======================TRANSMISSION_LINES====================== _____________________________ ->()____________________________) D_cm _____________________________ ->()____________________________) L_cm __ L_cm > D_cm __ | |__ __| | |__| | | |__| |*() () | \_/\_/\_/ MUTUAL INDUCTANCE M _ _ _ /*\/ \/ \ __ | () () | __ | |__| |__| | |__| |__| M_uH=.002*L_cm*( ln(2*L_cm/D_cm) -1 +D_cm/L_cm ) ------------------------------------------------------------------------------------- ___\__ --> I ______|___/__|________________ ->()___________\|/______________ | |_/____| _/___ | | ________\_______|_\___|_____| | <-()_____________________|_______| <-- I |___\_| INDUCTANCE CANCELATION __ / | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | Lb = 0 if (L1 = L2 = M) __ | () () | | | |__| |_____| |__| ------------------------------------------------------------------------------------- ___\__ --> I _______ ______|___/__|______________| | ->()___________\|/_____________| | INDUCTANCE CANCELATION |_/____| _/___ |50 Ohms| ________\_______|_\___|_____| | <-()_____________________|_____| | <-- I |___\_| |_______| / ------------------------------------------------------------------------------------- Voltage dropping current \ -----> \ \____\ \______\ \ \ \ \ \ \ _ \ _ ->E \| \ \ _ \| \ \|/ _ /_ \ ^ _ /_ v H |_/ \ _V Voltage \ |_/ \ __/_ \ Pulse \ __/_ |_/ \ \ \ |_/ \ | _V | voltage \ \ - + \ \____\ \______\ ELECT_MAG_WAVE \ \ \ \ \ ---> \ _ \ _ | E \| \ \ _ \| \ \|/ _ /_ \ ^ _ /_ v H |_/ \ _V \ |_/ \ __/_ \ __/_ ->E |_/ \ \ |_/ \ \|/ | | v H \ \ \ \____\ \______\ \ \ \ \ current <------ Voltage increasing ------------------------------------------------------------------------------------- _____________________________ ->()____________________________) <- d_cm | D_cm Z_ohms sqrt(L/C) | _____________________________ ->()____________________________) L_cm Z_ohms = 276.0*log(2*D_cm/d_cm) C_pf/meter = 12.06/log(2*D_cm/d_cm) L_uH/meter = 0.920*log(2*D_cm/d_cm) w0 = sqrt(L*C) = sqrt(dL*dC*X^2) = X*sqrt(dL*dC) velocity = (2*pi()/sqrt(dL*dC) ------------------------------------------------------------------------------------- __-----__ / d_inch \ Impedances inside coax / ___ \ | / ^ \ | | | |_ |__\| \ \___/ // \ D_inch/ \__ __/ ----- L_R_C Coaxial(D_inch,d_inch) Z_ohms = sqrt(L/C) = 138*log(D_inch/d_inch)/sqrt(E) C_pf/ft = 7.36*E/log(D_inch/d_inch) L_uH/ft = 0.14*log(D_inch/d_inch)) Delay_ns/ft = 1.016*sqrt(E) Propagation_%_c = 100/sqrt(E) CutOffFreq_Ghz = 7.5/( sqrt(E)*(D_inch+d_inch) ) Dielectric Constant E TFE 2.1 ethylene propylene 2.24 polyethylene 2.3 cellular polyethylene 1.4-2.1 silicone rubber 2.08-3.5 polyvinylchoride 3-8 ------------------------------------------------------------------------------------- Single coaxial line <--d---> __________ / ________ \ / / \ \ / / ____ \ \ / / / \ \ \ / / / \ \ \ \ \ \ / / / \ \ \____/ / / \ \ / / \ \________/ / \__________/ <-----D-----> Z0 = (138/e^0.5) log_10(D/d) (6O/e^0.5) ln(D/d) E = dielectric constant = 1 in air Balanced shielded For D>> d, h>>d, <--h---> __________ / ________ \ / / \ \ / / \ \ / / __ __ \ \ _ / / / \ / \ \ \ d \ \ \__/ \__/ / / _ \ \ / / \ \ / / \ \________/ / \__________/ <-----D-----> Z0 =( 276/e^.5)*log( 2*vu*( (1-sigma^2)/(1+sigma^2) ) ( 120/e^.5)*ln( 2*vu*( (1-sigma^2)/(1+sigma^2) ) vu = h/d sigma = h/D BeadsÑdielectric e_1 _________________ _________________ | | | | __|_|____|_|____ _________________ | | | | __|_|____|_|____ __________________ ><|<-->| w s For lines A. and B., if insulating beads are used at frequent intervalsÑcall new characteristic miÑ pedance Z0Õ ZoÕ= Zo/( (1+[(e1/e) Ñ 1)*sqrt( W/S) ) Open 2-wire line in air __ __ _ / \ / \ d \__/ \__/ _ <---D---> Z0 = 120*acosh(D/d) ~276*log(2D/d) ~120*ln(2D/d) Wires in parallel near ground __ __ _ / \ / \ d \__/ \__/ _ ^ <---D---> |h _______________ V ////////////// For d< |h _______________ V ////////////// For d< where rho= D/d A= (1+0.405*rho^-4)/ (1Ñ0.405 *rho^-4) B= (1+0.163*rho^-8)/ (1Ñ0.163 *rho^-8) C~ (1+0.067 *rho^-12)/(lÑO.067 *rho^-12) Balanced 4-wire <-d-> __ __ / +\ / o\ \__/ \__/ ^ \ / | \_/ D2 __ /| __ | / o\/ \/ +\ V \__/ \__/ <---D1-> d< __ __ | / +\ / +\ V \__/ \__/ <---D-> For d << D Z0= (173/e^0.5) log10(D/(0.933*d)) FR-4 fiberglass resin most common material Material r CTE LossTangent Cost ppm/C per sq. ft. FR-4 glass 4.1-4.8 +250 0.02-0.03 $2.5 GTEK 3.5-4.3 +250 0.012 $3.5 woven glass/ceramic loaded 3.38 +40 0.0027 $9.50 PTFE/ceramic (Teflon) 2.94 0 0.0012 $100.00 Copper Layers The conductive layer of a PCB is usually a sheet of copper which has been etched to form the circuit traces. The copper sheetÕs nominal thickness is designated by the weight of 1 square foot of copper of the nominal thickness. Copper Thicknessesƒ Weight (oz) Thickness (in) Weight (oz) Thickness (in) 1/8 0.00017 4 0.0056 1/4 0.00035 5 0.0070 1/2 0.0007 6 0.0084 1 0.0014 7 0.0098 2 0.0028 10 0.0140 3 0.0042 14 0.0196 For pc-board traces, bandwidth is proportional to the square of trace width, W, and inversely proportional to the square of trace length, L. This simple model holds reasonably well for all transmission lines in which skin effect dominates . digital application operating abandwidths higher than 10 MHz. Dielectric losses also play a minor role in the bandwidth equation, because skin effect causes bulk of pc-board-trace loss, the (W/L)^2 model holds fairly well for increasing trace length by k decreases bandwidth by a factor of k^2. Shrinking trace width (assuming that you also lower the trace height to maintain the same impedance) also reduces the bandwidth by a factor of four. Fortunately for us designers of high-speed systems, FR-4strip-line trace 6 mils wide and 12 in.long has a bandwidth 1.5 GHz and a 10 to 90% rise time of about 250 psec. If 1.5 GHz is not enough for your application, Use wider traces. While you make the trace wider, raise it farther away from the nearest solid plane. Core Materials The most common material is a fiberglass resin called FR-4. Material er CTEppm/oC Loss Tangent ( ) Cost per sq. ft. FR-4 glass 4.1-4.8 +250 0.02-0.03 $2.5 GTEK 3.5-4.3 +250 0.012 $3.5 woven glass/ceramic loaded 3.38 +40 0.0027 $9.50 PTFE/ceramic (Teflon) 2.94 0 0.0012 $100.00 Copper Layers The conductive layer of a PCB is usually a sheet of copper which has been etched to form the circuit traces. The copper sheet s nominal thickness is designated by the weight of 1 square foot of copper of the nominal thickness. Copper Thicknesses Weight (oz) Thickness (in) Weight (oz) Thickness (in) 1/8 0.00017 4 0.0056 1/4 0.00035 5 0.0070 1/2 0.0007 6 0.0084 1 0.0014 7 0.0098 2 0.0028 10 0.0140 3 0.0042 14 0.0196 Microstrip Faster signals possible due to lower capacitive coupling, but greater radiated RF W W_width ____ T_thickness _____|____|______ Dielectic er h_height _________________ _________________ W = 6mil h = 4mil t = 1mil er= 4 Microstrip Z0 = (87/sqrt(er +1.4141))*ln(5.98*h/(0.8*W +t)) ...53 tpd = 85*sqrt(0.475*er +0.67) (ps/in) ...136ps/in 53.5ps/cm C0 = 0.67( er +1.414)/ln(5.98*h/(0.8*W+t) ) (pF/in) ...2.56pF/in .1pf/cm L0 = Z^2*C0 = 5071.23*ln(5.98*H/(0.8*W+t)) (pH/in) ...7185pH/in 2838pH/cm 250pH .1pF is 80ps delay in 15 stages 15*5.36 with rise fall 20ps freq = 30Ghz brickwill lowpass here RC = 50*.1pf = 5psec 0dB _______________________________________________ | # # # . . | | . . . # . . | | . . . # . | | . . . . . | -2dB |...............................................