Notes 21 ECE 6340 Intermediate EM Waves Fall 2016 Prof. David R. Jackson Dept. of ECE Notes 21

Reflection from Slab d TEz qi y z Notes:  (1) (2) The origin is the reference plane for T.

Reflection from Slab (cont.) Find the reflection coefficient . Three methods: Plane-wave bounce method (interface reflections) Steady-state wave representation Transverse equivalent network (TEN)

Method #1 Plane-wave bounce method (interface reflections) Define interface plane-wave reflection and transmission coefficients:

Interface Reflections (cont.)

Plane-Wave Bounce Diagram z D d B A C q1 E y

Bounce Diagram (cont.) At z = 0: Note that (for p an integer) So we have

Bounce Diagram (cont.) Hence

Bounce Diagram (cont.) or Next, use Hence

Steady-State Wave Representation + B.C.s Method # 2 Steady-State Wave Representation + B.C.s #1 #2 #3 Three regions y z Steady-state waves 1 2 3 4 unknowns: , T, A, B 4 equations: Ex and Hy must match at both interfaces.

Transverse Equivalent Network (TEN) Method # 3 Transverse Equivalent Network (TEN) E0 z E0 G E0 T d I V + -

TEN (cont.) E0 z E0 G E0 T d E0 z E0 G d

TEN (cont.) E0 z E0 G d Equivalent circuit:

TEN (cont.) E0 E0 G We then have

Find the transmission coefficient T. TEN (cont.) Find the transmission coefficient T. #1 #2 #3 Region 2: Note: The phase reference point for the transmission coefficient is z = 0.

TEN (cont.) At z = 0: Hence

TEN (cont.) (now known) We then have, on the output side:

TEN (cont.) Region 3: Also where Hence

TEN (cont.) Final result: Note: The phase reference point for the transmission coefficient is z = 0.