ENE 428 Microwave Engineering

1. ENE 428Microwave Engineering Lecture 7 Waveguides RS

2. Review • Impedance matching to minimize power reflection from load • Lumped-element tuners • Single-stub tuners • Microstrip lines • The most popular transmission line • Knowing the characteristic impedance and the relative dielectric constant of the material helps determine the strip line configuration and vice versa. • Attenuation • conduction loss • dielectric loss • radiation loss

3. A pair of conductors is used to guide TEM wave • Microstrip • Parallel plate • Two-wire TL • Coaxial cable

4. The use of waveguide • Waveguide refers to the structure that does not support TEM mode, bring up “the cutoff frequency”

5. General wave behaviors along uniform guiding structures (1) • The wave characteristics are examined along straight guiding structures with a uniform cross section such as rectangular waveguides. We can write in the instantaneous form as We begin with Helmholz’s equations: assume WG is filled in with a charge-free lossless dielectric

6. General wave behaviors along uniform guiding structures (2) We can write and in the phasor forms as and

7. Use Maxwell’s equations to show and in terms of z components (1) From and we have

8. Use Maxwell’s equations to show and in terms of z components (2) We can express Ex, Ey, Hx, and Hyin terms of z-component by substitution so we get for lossless media  = j,

9. Propagating waves in a uniform waveguide • Transverse ElectroMagnetic (TEM) waves, no Ez or Hz • Transverse Magnetic (TM), non-zero Ezbut Hz = 0 • Transverse Electric (TE), non-zero Hzbut Ez = 0

10. Transverse ElectroMagnetic wave (TEM) • Since Ez and Hzare 0, TEM wave exists only when • A single conductor cannot support TEM

11. Transverse Magnetic wave (TM) From We can solve for Ez and then solve for other components from (1)-(4) by setting Hz = 0, then we have Notice that  or j for TM is not equal to that for TEM .

12. Eigen values We define Solutions for several WG problems will exist only for real numbers of h or “eigen values” of the boundary value problems, each eigen value determines the characteristic of the particular TM mode.

13. Cutoff frequency From The cutoff frequency exists when  = 0 or or We can write

14. a) Propagating mode (1) or and  is imaginary Then This is a propagating mode with a phase constant :

15. a) Propagating mode (2) Wavelength in the guide, where uis the wavelength of a plane wave with a frequency f in an unbounded dielectric medium (, )

16. a) Propagating mode (3) The phase velocity of the propagating wave in the guide is The wave impedance is then

17. b) Evanescent mode or Then Wave diminishes rapidly with distance z. ZTM is imaginary, purely reactive so there is no power flow

18. Transverse Electric wave (TE) From • Expanding for z-propagating field gets where We can solve for Hz and then solve for other components from (1)-(4) by setting Ez = 0, then we have Notice that  or j for TE is not equal to that for TEM .

19. TE characteristics • Cutoff frequency fc,, g, and up are similar to those in TM mode. • But • Propagating mode f > fc • Evanescent mode f < fc

20. Ex1 Determine wave impedance and guide wavelength (in terms of their values for the TEM mode) at a frequency equal to twice the cutoff frequency in a WG for TM and TE modes.