Chapter2_Notes

Waveguide higher order transmission lines figure 2 4

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Unformatted text preview: es based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines 10 Magnetic field lines Electric field lines Rg + Vg RL Coaxial line Generator Load Cross section Figure 2-5 Figure 5: Details of coaxial transmission line. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines 11 (a) Parallel-wire representation ∆z ∆z ∆z ∆z (b) Differential sections each ∆z long R’∆z L’∆z G’∆z ∆z R’∆z C’∆z L’∆z G’∆z R’∆z C’∆z ∆z L’∆z G’∆z R’∆z C’∆z ∆z L’∆z G’∆z C’∆z ∆z (c) Each section is represented by an equivalent circuit Figure 2-6 Figure 6: Equivalent circuit representation of a TEM transmission line. 1.2. Lumped element model We can represent TEM transmission lines of all kinds by a parallel wire configuration as shown in Fig. 6. But how do we describe this transmission lines model? The same figure is a starting point. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines 12 Lumped element model: • Represent the transmission line with equivalent lumped circuit, i.e. one consisting of resisitive, inductive and capacitive (R, L and C) components. Start by breaking into sections of length ∆z . • The transmission line parameters in the sections are: – R = resistance of both conductors per unit length Ω/m – L = inductance of both conductors H/m, – G = conductance of insulation medium S/m – C = capacitance of two conductors F/m • The same model is applicable to all TEM-mode wave propagation transmission lines. • Note that all parameters are in units/length (the prime is used as a reminder that these are per unit length). Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines 13 • The values for these parameters differ, depending on specifics of the transmission line. For now, we have to accept these but we will derive the expressions later on. • The transmission line parameters for coaxial, two wire and parallel plate waveguides are in Table 2-1 from the book, where µc , σc are magnetic permeability and conductivity of conductors, , µ, σ are electrical permittivity, magnetic permeability, and electrical conductivity of insulation material between conductors. This is illustrated for coaxial line in Fig.7. Let’s have a look at each transmission line parameters. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines b 14 Conductors (µc, σc) a Insulating material (ε, µ, σ) Figure 7: Cross-section of coaxial transmission line. Figure 2-7 • R is resistance of both inner and outer conductors. R= Rs 2π 11 + ab (Ω/m) (3) • The intrinsic resistance Rs is the surface resistance of conductors. Note the frequency depe...
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