1. Non-ideal property – crosstalk
인접한 전선들 사이에 간섭이 생긴다.
Voltage
Near end crosstalk voltage
Far end crosstalk voltage

2. Types of transmission lines
Microstrip line
Coaxial cable
Two-wire transmission line

3. Transmission line parameter - examples
Coax a b
Parallel Plate W d

4. Parallel wire a + - D
Coplanar waveguide

5. Transmission line 등가 회로
i (z, t)
i (z+z, t)
i (z, t)
v (z, t) + - +
v (z, t) + -
L z
C z
v (z+ z,t) - z z

6. Transmission line eq. solution

7. Reflection coefficient+ V -

8. Influence of line length on load voltage
Impedance mismatched + V -
Vin
Vout R R2
R=1k Ohm
MLIN R1
R=20 Ohm
VtPulse
SRC1 t + V -
Z0= 50  + V -
Zs = 20 
Z0= 50  + V -
ZL= 1k 
0.5m + V -

9. Line 길이에 따른 수신 신호 Impedance matched Z0= 50  Zs = 1  Z0= 50 + V -
Vin
Vout R R2
R=50 Ohm
MLIN R1
VtPulse
SRC1 t + V -
Z0= 50 
Zs = 1  + V -
Z0= 50 
ZL= 50  + V -
0.5m + V -

10. Ringing ~
Signal source
Load
Mismatched load

11. Impedance matching - Digital
Source matching ~
Load matching ~

12. Narrow band signal Typical time domain waveforms Spectrum
Fractional bandwidth

13. Frequency domain solution
β : propagation constant, vp : speed of light

14. Phasor representation+ V -

15. Transmission line terminated with short, open
Out of phase (180◦ ) for short
Vinc
Vrefl
short
open
Vrefl
In phase (0 ◦) for open
For reflection, a transmission line terminated in a short or open reflects all power back to source

16. Transmission Line Terminated with 25 ΩV
inc
Vrefl
Standing wave pattern does not go to zero as with short or open.

17. Standing wave of free end
Open circuit
Standing wave of fixed end
Short circuit
Standing waves of harmonics

18. Equivalent input impedance

19. Input impedance of short

20. Input impedance of open

21. Input impedance of ¼ wavelength line
Quarter wavelength transformer

22. Reflection measurement – slotted line
Standing wave ratio

23. Smith chart 각각의 반사계수에 해당하는 부하 임피던스를 표시한 그림 Normalized impedance
반사계수 측정을 위해 사용된 transmission line의 특성 임피던스 = Z0
Normalized impedance

24. Network analyzer

25. Rectilinear impedance plane
Smith chart review
Z-plane
+jX 90 o
Z-to-Γ transform
Polar plane
1.0 .8 .6 +R
¥ ® .4
180 o + - .2 o
-jX
Rectilinear impedance plane
-90 o
Constant X
Z = Zo
Smith Chart maps rectilinear impedance plane onto polar plane L
Constant R G =
Z = 0
(short)
Z =
(open) L L G G = 1
±180 O = 1 O
Smith Chart

26. Constant resistance, reactance circlesx
r=0
r=0.5
r=1
r=2 R
0.5 1 2 x 2
x=1
x=0.5 1
x=2
0.5 R
0.5 1
x=-2
x=-1
x=-0.5 2

27. Constant admittance circles
Y-plane
+jB
+jG
Z-plane
+jX
-jX

28. Basic Smith chart operation
1. Translation
2. Add series element L C

29. 3. Add shunt element L C

30. Matching with lumped elements
L-section matching networks. (a) Network for zL inside the 1 + jx circle. (b) Network for zL outside the 1 + jx circle.

31. Example 5.1 Smith chart – impedance chart ZL= 200-j 100  Z0= 100 
Figure 5.3a (p. 226) Solution to Example (a) Smith chart for the L-section matching networks.
ZL= 200-j 100  3
Z0= 100 
f = 500MHz 2 5 1 4

32. Impedance-admittance chart
ZL= 200-j 100 
Z0= 100 
f = 500MHz
0.0 1
0.2
Add series L
Add shunt C
0.5
1.2

33. Single stub tuning ZL= 60-j 80  Z0= 50  f = 2GHz Translate by ‘d’1 1
0.314
0.314
0.422
D를 변화시켜 1+jb 원의 원주 상에 yL이 오도록 한다.

34. Add shunt stub (shorted)
1+jb 원의 원주 상의 지점을 shunt stub(병렬 stub)을 달아서 Γ원의 원점으로 옮기면 impedance matching이 완료됨.

35. 0.422 0.314 Impedance matching 순서 zL이 1+jb 원의 원주 상에 올 수 있도록 d1을 조절한다.
(점선 원) 상에zL이 옮겨 올 수 있도록 L1을 조절한다. 1
0.314

36. Figure 5. 5b (p. 231) (b) The two shunt-stub tuning solutions
Figure 5.5b (p. 231) (b) The two shunt-stub tuning solutions. (c) Reflection coefficient magnitudes versus frequency for the tuning circuits of (b).