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

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

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

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

5. Interface Reflections (cont.)

6. Plane-Wave Bounce Diagramz D d B A C q1 E y

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

8. Bounce Diagram (cont.)
Hence

9. Bounce Diagram (cont.) or
Next, use
Hence

10. 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.

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

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

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

14. TEN (cont.) E0
E0 G
We then have

15. 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.

16. TEN (cont.)
At z = 0:
Hence

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

18. TEN (cont.)
Region 3:
Also
where
Hence

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