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Slide -1 What Really is Characteristic Impedance? or Developing Engineering Intuition about Interconnect Design Eric Bogatin Signal Integrity Evangelist www.BeTheSignal.com PCB West March 27, 2007 Eric Bogatin 2007 www.BeTheSignal.com Slide -2 For More Information www.BeTheSignal.com Feature articles and columns Signal integrity public classes Online lectures (30 hours of web based training) Resources Published by Prentice Hall, 2004 Contact : [email protected] 913-393-1305 Eric Bogatin 2007 www.BeTheSignal.com Slide -3 What is the Designer’s Most Important Tool? To Here From Here Or Here ? Eric Bogatin 2007 www.BeTheSignal.com Slide -4 Creativity is the key ingredient to the design process Intuition is the designer’s most important tool Eric Bogatin 2007 www.BeTheSignal.com Slide -5 What Does a Signal See as it Propagates Down an Interconnect? “…be the signal” Eric Bogatin 2007 www.BeTheSignal.com Slide -6 A Propagating Signal • A real, physical transmission line • A signal • A propagating signal Vsignal V Signal path Vin V Return path GROUND Eric Bogatin 2007 www.BeTheSignal.com Slide -7 What Determines the Speed of a Signal? Ans: the dielectric constant of the laminate v signal Dk return in air: v = 186,000 miles per sec v= 12 inches n sec 4 = v = 12 inches/nsec 12 inches n sec = 6 inches n sec 2 Eric Bogatin 2007 www.BeTheSignal.com Slide -8 What is the Most Important Electrical Quality the Signal Cares About? Ans: the impedance Vsignal V Signal path Vin V Return path GROUND Eric Bogatin 2007 www.BeTheSignal.com Slide -9 Electrical Model of a Lossless Transmission Line Telegraphers’ equation ∂ ∂ V (x, t ) = −L I(x, t ) ∂x ∂t ∂ ∂ I(x, t ) = −C V (x, t ) ∂x ∂t Wave equation ∂2 1 ∂2 V (x, t ) = V (x, t ) 2 ∂t LC ∂x 2 ∂2 1 ∂2 I(x, t ) = I(x, t ) 2 ∂t LC ∂x 2 derive Z0 = L C Eric Bogatin 2007 v= 1 LC www.BeTheSignal.com Slide -10 “…be the signal” Charging up a transmission line +++++ - - - - - Eric Bogatin 2007 www.BeTheSignal.com Slide -11 What is Impedance? Z= Voltage applied Current through I C ∆x V Eric Bogatin 2007 www.BeTheSignal.com Slide -12 A Propagating Signal I +++++ V ------Charged line after 1 nsec I +++++ +++++ V ------- ------- Charged line after 2 nsec Eric Bogatin 2007 www.BeTheSignal.com Slide -13 Geometry, Current and Impedance Line width increases, capacitance ______________, impedance______________ increases decreases Line width decreases, capacitance ______________, impedance ______________ decreases increases Dielectric thickness increases, capacitance ___________, ___________ decreases impedance, increases www.BeTheSignal.com Eric Bogatin 2007 Slide -14 Instantaneous Impedance the Signal Sees Z= Voltage applied Current through C ∆x instantaneous impedance of the transmission line Eric Bogatin 2007 www.BeTheSignal.com Slide -15 0th Order Model of Transmission Line CL= Capacitance per length [pF/in] ∆x Vin C C C C C C C C C C = C L ∆x ∆x every ∆t = v ∆Q = CV, What is the current into the line? www.BeTheSignal.com Eric Bogatin 2007 Slide -16 Current Into Transmission Line CL= Capacitance per length [pF/in] ∆x Vin C C C C C C C C C C = C L ∆x ∆Q = CV, ∆x every ∆t = v I, V definition of Transmission Line: I = ∆∆Qt = vCL ∆ x V = vCLV ∆x What’s the impedance? Eric Bogatin 2007 www.BeTheSignal.com Slide -17 Instantaneous Impedance of a Transmission Line I = v C LV V = 1 Z = V = vC vCL I LV Features of the instantaneous impedance: • • • • varies inversely with capacitance looks like a resistor dependant on intrinsic properties independent of length Eric Bogatin 