EMLAB Chapter 2. Transmission line theory 1. EMLAB Types of transmission lines Microstrip line Coaxial cable Two-wire transmission line 전기 신호를 손실이 적게.

Presentation on theme: "EMLAB Chapter 2. Transmission line theory 1. EMLAB Types of transmission lines Microstrip line Coaxial cable Two-wire transmission line 전기 신호를 손실이 적게."— Presentation transcript:

1 EMLAB Chapter 2. Transmission line theory 1

2 EMLAB Types of transmission lines Microstrip line Coaxial cable Two-wire transmission line 전기 신호를 손실이 적게 전송하기 위한 구조 2

3 EMLAB Signal propagation in tx-line +V-+V- + 전기장의 진행 속도는 빛 의 속도 c 임 전기장의 방향 3

4 EMLAB i (z, t) v (z, t) + - zz L  z C  z zz i (z+  z, t) v (z+  z,t) + - i (z, t) v (z, t) Transmission line circuits modeling 4

5 EMLAB Transmission line eq. solution 5

6 EMLAB Coax a W Parallel Plate d Transmission line parameter - examples b 6

7 EMLAB + - Parallel wire Coplanar waveguide a D 7

8 EMLAB +V-+V- Transmission line 의 특징 H E 진행 방향 H 1. 한 방향으로 진행하는 전파의 E + /H + 의 비율이 일 정. 2. 한 방향으로 진행하는 V + /I + wave 의 amplitude 비 율도 일정. → 특성 임피던스 Z 0 3. 비율이 맞지 않는 경우 반사파 생김. 8

9 EMLAB +V-+V- Reflection coefficient 9

10 EMLAB +V-+V- +V-+V- +V-+V- +V-+V- +V-+V- Z s = 20  Z 0 = 50  Z L = 1k  0.5m Line 길이에 따른 반사파 영향 Impedance mismatched VinVout R R2 R=1k Ohm MLIN R R1 R=20 Ohm VtPulse SRC1 t Z 0 = 50  10

11 EMLAB +V-+V- +V-+V- +V-+V- +V-+V- Z s = 1  Z 0 = 50  Z L = 50  0.5m +V-+V- Impedance matched Line 길이에 따른 수신 신호 VinVout R R2 R=50 Ohm MLIN R R1 R=50 Ohm VtPulse SRC1 t Z 0 = 50  11

12 EMLAB Narrow band signal 12

13 EMLAB Frequency domain solution β : propagation constant, v p : speed of light 13

14 EMLAB 14

15 EMLAB Phasor representation +V-+V- 15

16 EMLAB Transmission line terminated with short, open Z s = Z o V refl V inc For reflection, a transmission line terminated in a short or open reflects all power back to source In phase (0 ) for open o Out of phase (180 ) for short V refl o 16

17 EMLAB Transmission Line Terminated with 25 Ω Zs = Zo Z L = 25  V refl V inc Standing wave pattern does not go to zero as with short or open 17

18 EMLAB Equivalent input impedance 18

19 EMLAB Input impedance of short 19

20 EMLAB Input impedance of open 20

21 EMLAB Input impedance of ¼ wavelength line Quarter wavelength transformer 21

22 EMLAB Reflection/Transmission 22

23 EMLAB Reflection measurement – slotted line Standing wave ratio 23

24 EMLAB Smith chart 각각의 반사계수에 해당하는 부 하 임피던스를 표시한 그림 Normalized impedance 반사계수 측정을 위해 사용된 transmission line 의 특성 임피던스 = Z 0 24

25 EMLAB 25

26 EMLAB Network analyzer 26

27 EMLAB Smith chart review. -90 o 0 o 180 o + -.2.4.6.8 1.0 90 o   0 +R +jX -jX  Smith Chart maps rectilinear impedance plane onto polar plane Rectilinear impedance plane Polar plane Z = Z o L = 0  Constant X Constant R Z = L = 0 O 1  Smith Chart (open)  L Z = 0 = ±180 O 1 (short) Z-plane Γ-plane Z-to-Γ transform 27

28 EMLAB Smith chart : graphical representation in the reflection coefficient plan plane passive impedance plane Re(z) z one-to-one correspondance Constant resistance, reactance circles 28

29 EMLAB 29

30 EMLAB x R 00.512 r=2 r=1 r=0.5 r=0 x R 2 1 0.5 1 2 x=2 x=0.5 x=1 x=-0.5 x=-1 x=-2 Constant resistance, reactance circles 30

31 EMLAB Constant admittance circles 0 +jX -jX Z-plane 0 +jB Y-plane +jG Impedance chart 를 원점에 대칭 이동하면 admittance chart 가 됨. 31

32 EMLAB Basic smith chart operation Wavelength toward generator 32

33 EMLAB Example 2.2 Z L = 40 + j 70Ω 의 부하가 특성 임피던스 100 Ω 이고 길이가 0.3λ 인 transmission line 에 연결되어 있다. 부하단에서 반사계수, transmission line 의 입력단에서 반사계수, 입력 임피던스, SWR, return loss 를 구하라. 33

34 EMLAB 34

35 EMLAB Example 2.4 0.2, 2.2, 4.2cm 0.72, 2.72, 4.72cm 특성 임피던스 50Ω 인 slotted line 을 이용한 측정 결과이다. 부하 임피던스를 구하라. SWR =1.5 35

36 EMLAB Example 2.5 36

37 EMLAB 2.7 Lossy transmission line 37

38 EMLAB Lossy transmission line 38

39 EMLAB Wave Solution : Characteristic Impedance For Lossless Line 39