| | . . . . # . | | . . . . . | | . . . . . | | . . . . . | -4dB |_____________________________________#_________| 1GHz 10GHz 100GHz 2500pH 1pF is 840ps delay in 15 stages 15*53.6 with rise fall 170ps freq = 3Ghz brickwill lowpass here RC = 50*1pf = 50psec Frequency knee (Fknee) = 0.35/Tr (so if Tr is 1nS, Fknee is 350MHz) This is the frequency at which most energy is below Tr is the 10-90% edge rate of the signal Assignment: At what frequency can your thumb be used to determine which elements are lumped? Assume 150 ps/in W_width ____ T_thickness _____|____|______ Dielectic er h_height _________________ _________________ phase_velocity = v_p = c/sqrt(er) Microstrip Z0 = (60/sqrt(er))*ln( 8*h/w + W/4*h ) ...for W/h < 1 Z0 = (120*PI/(sqrt(er)*(W/h + 1.393 +0.667*ln(W/h+1.444)) ...for W/h > 1 tpd = 85*sqrt(0.475*er +0.67) (ps/in) C0 = 0.67( er +1.414)/ln(5.98*h/(0.8*W+t) ) (pF/in) L0 = Z^2*C0 = 5071.23*ln(5.98*H/(0.8*W+t)) (pH/in) 5/1/2003 Transmission Lines Class 6 16 Other Rules of Thumb Frequency knee (Fknee) = 0.35/Tr (so if Tr is 1nS, Fknee is 350MHz) This is the frequency at which most energy is below Tr is the 10-90% edge rate of the signal Assignment: At what frequency can your thumb be used to determine which elements are lumped? Assume 150 ps/in The 3-W Rulex will reduce the cross-talk flux by approximately 70%. (For a 98% reduction, change the 3 to 10.) Seperation between traces must be three times width of the traces, measured center-line to center-line. >2W W_width __ __ _____|__|______|__|______ 2*W Diff pair __ __ __ _____|__|______|__|__|__|___ 2*W W W W 2W http://www.davidcorbin.com/MMentality.htm I have been investigating whether there may be an addition detail which define the bandwidth of transmission line. My curiosity comes from the amount of magnetic cancelation that occurs in a transmission line. __\_ H | / | _______________|_____________ ()_____________\|/____________) R_cm --> I | V L_cm |_/_ \ L_uH =.002*L_cm*( ln(2*L_cm/R_cm) -.75 ) Rule of Thumb Single conductors inductance of 1uH/m. (r=0.5mm ) Apparently there is some industrial rule of thumb of 1uH/m for single conductors. A more exact equation is given above it. But in a transmission line, signal and its return current are right next to each other. So there is a fair amount of mutual inductance which make the effective inductance much smaller. ___\__ --> I ______|___/__|______________ 50 Ohm ->()___________\|/_____________|__/\ __ |_/____| _/___ \/ | ________\_______|_\___|_____ | <-()_____________________|_____|_ | <-- I |___\_| |______| __ | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | if L1 = L2 =M __ | () () | | | |__| |_____| then Lb=0 |__| The equations for the transmission line which include mutual inductance is given below. Transmission lines ZO = sqrt(Leff / C) Leff = L1 + L2 -2*M, k = sqrt((L1 + L2) / M) PCB => 0.6 < k < 1 When k is high effective inductance will decrease rapidly. Because of this high level of coupling for the spacing of the metal traces on the PCB, is there some small distance or unit_L where the transmission can be modeled more like a single L and C? <--unit_L---> _ _ _ --> I ______\_\___|_|__/_/_________ 50 Ohm ->()________\____|___/__________|__/\ __ \ \ | |/ / \/ | _________\_\|_|_/____________ | <-()___________\_|/_____________|_ | <-- I \_\| |______| signal coupling This led to investigating an array of critically damped tuned circuits as is shown below. This led to discovering some interesting facts. L1 L2 L3 L4 _ _ _ _ _ _ _ _ _ _ _ _ / \/ \/ \ ..\ / \/ \/ \ / \/ \/ \ / \/ \/ \ ___ | () () | : / | () () | | () () | | () () | | |__| |____:___| |___| |___| |__.... |___| _|_ : _|_ _|_ _|_ C1 ___ : C2 ___ C3 ___ C4 ___ _|_ :.