中華大學 通訊系 1 Transmission Line Effects in High Speed Digital PCBs 中華大學 通訊系 田慶誠

中華大學 通訊系 2 Introduction of Waves  V p : Phase velocity

中華大學 通訊系 3 Lumped v.s. Distributed Circuit  Lumped Circuits

中華大學 通訊系 4 Lumped v.s. Distributed Circuit  Definitions of lumped element  (1) Input current amplitude = Output current amplitude  (2) Input current phase = Output current phase

中華大學 通訊系 5 Lumped v.s. Distributed Circuit  Distributed Circuit

中華大學 通訊系 6 Lumped v.s. Distributed Circuit  What “Distributed” means

中華大學 通訊系 7 Rise Time v.s. Travel Time  Tr: Rise TimeTd: Delay Time

中華大學 通訊系 8 Digital Interconnection Rules  數位工程師的 Rule of thumb  Signal path can be treated as:  A lumped element, if Tr > 6 Td  (Short ckt, series resistor, shunt capacitor)  A lumped model, if 2.5 < Tr/Td < 6  (Series inductor with shunt capacitor)  A distributed model, if Tr < 2.5 Td  (Transmission Line or multi-section LC model)

中華大學 通訊系 9 Why Tr > 6 Td ?  Example: Rs = 0.25 Zo, R L = 

中華大學 通訊系 10 Why Tr > 6 Td ?  Multi-reflections occurred at load  Tr = 2 TdTr = 4 Td

中華大學 通訊系 11 Why Tr > 6 Td ?  Strong ringingSmooth ripple  Tr = 2 TdTr = 4 Td

中華大學 通訊系 12 Example of High-Speed IC Interconnection  CMOS On-chip 1mm interconnection  Vp= 0.5c = 150mm/ns  Td=1mm/Vp = 0.067ns  Rule of Thumb only worked as:  Tr > 6Td= 0.04ns  F CLK < (8Tr) -1 = 3GHz  Inductance extraction now is very important !!

中華大學 通訊系 13 Example of High-Speed IC Interconnection  10mm interconnection between IC’s  Vp= 0.6c =180mm/ns  Td= 10mm/Vp = 0.056ns  Rule of Thumb only worked as:  Tr > 6Td= 0.33ns  F CLK < (8Tr) -1 = 375 MHz  Distributed analysis now is very important !!

中華大學 通訊系 14 Sinusoidal EM Wave  Oscillations in Time

中華大學 通訊系 15 Sinusoidal EM Wave  Wave Motion in Space

中華大學 通訊系 16 Period v.s. Travel Time  Period T = 1/freqTd= L/(freq* )  V BB’ (t) is different from V AA’ (t)

中華大學 通訊系 17 Period v.s. Travel Time  類比工程師的 Rule of thumb  Signal path can be treated as:  A lumped element, if Td < T/100  (Short ckt, series resistor, shunt capacitor)  A lumped model, if T/100 < Td < T/20  (Series inductor with shunt capacitor)  A distributed model, if Td > T/20  (Transmission Line or multi-section LC model)

中華大學 通訊系 18 Trace v.s. Wavelength  類比工程師的 Rule of thumb  Signal path can be treated as:  A lumped element, if L < /100  (Short ckt, series resistor, shunt capacitor)  A lumped model, if /100 < L < /20  (Series inductor with shunt capacitor)  A distributed model, if L > /20  (Transmission Line or multi-section LC model)

中華大學 通訊系 19 Example of Radio-Frequency Interconnection  For 1GHz RF signal in PCB circuits  Vp= 0.6c =180mm/ns  = Vp/freq =180mm  Rule of Thumb only worked as:  Td < T/100 = 0.01ns  L < /100 = 1.8mm = 71 mil  Distributed analysis is needed for RF PCB design !!

中華大學 通訊系 20 Component size v.s. Wavelength

中華大學 通訊系 21 Component size v.s. Wavelength  Definitions of lumped element  (1) Input current amplitude = Output current amplitude  (2) Input current phase = Output current phase  Only at 100MHz, 2cm resistor can be treated as a lumped resistor !

