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

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

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

Parallel wire a + - D Coplanar waveguide

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

Transmission line eq. solution

Reflection coefficient + V -

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 -

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 -

Ringing ~ Signal source Load Mismatched load

Impedance matching - Digital Source matching ~ Load matching ~

Narrow band signal Typical time domain waveforms Spectrum Fractional bandwidth

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

Phasor representation + V -

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

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

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

Equivalent input impedance

Input impedance of short

Input impedance of open

Input impedance of ¼ wavelength line Quarter wavelength transformer

Reflection measurement – slotted line Standing wave ratio

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

Network analyzer

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

Constant resistance, reactance circles x 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

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

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

3. Add shunt element L C

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.

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

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

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.

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

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

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).