\ _|_ _|_ _|_ /// / 50 Ohm /// /// /// To behave just like a transmission line, only one rule needs to apply. Each L with its C needs to have the same resonance impedance as the transmission line. But the sharing of the same resonance frequency does not appear to be a requirement. For the example above, all the inductors can be different. The requirement is that when L2 and C2 are their resonance frequency, that they both be 50 ohms. So all the tuned circuits may have their own unique resonance frequency. But each one will be critically damped since every capacitor resonants at 50 ohms and sees a 50 "real" impedance across it. If an array of critically damped tuned circuits is identical to a transmission line, then handling things like ESD structures, pads, bond wires, package leads, PCB traces , crossunders, cable terminals, etc.. could now only involve a tuning process. So thinking of bond wires as a LC tuned circuit, it should be possible to make some adjustments so that it resonants at say 50 ohms. And seeing what works should be possible to observe in the lab by monitoring reflections. Why can't we just tune everything in? _ _ _ _ _ _ _ _ _ _ _ _ / \/ \/ \ ..\ / \/ \/ \ / \/ \/ \ / \/ \/ \ ___ | () () | : / | () () | | () () | | () () | | |__| |____:___| |___| |___| |__.... |___| _|_ : _|_ _|_ _|_ ___ : ___ ___ ___ _|_ :.\ _|_ _|_ _|_ /// / /// /// /// ZO = sqrt(Leff / C) freq = 1/sqrt(L*C/2*PI) The modeling of a transmission line as an array of tuned circuits appears to work very well with one exception. A brickwall bandwidth has been added. If it is possible to model the unit_L as being effectively zero, then both the L and C in that unit_L become very small with a very large resonance frequency. Given the amount of data on the web, it may be possible to check this out. <--unit_L---> _ _ _ --> I ______\_\___|_|__/_/_________ 50 Ohm ->()________\____|___/__________|__/\ __ \ \ | |/ / \/ | _________\_\|_|_/____________ | <-()___________\_|/_____________|_ | <-- I \_\| |______| signal coupling Take a classical Microstrip with the following dimensions and equation given below. Notice that as a tranmission is divided up into smaller and smaller unit_L, the C L and prop delay get proportionally smaller while the total prop delay always remains the same. W_width = 6mil ____ T_thickness = 1mil(one ft^2 copper at 0.0014in thick weights 1 ounce) _____|____|______ Dielectic er = 4 h_height = 4mil _________________ _________________ unit_L unit_L unit_L Microstrip in cm mm Z0 =(87/sqrt(er +1.42))*ln(68*h/(0.8*W+t)) 53 53 53 C0_pF/in =0.67( er +1.414)/ln(5.98*h/(0.8*W+t)) 2.56pF 1.00pf 0.1pf L0_pH/in =Z^2*C0 = 5071.23*ln(5.98*H/(0.8*W+t)) 7185pH 2838pF 283pF tpd_ps/in =85*sqrt(0.475*er +0.67) 136ps 54.0ps 5.4ps Freq_GHz/in=1/sqrt(L*C/(2*PI)) 1.2GHz 3.0GHz 30GHz Trise_ps/in=simulated 170ps 20ps Simulating an array of tuned circuits using the L/unit_L and C/unit_L gives almost the exact behavour as the classic transmission equations given above. But there is the additional feature of resonance frequency. One interesting thing to notice is that the signal is passing through each tuned circuit at it's own resonance frequency. In fact, the prop delay always appears to equal the RC time constant of R being 50 ohms and C being the capacitance of unit_L. For the simulations, this is saying that things like bandwidth and rise and fall time are completely defined by the L and C of the transmission line. There exists a rule of thumb commonly used here. Rules of Thumb Frequency knee (Fknee) = 0.35/Tr (so if Tr is 1nS, Fknee is 350MHz) Tr is the 10-90% edge rate of