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1、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 tienchu.edu.tw 03 5186030,中華大學 通訊系,2,Introduction of Waves,Vp: 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 cur
2、rent 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,Dig
3、ital 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 mod
4、el),中華大學 通訊系,9,Why Tr 6 Td ?,Example: Rs = 0.25 Zo, RL= ,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=
5、0.5c = 150mm/ns Td=1mm/Vp = 0.067ns Rule of Thumb only worked as: Tr 6Td= 0.04ns FCLK (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 ICs Vp= 0.6c =180mm/ns Td= 10mm/Vp = 0.056ns Rule of Thumb only worked
6、 as: Tr 6Td= 0.33ns FCLK (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*) VBB(t) is different from VAA(t),中華大學 通訊系
7、,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/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 /20 (Transmission Line or multi-sect
8、ion 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. Wavel
9、ength,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 Element
10、s,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 t= 0+
11、, Vc can be finite value? Ic= infinity ! impossible!# (b) t=0+, Vc= 0, Short circuit for instant (c) Ballastor for impulse voltage Frequency domain : ic= jwC vc,中華大學 通訊系,25,Inductor,Time domain : VL= L (dIL/dt) t= 0-, IL=0 t= 0+, IL can be finite value? VL = infinity ! impossible!# (b) t=0+, IL= 0,
12、Open circuit for instant (c) Ballastor for impulse current Frequency domain : vL= jwL iL,中華大學 通訊系,26,Practical Capacitor,With Parasitic Resistor Rs and Inductor Ls,RS,LS,C,|ZC|,Freq (log),Capacitive,Inductive,中華大學 通訊系,27,Practical Inductor,With Parasitic Resistor Rp and Capacitor Cp,RP,L,CP,|YC|,Fre
13、q (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 u
14、nit length (W/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 L
15、ine Equations,Kirchhoffs voltage law,中華大學 通訊系,36,Transmission Line Equations,Kirchhoffs 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
16、,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= 2x108m/s L= 250nH/m C= 100pF/m =2m 100MHz l= 40cm=0.2 100MHz 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) Its well.,Time delay=2.11ns (5.5% Error) Its g
