======================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 1.42.1
silicone rubber 2.083.5
polyvinylchoride 38

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*( (1sigma^2)/(1+sigma^2) )
( 120/e^.5)*ln( 2*vu*( (1sigma^2)/(1+sigma^2) )
vu = h/d
sigma = h/D
Beadsdielectric e_1
_________________
_________________
   
____________
_________________
   
____________
__________________
><<>
w s
For lines A. and B., if insulating beads are used at frequent intervalscall
new characteristic mi pedance Z0
Zo= Zo/( (1+[(e1/e) 1)*sqrt( W/S) )
Open 2wire 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)/ (10.405 *rho^4)
B= (1+0.163*rho^8)/ (10.163 *rho^8)
C~ (1+0.067 *rho^12)/(lO.067 *rho^12)
Balanced 4wire <d>
__ __
/ +\ / o\
\__/ \__/ ^
\ / 
\_/ D2
__ / __ 
/ o\/ \/ +\ V
\__/ \__/
<D1>
d<
__ __ 
/ +\ / +\ V
\__/ \__/
<D>
For d << D
Z0= (173/e^0.5) log10(D/(0.933*d))
FR4 fiberglass resin most common material
Material r CTE LossTangent Cost
ppm/C per sq. ft.
FR4 glass 4.14.8 +250 0.020.03 $2.5
GTEK 3.54.3 +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 sheets 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
For pcboard 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 pcboardtrace 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 highspeed systems,
FR4stripline 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 FR4.
Material er CTEppm/oC Loss Tangent ( ) Cost per sq. ft.
FR4 glass 4.14.8 +250 0.020.03 $2.5
GTEK 3.54.3 +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 1090% 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 1090% 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 3W Rulex
will reduce the crosstalk 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 centerline to centerline. >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 1090% 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" FR4 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) 2.12.5 0.00020.002
BT Resin 2.93.9 0.0030.012
Polyimide 2.83.5 0.0040.02
Silica (Quartz) 3.84.2 0.00060.005
Polyimide/Glass 3.84.5 0.0030.01
Epoxy/Glass (FR4) 4.15.3 0.0020.02
GETEK 3.83.9 0.0100.015 (1MHz)
ROGERS4350 Core 3.48 0.05 0.004 @ 10G, 23C
ROGERS4430 Prepreg 3.48 0.05 0.005 @ 10G, 23C
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" FR4 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 SemiRigid Coaxial Cable
PCB (48' Trace) stripline 7milx48" FR4 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) )