Transcript EE464 Lecture 1 Introduction to Digital Systems

CSE464
Coupling Calculations via Odd/Even Modes
Spring, 2009
David M. Zar
(Based on notes by
Fred U. Rosenberger)
[email protected]
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Coupled Lines
1
I1
2
Here are two
coupled lines
I2
VD  (V1  V2 )/2
I D  ( I1  I 2 )/2 ( Odd, Difference)
VC  (V1  V2 )/2
I C  ( I1  I 2 )/2 ( Even,Common)
VC  VCf  VCr
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VD  VDf  VDr
Coupled Lines
• Even-mode impedance, ZOE
– impedance seen on each line by a common-mode signal
• Odd-mode impedance, ZOO
– impedance seen on each line by differential mode signal
• Differential impedance, ZOD = 2ZOO
– impedance seen across a pair of lines by differential mode signal
• Common-mode impedance, ZOC = 0.5ZOE
– impedance seen between a pair of lines and a common return by a
common-mode signal.
Z OE
 LM
 
 C  Cd
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


1
2
Z OO
 LM
 
 C  Cd



1
2
C = total line
Capacitance (line to
GND + Cd)
Cd= line to line
capacitance
Coupled Lines
Line 1
Line 2
Matched termination
( No reflection )
R1  ZOE
 Z Z

R2  2 OO OE 
 Z OE  Z OO 
2 VD 
Line 1
2 R1  R2
R1
Line 2
Coupled line equivalent circuit
( T-line only, no external components )
2*VC
Equivalent circuit at sending end
VC  VC 0r ;
VD  VD0r
Equivalent circuit at receiving end
VC  VClf ;
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VD  VDlf
2*VC
Coupled Lines
Matched termination (Wye)
( No reflection )
R3  Z OO
 Z  Z OO 
R4   OE

2


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Line 1
Line 2
R3
R3
R4
Coupled Lines
Procedure: ( AssumingV1  V2  0 t  0 )
1.Solve for V1 & V2 at sending end ( V10 & V20 )
2. Find VD0 f & VC 0 f at sendingend ( VD0r  VC 0r  0 )
3. Find V1 & V2 at receivingend
 l 
 l 
l
at t 
( V1l   , V2l   )
v
v
v
4. Find VD & VC at receivingend
5. Find VDr & VCr at receivingend
VDlr  VDl  VDlf ; VClr  VCl  VClf
 2l  
 2l  
 , V20 
 fromEQ circuit
6. Find V10 
 v 
 v 
7. Continueuntilexhaustionor small changes
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Backward Crosstalk Next
Boxes represent transmission line impedances, Resistor symbols are physical resistors. R t is an external
termination resistor. V20 is the voltage coupled into Line 2 at x=0. Vc and Vd are zero in this case since the
far end is matched. The voltage on line 2, and the coupling coefficient is given by the voltage divider.
2 VD 
Line 1
x=l
VS
1
2 R1  R2
R1
Line 2
V20
Rt
2*VC
2*VC
2
x=0
1v
VS
0v
t=0
Tr
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Rt
Line 2 at x  0 : V20  VS 
R1 // Rt
R2  R1 // Rt
krx 
R1 // Rt
R2  R1 // Rt
(Dally Eq 6 - 16)
Forward Crosstalk Next
For inhomogeneous media,same procedureappliesbut now vC  vD .
T heydo not arriveat same timeso calculation is a littlemoretedious.
Matched
Termination
x=l
VClf
0.5v
1
2
x=0
1v
0.5v
VDlf
VS
l/vC
0v
l/vD
t=0
Tr
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Forward Crosstalk Next (cont.)
V2lfx forwardcrosstalk
V2l  VCl  VDl
 1
1
l  
 vD vC
for
l
 Tr
vC
l
vC
OR
l
vD
l
 Tr
vD
for
 1
dV
1  VElf
l  v  1 dVS 1  vD 
V2l  l    
 1  D  
 1    t x  S
vD  vC  2 dt
2  vC 
dt
 vD vC  Tr
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
  Tr

 1
1 
l     Tr
 vC vD 
&
&
vD  vC
vC  vD
1 v 
(Dally,Eq 6 - 18) k fx  1  D 
2  vC 
Configurations
• vO > vE
air
dielectric
– Microstrip
• vO < vE
– 300 Ohm TV or Twisted
Pair or flat cable (ground
alternate conductors,
may have gnd plane)
Conductors
Flat cable
dielectric
• vO = vE
– Ansley “Black Magic” flat
cable. Note wide
ground, narrow signal to
reduce backward
crosstalk
– PC board stripline
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ground
signal
r1
r2
Multiple Aggressors
• We calculate for single aggressor, use superposition
for multiple aggressor lines
• Typical coupling is a little more than twice that for
single agressor line
Major Crosstalk Contributors
Victim
Small Contribution
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What Else?
• Simulation (SPICE) is widely used in
evaluating/calculating transmission line waveforms
– Can easily deal with lossy lines, non-linear termination, etc
– Time consuming to setup and evaluate
– Has replaced measurement for the most part (still want to
get some confirmation from measurement (reality))
– You must know what questions to ask
– If you don’t simulate critical cases, don’t learn much
• Parameters are obtained by Field Solver programs
– Maxwell, Mentor, … ($50K or so)
– Describe geometry, get L, C, etc
– 2D (uniform cross-section) and 3D
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Crosstalk Wrapup
• Non-Linear terminations: Use Bergeron method (covered later)
• Backward crosstalk lasts for round-trip propagation delay and
amplitude is independent of coupled length (for tr < round-trip
delay)
• Forward crosstalk is proportional to length, zero for
homogeneous dielectric, width equal to Tr and amplitude
inversely proportional to Tr. Typically small for moderate length
with inhomogeneous dielectric.
• Both forward and backward crosstalk will be reflected from nonmatched terminations.
• Separate signals, place signals close to ground plane, use
differential signals, …
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Need to Mention Limits
• We have not considered radiation or energy loss.
• When distance between conductor and return is small with
respect to rise/fall time our approximation is good.
• When rise/fall time becomes comparable to signal-return
spacing the system acts as antenna radiating energy.
– Our model is no longer valid
• Loss of signal amplitude or energy
• EMI (electromagnetic interference) which is frowned on by FCC and
any one with radio or tv receivers.
– Not usually a problem of coupling to digital signals, energy is too
small.
– More complicated problem than digital crosstalk and not dealt with
in CSE464. However, keep lateral dimensions and spacings small!
– Electromagnetic fields and antennas
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