中華大學 通訊系 22 Electromagnetic Component Lumped Elements Coaxial Cable Waveguide Optical Fiber

中華大學 通訊系 23  ResistorCapacitorInductor  Definitions of lumped element  (1) Input current amplitude = Output current amplitude  (2) Input current phase = Output current phase Basic Lumped Elements

中華大學 通訊系 24 Capacitor Time domain : Ic= C (dVc/dt) t= 0 -, Vc=0 (a)t= 0 +, Vc can be finite value? Ic= infinity !! (b) t=0+, Vc= 0, Short circuit for instant (c) Ballastor for impulse voltage Frequency domain : i c = j  C v c

中華大學 通訊系 25 Inductor Time domain : V L = L (dI L /dt) t= 0 -, I L =0 (a)t= 0 +, I L can be finite value? V L = infinity !! (b) t=0+, I L = 0, Open circuit for instant (c) Ballastor for impulse current Frequency domain : v L = j  L i L

中華大學 通訊系 26 Practical Capacitor With Parasitic Resistor Rs and Inductor Ls RSRS LSLS C |Z C | Freq (log) Capacitive Inductive

中華大學 通訊系 27 Practical Inductor With Parasitic Resistor Rp and Capacitor Cp RPRP L CPCP |Y C | Freq (log) Capacitive Inductive

中華大學 通訊系 28 Murata Chip L/C Library

中華大學 通訊系 29 Murata Chip L/C Library

中華大學 通訊系 30 Transmission Line Behavior  電容起始電壓從 0 開始  電感起始電流從 0 開始  電壓及電流往右移動需要花時間

中華大學 通訊系 31 Distributed circuit of a uniform transmission line

中華大學 通訊系 32 Transmission Line Parameters  R: Resistance per unit length (  /m)  Due to conductor loss  L: Inductance per unit length (H/m)  C: Capacitance per unit length (F/m)  G: Conductance per unit length (S/m)  Due to dielectric loss

中華大學 通訊系 33 Lumped circuit models for a short segment of a TL

中華大學 通訊系 34 Transmission Line Equations

中華大學 通訊系 35 Transmission Line Equations  Kirchhoff’s voltage law

中華大學 通訊系 36 Transmission Line Equations  Kirchhoff’s current law

中華大學 通訊系 37 Wave Equations for Lossless Line  For a lossless line, R= 0 and G= 0

中華大學 通訊系 38 Traveling-Wave solutions  V + :voltage wave traveling in +z direction  V - :voltage wave traveling in -z direction

中華大學 通訊系 39 Traveling-Wave solutions

中華大學 通訊系 40 Characteristic Impedance

中華大學 通訊系 41 Transmission line lumped model 如何正確使用？

Using PSPICE to simulate 100MHz sinusoidal wave propagating in 40cm RG-58/U coaxial cable by lumped model. RG-58/U cable Z0=50  v= 2x10 8 m/s L= 250nH/m C= 100pF/m l= Delay= 2ns Ideal Line

Time delay=3.2ns (60% Error, Too bad !) Time delay=2.55ns (27.5% Error, Not good !)

Time delay=2.25ns (12.5% Error) It’s well.

Time delay=2.11ns (5.5% Error) It’s good enough!!

中華大學 通訊系 46 Transmission line lumped model 使用重點 (1)  Z  0, 在工程的眼光下，可近似成  Z< /20 。 (2) 若要以 Lumped model 建立傳輸線電路的模型，例如 IC Pakage interconnection lines 等，必須先知道傳輸信號所 佔頻寬中的最大頻率 F max 。 (3) 波長 min = 波速 v / F max 。 (4) Transmission lines 超過 min /20 就必須做適當的切割，分 別建立獨立的 Lumped model 。

中華大學 通訊系 47 Cross-sectional View of common uniform TL

中華大學 通訊系 48 Transmission Line Parameters

中華大學 通訊系 49 Skin Effect  For low frequency  For high frequency  Skin depth  A   

中華大學 通訊系 50 Microstrip Lines (Agilent APPCAD)

中華大學 通訊系 51 Coplanar Waveguide ( 側邊鋪銅 )

中華大學 通訊系 52 Safety Separation Distance G >2H

中華大學 通訊系 53 Potentially Dangerous Parasitic Transmission Lines  Parallel plates TL for TEM wave  Slab waveguide for surface wave

中華大學 通訊系 54 Excitation of parasitic TL  Parallel-plate mode excitation  Surface wave excitation

中華大學 通訊系 55 利用鋪銅抑制 parasitic waves

中華大學 通訊系 56 Adding Bypass Capacitors