F (W / h) được cho bởi (14,3). Sử dụng các phương trình trước đó, trở kháng đặc tính của microstrip bảo vệ có thể được tính từ 0 Z = Z 0 / √ lại. Đối với phạm vi của các thông số, 1 ≤ r ≤ 30, 0,05 W / h ≤ ≤ 20, t / h ≤ 0,1, và 1 | 442 Lumped Elements for RF and Microwave Circuits Figure Total Ũ for a quarter-wave resonator on RT Duroid er quartz er and alumina er versus substrate thickness. qc tanh S h - h D h h Here F W h is given by . Using the preceding equations the characteristic impedance of the shielded microstrip can be calculated from Z 0 Z a ere. For the range of parameters 1 er 30 W h 20 t h and 1 h h the maximum error in Z0 and ere is found to be less than 1 . When hh h 5 the effect of the top cover on the microstrip characteristics becomes negligible. The effect of sidewalls on the characteristics of microstrip must also be included. It is found that the sidewall effect is negligible when s h 5 where Microstrip Overview 443 Figure Enclosed microstrip configuration. s is the separation between the microstrip conductor edge and the sidewall of the enclosure. Frequency Range of Operation The maximum frequency of operation of a microstrip is limited due to several factors such as excitation of spurious modes higher losses pronounced discontinuity effects low Q due to radiation from discontinuities effect of dispersion on pulse distortion tight fabrication tolerances handling fragility and of course technological processes. The frequency at which significant coupling occurs between the quasi-TEM mode and the lowest order surface wave spurious mode is given here 1 3 fT p a e2 1 er where fp is in gigahertz and h is in millimeters. Thus the maximum thickness of the quartz substrate er for microstrip circuits designed at 100 GHz is less than mm. The excitation of higher order modes in a microstrip can be avoided by operating below the cutoff frequency of the first higher order mode which is given approximately by 300 ic yfe- 2W where fc is in gigahertz and W and h are in millimeters. This limitation is mostly applied to low impedance lines that have wide microstrip conductors. 444 Lumped .
