LCRG parameters p.u.l. and characteristic impedance Waves of I and V in a finite TL Its input impedance and matching concept Open circuit and short circuit terminations of a TL Useful formulas TM waves in a general WG TE waves in a general WG Cutoff and characteristic impedance of TM waves Elements of electromagnetic field theory and guided waves

LCRG parameters p.u.l. and characteristic impedance

V and I waves in a finite TL Matched termination: Z L =Z 0 → no reflection  =0

Impedance of a finite TL Lossless: Z L =R 0 ÷ Z i =R 0  ÷  =0 Maximal power transfer condition

Open-circuit termination Z L →∞ Low-loss case: X in R in Z io Lossless case: Set of parallel and series resonances

Short-circuit termination R in f Z is Amplitude (z) for a SW

Useful formulas Lossless line, resistive termination: Amplitude (z) for SW +TW

WG – vector generalization of TL E H E=Re(E 0 e j  t-  z ) H=Re(H 0 e j  t-  z ) Now E 0 (x,y) and H 0 (x,y) Not scalar V and I Maxwell’s equations + BC on the walls  j   Lossless approx.  j  azaz ∂/ ∂z E 0 = -  E 0 e -  z ∂/ ∂z H 0 = -  H 0 e -  z For a given mode:

TEM, TM and TE waves in WGs E 1.TEM. Already studied: H E H H=a z ×E       jk  j  1/2 v p =  /k 2. TM waves: z x E H 3. TE waves: x H E z 4. Hybrid waves (in dielectric WG and in lossy metal WG) Quasi-TEM Truly hybrid waves E H x z Usual transmission lines! < 1 GHz >1 GHz

TM waves: eigenvalue and Z TM If H z =0 E z - reference component. If E z =0 H z - reference component.