Chapter2_Notes

# It depends the generator sends a cosinusoidal signal

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Unformatted text preview: soidal signal VAA = Vg (t) = V0 cos ωt. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines 5 • Assume that the signal (current or voltage) travels with speed of light in vacuum c = 3 × 108 m/s • How much is the signal delayed going from AA to BB ? • If there are no ohmic losses VBB (t) = VAA (t − l/c) = V0 cos[ω (t − l/c)](V) (1) • Take a wire length of l = 5 cm . Set the time to t = 0 s. For f = 1 kHz, this case gives VBB = 0.999 . . . V0 , i.e. VBB and VAA are indistinguishable. • In the second case take l = 20km. This gives VBB = 0.91V0 , i.e. quite a diﬀerence between VBB and VAA . • Where is this coming from? The term ωl/c. That can be reexpressed using up = c (here) so c = f λ (m/s), so that 2πf l l ωl = = 2π radians c c λ Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. (2) Electromagnetics I: Transmission lines 6 • If l/λ is small ⇒ transmission line eﬀects negligible • If l/λ 0.01 ⇒ transmission line eﬀects must be considered • In addition to time delay (shift), we also need to take into account reﬂections, power loss and dispersion. • What’s dispersion? Wave velocity is not constant but is a function of frequency. Figure 3 shows dispersive eﬀects. Could aﬀect operation of digital circuits (“signal integrity”). Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines Dispersionless line Short dispersive line Long dispersive line Figure 3: Transmission line as a source of distortion. Figure 2-3 Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. 7 Electromagnetics I: Transmission lines 8 • Propagation modes Have a look at a few transmission lines in Fig. 4 • There are two basic types: TEM and higher order • TEM = Transverse ElectroMagnetic lines. Electric and magnetic ﬁelds are transverse to the direction of propagation. Coaxial lines are one type. Microstrip not exactly TEM but can be a close approximation to a TEM waveguide. • Metalic waveguides (e.g. rectangular) and ﬁber optic lines are typical for higher order transmission lines. These have at least one component of the E or H ﬁeld that points in the direction of waveguide propagation. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines 9 metal metal 2b w 2a 2a d d dielectric spacing dielectric spacing (a) Coaxial line (b) Two-wire line (c) Parallel-plate line metal strip conductor w metal d metal ground plane dielectric spacing dielectric spacing (d) Strip line (e) Microstrip line TEM Transmission Lines metal metal Concentric dielectric layers (f) Rectangular waveguide (g) Optical fiber metal ground plane dielectric spacing (h) Coplanar waveguide Higher Order Transmission Lines Figure 2-4 Figure 4: Various transmission lines. Not...
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## This note was uploaded on 09/25/2013 for the course ECE 331 taught by Professor Martinsiderious during the Fall '12 term at Portland State.

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