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Electromagnetic Waves and Antennas combined - Chapter 10

Tổng Tài sản của dòng truyền TEM Chúng tôi đã thấy trong Sec. 9,3 chế độ TEM được mô tả bằng EQS. (9.3.3) và (9.3.4), sau này là tương đương với một vấn đề tĩnh điện hai chiều: HT = 1 × ET z (TEM chế độ) (10.1.1) Đặc biệt, trên các bề mặt dẫn điện từ trường tiếp tuyến. Theo quy định của pháp luật Amp `lại, tích phân đường của từ trường xung quanh dây dẫn mỗi e sẽ cho kết quả vào dòng tổng số của tôi và tôi chảy trên các dây dẫn theo hướng-z. Những dòng bằng. | 10 Transmission Lines 10.1 General Properties of TEM Transmission Lines We saw in Sec. 9.3 that TEM modes are described by Eqs. 9.3.3 and 9.3.4 the latter being equivalent to a two-dimensional electrostatic problem Hi z X E V T X E 0 V T Et 0 TEM modes 10.1.1 The second of 10.1.1 implies that Et can be expressed as the two-dimensional gradient of a scalar electrostatic potential. Then the third equation becomes Laplace s equation for the potential. Thus the electric held can be obtained from Vj- p 0 Et equivalent electrostatic problem 10.1.2 Because in electrostatic problems the electric held lines must start at positively charged conductors and end at negatively charged ones a TEM mode can be supported only in multi-conductor guides such as the coaxial cable or the two-wire line. Hollow conducting waveguides cannot support TEM modes. Fig. 10.1.1 depicts the transverse cross-sectional area of a two-conductor transmission line. The cross-section shapes are arbitrary. The conductors are equipotentials of the electrostatic solution. Let pa ũpị be the constant potentials on the two conductors. The voltage difference between the conductors will be V pa - pb. The electric held lines start perpendicularly on conductor a and end perpendicularly on conductor b . The magnetic held lines being perpendicular to the electric lines according to Eq. 10.1.1 are recognized to be the equipotential lines. As such they close upon themselves surrounding the two conductors. 398 10. Transmission Lines Fig. 10.1.1 Two-conductor transmission line. In particular on the conductor surfaces the magnetic held is tangential. According to Ampere s law the line integrals of the magnetic held around each conductor will result into total currents I and - flowing on the conductors in the z-direction. These currents are equal and opposite. Impedance Inductance and Capacitance Because the helds are propagating along the z-direction with frequency co and wavenumber co c the z t dependence of the voltage