the signal To see what impacts a resonance frequency would have a simulation can be done using L and C values for a unit_L of 1 cm and for 1 mm as well, <--unit_L---> _ _ _ --> I ______\_\___|_|__/_/_________ 50 Ohm ->()________\____|___/__________|__/\ __ \ \ | |/ / \/ | _________\_\|_|_/____________ | <-()___________\_|/_____________|_ | <-- I \_\| |______| signal coupling The 1 cm simulation may be stretching it, but the simulation results shown below shows what happens when a AC gain analysis is performed on the 1 cm and 1 mm array of tuned circuits. Notice the sharp brickwall roll off happening at the resonance frequency. A real PCB trace (off the web) is plotted on the same graph. Obvious unit_L is not 1 cm. PCB (48 in. Trace) stripline 7mil x 48" FR-4 losstan=0.02 0dB _______________________________________________ |cm mm mm mm . . | | cm . . mm . | | . . . . . | | . . . . . | -10dB |R.......cm.....................mm..............| | R . . . . . | | R . . . . . | | R cm . . mm . | | . R . . . . | -20dB |..........cm....................mm.............| | . R . . . . | | . R . . . | | . cm .R . . mm . | | . . R . . . | -30dB |___________cm______R_______________mm__________| 1GHz 10GHz 100GHz Frequency R = Real cm =Simulated_cm mm =Simulated_mm The 1mm simulations are much closer to reality. But it looks like bandwidth is really being defined the Dielectric losses in the material between the two metal traces. Attenuation dB/100ft 0dB _______________________________________________ |mm mm mm mm mm . . | |3 . . . .mm . | |2 3 . . mm . | | 2 3 . . . . | -20dB |1................3................mm...........| | . 2 . . . . | | 1 . . 3 . mm . | | . 2 . . . | | . 1 . . . . | -40dB |...................2.......3...................| | . . . . . | | . . 2 3 . . | | . 1 . . . | | . . . . . | -60dB |.................1........2....................| | . . . . . | | . . 1 . . . | | . . . 2 . . | | . . . . . | -80dB |.......................1.......................| | . . . . . | | . . . . . | | . . . 1 . . | | . . . . . | -100dB |...........................1...................| | . . . . . | | . . . . . | | . . . . . | | . . . . . | -120dB |_____________________________1_________________| 1GHz 10GHz 100GHz Frequency R = Real_Skin_Effect cm =Simulated_cm mm =Simulated_mm Dielectric constant becomes complex with losses PWB board manufacturers specify as Loss Tangent or Tan(sigma) e = e'-je" => Tan(sigma) = e"/e' real portion is the typical dielectric constant, imaginary portion represents the losses, or conductivity of dielectric real_dielectric = 2*pi*freq*e" PCB Material Dielectric Constant (er) Loss Tangent Air 1.0 0 PTFE (Teflon) 2.1-2.5 0.0002-0.002 BT Resin 2.9-3.9 0.003-0.012 Polyimide 2.8-3.5 0.004-0.02 Silica (Quartz) 3.8-4.2 0.0006-0.005 Polyimide/Glass 3.8-4.5 0.003-0.01 Epoxy/Glass (FR-4) 4.1-5.3 0.002-0.02 GETEK 3.8-3.9 0.010-0.015 (1MHz) ROGERS4350 Core 3.48 ± 0.05 0.004 @ 10G, 23°C ROGERS4430 Prepreg 3.48 ± 0.05 0.005 @ 10G, 23°C The equations for two wires in air are given above. Notice there is no dielectric term. But this then moves the problem to the skin effect. Skin Depth =sqrt(rho/(pi*freq*mu)) Skin effect confines 63% current to 1 skin depth total area of current flow approximated one skin depth Skin Depth In Copper _______________________________________________ | . . . . . | 9um S...............................................| | . . . . . | 8um |...............................................| | . . . . . | 7um |...............................................| | . . . . . | 6um |S..............................................| | . . . . . | 5um |...............................................