2007 www.BeTheSignal.com Slide -18 Characteristic Impedance Z0 = 1 v CL only applies to uniform transmission lines the one instantaneous impedance that characterizes a uniform transmission line independent of length is the instantaneous impedance a signal will see when propagating down a uniform section Eric Bogatin 2007 www.BeTheSignal.com Slide -19 The Ideal, Lossless Transmission Line Model A “transmission line” is the name we use to refer to the ideal electrical circuit element a new, fundamental, ideal circuit element: T • Characteristic impedance, Z0, • Time delay: TD A “transmission line” is also the name we use to refer to a real, physical interconnect www.BeTheSignal.com Eric Bogatin 2007 Slide -20 Controlled Impedance Interconnects • A uniform transmission line • Same instantaneous impedance everywhere on the line • Any value Z0 can be controlled impedance Controlled impedance structures twisted pair coax microstrip embedded microstrip stripline asymmetric stripline coplanar Famous Characteristic Impedances: RG174 50 Ω RG58 52 Ω RG59 75 Ω RG62 93 Ω TV Antenna 300 Ω Cable TV 75 Ω Twisted pairs 100-130 Ω Eric Bogatin 2007 www.BeTheSignal.com Slide -21 What Does it Mean to Refer to a Cable as a “50 Ohm Cable”? hm ng 50 O 3 foot lo coax Ω Eric Bogatin 2007 www.BeTheSignal.com Slide -22 What Does it Mean to Have a 50 Ohm Line? Ve 0 ggggg 5 rrrry lon ax Ohm co Ω Eric Bogatin 2007 www.BeTheSignal.com Slide -23 open Characteristic impedance Impedance (Ohms) The Input Impedance of a Transmission Line is Time Dependent Round trip time of flight Many round trip time of flights Eric Bogatin 2007 Time www.BeTheSignal.com Slide -24 “…the impedance” of a Transmission Line is Ambiguous • The input impedance of the transmission line - may be time dependent • The instantaneous impedance of the transmission line • The Characteristic impedance of the transmission line Eric Bogatin 2007 www.BeTheSignal.com Slide -25 What Influences Z0 of Microstrip? • First order terms: w h Dk • Second order terms: Mixed dielectrics t Solder mask Etch back Eric Bogatin 2007 www.BeTheSignal.com Slide -26 Calculating Characteristic Impedance • 2D field solvers • Approximations • Rules of thumb Eric Bogatin 2007 www.BeTheSignal.com Slide -27 Calculating Characteristic Impedance: Approximations w Z0 = h b h2 87 h ln 7.5 (ε r + 1.41) w w Z0 = 60 b ln 2.35 Ω εr w w Z0 = 80 h1 h1 ln 4.75 1 − εr w 4h 2 h1 IPC-2141 Eric Bogatin 2007 www.BeTheSignal.com Slide -28 Using a Field Solver Does Not Require Knowing Maxwell’s Equations! Time Domain ∇ • εE = ρ ε0 ∇•B = 0 ∂B =0 ∂t µε ∂E ∇x B − 2 = µ0 J c ∂t ∇x E + Frequency Domain ∇ • εE = ρ ε0 ∇ • µH = 0 ∇x E + jωµ H = 0 ∇x H − jωε E = J “But this is the simplified version for the general public” Eric Bogatin 2007 www.BeTheSignal.com Slide -29 Characteristic Im pedance (Ohm s) IPC Microstrip Accuracy 120 110 100 90 80 70 60 50 40 30 20 10 0 Ansoft Polar IPC 0 2 4 6 8 10 12 14 16 18 20 Line W idth (m ils) 0% Polar -10% IPC -15% -20% -25% -30% -35% 0 2 4 6 8 10 12 14 16 18 20 Line W idth, m ils www.BeTheSignal.com Eric Bogatin 2007 Slide -30 Stripline Example 60.0 50.0 40.0 Zo 30.0 20.0 10.0 7. 00 10 .0 0 13 .0 0 16 .0 0 19 .0 0 22 .0 0 25 .0 0 4. 00 0.0 1. 