慢波的导波系统中，其导模将被电抗表面束缚在波导内或波导表面附近沿其轴向传输，即其导模为表面波。 表面波场的特征是：离开导行波系统表面横向指数衰减，大部分场束缚在波导内和波导表面附近，其相速度小于光速。,2019/7/20,微带线尺寸选择,微带线中除准TEM模以外，还可能出现表面波模和波导模。 为抑制高次模式，微带线的横向尺