Transmission Line Effects in High Speed Digital PCBs

Transmission Line Effects in High Speed Digital PCBs 中華大學通訊系田慶誠 tien@chu. edu. tw 03 5186030 中華大學通訊系 1

Introduction of Waves § Vp: Phase velocity 中華大學通訊系 2

Lumped v. s. Distributed Circuit § Definitions of lumped element（RLC） § 定义：流入流出的电流和相位一样，没有差值 § (1) Input current amplitude （） = Output current amplitude § (2) Input current phase = Output current phase 中華大學通訊系 4

Lumped v. s. Distributed Circuit § Distributed Circuit（）分散电路中華大學通訊系 5

Rise Time v. s. Travel Time § Tr: Rise Time Td: Delay Time Vin过Rs，从l端左边到右边的时延是td 中華大學通訊系 7

Digital Interconnection Rules § 數位程師的 Rule of thumb § Signal path can be treated as: A lumped element, （RLC单器件） if Tr > 6 Td § (Short ckt, series resistor, shunt capacitor) A lumped model, if 2. 5 < Tr/Td < 6 § (Series inductor with shunt capacitor)（集总式原件的组合） A distributed model, if Tr < 2. 5 Td § (Transmission Line or multi-section LC model) 中華大學通訊系 8

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

Example of High-Speed IC Interconnection § § CMOS On-chip 1 mm interconnection Vp= 0. 5 c = 150 mm/ns Td=1 mm/Vp = 0. 067 ns Rule of Thumb only worked as: Tr > 6 Td= 0. 04 ns -1 = 3 GHz FCLK < (8 Tr) § Inductance extraction now is very important !! F《3 G，IC内部 1 mm的连接线可以做为一个Lumped元件中華大學通訊系 12

Example of High-Speed IC Interconnection § § 10 mm interconnection between IC’s Vp= 0. 6 c =180 mm/ns Td= 10 mm/Vp = 0. 056 ns Rule of Thumb only worked as: Tr > 6 Td= 0. 33 ns -1 = 375 MHz FCLK < (8 Tr) § Distributed analysis now is very important !! § IC和IC之间 1 cm的连接线，在FCLK < 375 MHz时才可以视为一个Lumped 元件中華大學通訊系 13

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

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

Period v. s. Travel Time § Period T = 1/freq Td= L/(freq* ) § VBB’(t) is different from VAA’(t) 中華大學通訊系 16

Period v. s. Travel Time § 類比程師的 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 17

Trace v. s. Wavelength § 類比程師的 Rule of thumb § Signal path can be treated as: A lumped element, if L < /100 § (Short ckt, series resistor, shunt capacitor) A lumped model（LC电路）, if /100 < L < /20 § (Series inductor with shunt capacitor) A distributed model, if L > /20 § (Transmission Line or multi-section LC model) § 每 1/20 波长LC电路（A lumped model）来表示中華大學通訊系 18

Example of Radio-Frequency Interconnection § § For 1 GHz RF signal in PCB circuits Vp= 0. 6 c =180 mm/ns = Vp/freq =180 mm Rule of Thumb only worked as: Td < T/100 = 0. 01 ns L < /100 = 1. 8 mm = 71 mil § Distributed analysis is needed for RF PCB design !! 中華大學通訊系 19

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 100 MHz, 2 cm resistor can be treated as a lumped resistor ! 中華大學通訊系 21

Basic Lumped Elements § Resistor Capacitor Inductor § 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 23

Capacitor Time domain : Ic= C (d. Vc/dt) t= 0 -, Vc=0 (a) t= 0+, Vc can be finite value? Ic= infinity !! impossible!!@# (b) t=0+, Vc= 0, Short circuit for instant（接通瞬间, 电压为 0） (c) Ballastor for impulse voltage Frequency domain : ic= jw. C vc 中華大學通訊系 24

Inductor Time domain : VL= L (d. IL/dt) t= 0 -, IL=0 (a) t= 0+, IL can be finite value? VL = infinity !! impossible!!@# (b) t=0+, IL= 0, Open circuit for instant（接通瞬间，电流为 0） (c) Ballastor for impulse current（为突然的脉冲电流做稳流作用，电流不会突变） Frequency domain : v. L= jw. L i. L 中華大學通訊系 25

Practical Capacitor RS C LS With Parasitic Resistor Rs and Inductor Ls（有寄生电感和寄生电阻） Capacitive |ZC| Inductive 共振频率（可以做 bypass电容） Freq (log) 中華大學通訊系 26

Practical Inductor RP CP L |YC| With Parasitic Resistor Rp and Capacitor Cp Inductive Capacitive Freq (log) 可以做RF chock，此时阻抗最大中華大學通訊系 27

Murata Chip L/C Library 中華大學通訊系 28

Murata Chip L/C Library 中華大學通訊系 29

Transmission Line Parameters § R: Resistance per unit 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 32

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

Transmission Line Equations 中華大學通訊系 34

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

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

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

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

Traveling-Wave solutions 中華大學通訊系 39

Characteristic Impedance 中華大學通訊系 40

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

Using PSPICE to simulate 100 MHz sinusoidal wave propagating in 40 cm RG -58/U coaxial cable by lumped model. RG-58/U cable Z 0=50 v= 2 x 108 m/s Ideal Line L= 250 n. H/m C= 100 p. F/m =2 m @100 MHz l= 40 cm=0. 2 @100 MHz Delay= 2 ns