00 H1 = 5 mils Er1 = 4 T1 = 1.4 mils W1=W2 = changing Absolute Error -5% Height (H1) Eric Bogatin 2007 www.BeTheSignal.com Slide -31 Rules of Thumb w • Microstrip in FR4: w=2xh • Dual stripline in FR4: b=3xh h=w h wh h h w b www.BeTheSignal.com Eric Bogatin 2007 Slide -32 The Input Impedance of a Transmission Line TD If rise time < 2 x TD, what impedance does driver see during transition? Vunloaded Rsource Rsource Z0 = Eric Bogatin 2007 Z0 www.BeTheSignal.com Slide -33 Important Principles • A signal is a changing voltage AND a current loop • The signal sees an instantaneous impedance each step along a uniform transmission line • Characteristic impedance depends inversely on the capacitance per length of the interconnect • The instantaneous impedance the signal sees depends as much on the signal path as the return path • The input impedance of a uniform transmission line is the characteristic impedance for times short compared to the round trip delay Eric Bogatin 2007 www.BeTheSignal.com Slide -34 Thanks for listening! Eric Bogatin 2007 www.BeTheSignal.com Slide -35 For More Information www.BeTheSignal.com Feature articles and columns Signal integrity public classes Online lectures (30 hours of web based training) Resources Published by Prentice Hall, 2004 Contact : [email protected] 913-393-1305 Eric Bogatin 2007 www.BeTheSignal.com Slide -36 Current Return Path in T Lines Current into signal line TD = 1 nsec When does the return current return? For DC currents: For high speed currents? When does current come out return path? Eric Bogatin 2007 www.BeTheSignal.com Slide -37 How Does Current Get Through A Capacitor? I insulating dielectric At DC, the current = 0 www.BeTheSignal.com Eric Bogatin 2007 Slide -38 Add Charge to Conductors +++ Capacitance is ALWAYS constantjust depends on geometry V= ∆V = --- Q C ∆Q C ∆Q = C x ∆V Eric Bogatin 2007 www.BeTheSignal.com Slide -39 Equivalent Views +++ +++ = I --- +++ Do actual + charges move through the insulating dielectric? www.BeTheSignal.com Eric Bogatin 2007 Slide -40 Return Current Paths in Transmission Lines signal C C C C C C C C C C C C C C C C C C To control impedance, manage the return path as carefully as the signal path Eric Bogatin 2007 www.BeTheSignal.com Slide -41 Current Distributions 50 Ohm microstrip, FR4 t = 3 mils 1 MHz 10 MHz 100 MHz Eric Bogatin 2007 www.BeTheSignal.com Slide -42 Microstrip vs. Frequency • Above 1 MHz, current in return path is mostly under signal path • As frequency increases, current in return path concentrates more at the surface Skin depth ~ 2 microns x sqrt(1/f), f in GHz • What drives current re-distribution? The path of lowest loop inductance Current within each conductor spreads out Current between conductors get as close together as possible Eric Bogatin 2007 www.BeTheSignal.com Slide -43 Symmetrical Stripline 50 Ohms, FR4, w = 5 mils, t = 3 mils b = 19 mils b @ 100 MHz www.BeTheSignal.com Eric Bogatin 2007 Slide -44 Asymmetrical Stripline, @ 100 MHz Observations: symmetrical 1. Doesn't matter what the DC voltage is on the planes- any plane can be a return path 2. Return current is symmetrical when trace is symmetrical 3. The closer trace is to a plane, the more return current is in it asymmetrical Eric Bogatin 2007 • Driven by lowest loop inductance www.BeTheSignal.com Slide -45 Important Principles • A signal is a changing voltage AND a current loop • The signal sees an instantaneous impedance each step along a uniform transmission line • Characteristic impedance depends inversely on the capacitance per length of the interconnect • The instantaneous impedance the signal sees depends as much on the signal path as the return path • The input impedance of a uniform transmission line is the characteristic impedance • Above 10 MHz the current through a transmission line is limited to near the conductor surface Eric Bogatin 2007 www.BeTheSignal.com Slide -46 Thanks for listening! Eric Bogatin 2007 www.BeTheSignal.com