| | . . . . . | 4um |...............................................| | S . . . . . | 3um |...............................................| | . . . . . | 2um |.......S.......................................| | . S . . . | 1um |..............................S........S.......| | . . . . . | 0um |_______________________________________________| 0GHz 1GHz 2GHz 3GHz 4GHz 5GHz To simulate these loses in the tuned circuit model, a resistor need to be shunted across each capacitor. There is only one materal which does not have this loss, and that is air. _____________________________ ->()____________________________) <- d_cm | D_cm Z_ohms sqrt(L/C) | _____________________________ ->()____________________________) L_cm Z_ohms = 276.0*log(2*D_cm/d_cm) C_pf/meter = 12.06/log(2*D_cm/d_cm) L_uH/meter = 0.920*log(2*D_cm/d_cm) The predicted skin effect losses are given below. The data only went out to 10GHz. Given that fiber optics is presently pushing the 40GHz limit, there may not be much data higher than this. The skin effect loss can be simulated by adding a resistors in series with all the inductors. PCB (48' Trace) stripline 7milx48" FR-4 losstan=0.02 0dB _______________________________________________ |mm mm mm mm . . | | R . . . mm . | | . R . . . . | | . R . . . | -10dB |.......................R.......mm..............| | . . . . . | | . . . . . | | . . . mm . | | . . . . . | -20dB |................................mm.............| | . . . . . | | . . . . . | | . . . . mm . | | . . . . . | -30dB |___________________________________mm__________| 1GHz 10GHz 100GHz Frequency R = Real_Skin_Effect cm =Simulated_cm mm =Simulated_mm Given the ever increasing speed for transistors, will we be running into a speed limit defined by geometry? Things like package leads and bondwires look like they can be modeled as tuned ciruits. We may be able to tune in everything to resonate at 50 ohms. The question is what speeds do they all resonate at? For now, speed seems to be dominated by dielectric loss. Remove that by going to air, and speed is now dominated by skin effect. If we find away around that, do we have still a future speed limit set on just the various levels of electrical and magnetic coupling between wires? http://www.rhophase.co.uk/semi.htm#Reformable Semi-Rigid Coaxial Cable PCB (48' Trace) stripline 7milx48" FR-4 losstan=0.02 _____________________________ ->()____________________________) <- d_cm | D_cm Z_ohms sqrt(L/C) | _____________________________ ->()____________________________) L_cm Z_ohms = 276.0*log(2*D_cm/d_cm) C_pf/meter = 12.06/log(2*D_cm/d_cm) L_uH/meter = 0.920*log(2*D_cm/d_cm) w0 = sqrt(L*C) = sqrt(dL*dC*X^2) = X*sqrt(dL*dC) velocity = (2*pi()/sqrt(dL*dC) W_width ____ T_thickness _____|____|______ Dielectic er h_height _________________ _________________ W = 6mil h = 4mil t = 1mil one ft^2 copper at 0.0014in thick weights 1 ounce er= 4 Microstrip Z0 = (87/sqrt(er +1.4141))*ln(5.98*h/(0.8*W +t)) 53 53 53 C0 = 0.67( er +1.414)/ln(5.98*h/(0.8*W+t) ) (pF/in) 2.56pF/in 1.00pf/cm 0.1pf/mm L0 = Z^2*C0 = 5071.23*ln(5.98*H/(0.8*W+t)) (pH/in) 7185pH/in 2838pF/cm 283pF/mm Freq = 1/sqrt(L*C/(2*PI)) (GHz/in) 1.2GHz/in 3.0GHz/cm 30GHz/mm tpd = 85*sqrt(0.475*er +0.67) (ps/in) 136ps/in 54.0ps/cm 5.4ps/mm Trise = simulated 170ps/cm 20ps/mm Diff pair __ __ _________ t __|__|__|__|______|_________ W S W ^ | __ __ h b |__| |__| t | W S W ________________V____________ ____________________________ Microstrip Stripline ZO Ohms In Microstrip = (60/sqrt(0.475*er + 0.67))*ln(4h/(0.67*(0.8*W +t)) ZO Stripline = (60/sqrt(er ))*ln(4b/(0.67*(0.8*W +t)) ZDIFF Ohms Microstrip = 2*ZO*(1 - 0.480*exp(-0.96*S/h) ) ZDIFF Ohms Stripline = 2*ZO*(1 - 0.374*exp(-2.90*S/h) )