ece 451 coupled linesemlab.uiuc.edu/ece451/appnotes/coupledtl.pdf · 2015. 3. 3. · ece 451...
TRANSCRIPT
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ECE 451 – Jose Schutt‐Aine 1
ECE 451Coupled Lines
Jose E. Schutt-AineElectrical & Computer Engineering
University of [email protected]
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ECE 451 – Jose Schutt‐Aine 2
Signal Integrity
Crosstalk Dispersion Attenuation
Reflection Distortion Loss
Delta I Noise Ground Bounce Radiation
Sense Line
Drive Line
Drive Line
Crosstalk Noise
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ECE 451 – Jose Schutt‐Aine 3
TEM PROPAGATION
L
z
C
I
V
+
-
z
Zo Z1 Z2
Vs
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ECE 451 – Jose Schutt‐Aine 4
Telegrapher’s Equations
L: Inductance per unit length.
C: Capacitance per unit length.
L
z
C
I
V
+
-
V ILz t
I VCz t
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ECE 451 – Jose Schutt‐Aine 5
50 line 1
line 2
50
line 1
line 2
50 line 1
line 2
line 1
line 2
Crosstalk noise depends on termination
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ECE 451 – Jose Schutt‐Aine 6
50 line 1
line 2
50
line 1
line 2
line 1
line 2
tr = 1 ns tr = 7 ns
Crosstalk depends on signal rise time
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ECE 451 – Jose Schutt‐Aine 7
50 line 1
line 2
50
line 1
line 2
line 1
line 2
tr = 1 ns tr = 7 ns
Crosstalk depends on signal rise time
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ECE 451 – Jose Schutt‐Aine 8
tr = 1 ns tr = 7 ns
Crosstalk depends on signal rise time
50 line 1
line 2
line 1
line 2
line 1
line 2
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ECE 451 – Jose Schutt‐Aine 9
Coupled Transmission Lines
r
w s
h
Cs
V1
V2
I1
I2
Cs
Cm Lm
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ECE 451 – Jose Schutt‐Aine 10
1 1 211 12
V I IL Lz t t
1 1 211 12
I V VC Cz t t
2 1 221 22
I V VC Cz t t
Telegraphers Equations for Coupled Transmission Lines
Maxwellian Form
2 1 221 22
V I IL Lz t t
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ECE 451 – Jose Schutt‐Aine 11
1 1 2s m
V I IL Lz t t
2 1 2m s
V I IL Lz t t
1 1 1 2s m m
I V V VC C Cz t t t
2 1 2 2m m s
I V V VC C Cz t t t
Telegraphers Equations for Coupled Transmission Lines
Physical form
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ECE 451 – Jose Schutt‐Aine 12
Relations Between Physical and Maxwellian Parameters
(symmetric lines)
L11 = L22 = Ls
L12 = L21 = Lm
C11 = C22 = Cs+Cm
C12 = C21 = - Cm
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ECE 451 – Jose Schutt‐Aine 13
11 12e eV IL Lz t
11 12e eI IC Cz t
Add voltageand currentequations
Ze = L11 + L12C11 + C12
= Ls + LmCs
ve = 1
(L11 + L12 )(C11 + C12 )= 1
(Ls + Lm )Cs
Ve : Even mode voltage
Ie : Even mode current
Ve =12
V1 + V2( )
Ie =12
I1 + I2( )
Impedance
velocity
Even Mode
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ECE 451 – Jose Schutt‐Aine 14
Subtract voltageand currentequations
Vd : Odd mode voltage
Id : Odd mode current
Impedance
velocity
Odd Mode
11 12d dV IL Lz t
11 12d dI IC Cz t
d 1 21V2
V V
d 1 21I2
I I
11 12d
11 12 2Z = = s m
s m
L L L LC C C C
d11 12 11 12
1 1v = = ( )( ) ( )( 2 )s m s mL L C C L L C C
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ECE 451 – Jose Schutt‐Aine 15
+1 +1
EVEN
+1 -1
ODD
Mode Excitation
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ECE 451 – Jose Schutt‐Aine 16
PHYSICAL SIGNIFICANCE OF EVEN- ANDODD-MODE IMPEDANCES
* Ze and Zd are the wave resistance seen by the even and odd mode travelling signals respectively.
V1 = Z11 I1 + Z12 I2V2 = Z21 I1 + Z22 I2
* The impedance of each line is no longer describedby a single characteristic impedance; instead, we have
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ECE 451 – Jose Schutt‐Aine 17
Even-Mode Impedance: ZeImpedance seen by wave propagating through the coupled-line system when excitation is symmetric (1, 1).
Odd-Mode Impedance: ZdImpedance seen by wave propagating through the coupled-line system when excitation is anti-symmetric (1, -1).
Common-Mode Impedance: Zc = 0.5ZeImpedance seen by a pair of line and a common return by a common signal.
Differential Impedance: Zdiff = 2ZdImpedance seen across a pair of lines by differential mode signal.
Definitions
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ECE 451 – Jose Schutt‐Aine 18
EVEN AND ODD-MODE IMPEDANCES
Z11, Z22 : Self Impedances
Z12, Z21 : Mutual Impedances
For symmetrical lines,
Z11 = Z22 and Z12 = Z21
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ECE 451 – Jose Schutt‐Aine 19
EXAMPLE(Microstrip)
r = 4.3Zs = 56.4
Single LineDielectric height = 6 milsWidth = 8 mils
r = 4.3
Coupled LinesHeight = 6 milsWidth = 8 milsSpacing = 12 mils
Ze = 68.1 Zd = 40.8 Z11 = 54.4 Z12 = 13.6
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ECE 451 – Jose Schutt‐Aine 20
( ,0) ( ,0) ( ,0) ( ,0)e d e dtdr
e d e d
a t a t a t a tIZ Z Z Z
( ,0) ( ,0)tdr e dV a t a t da ( ,0) 0t
= 2
tdr e
tdr
V ZI
Even Mode
coaxial line
Zgline 1
line 2
Zg
stepgenerator
Vb
Vf IT+
-VT I2
I1
reference plane tied to ground
e g1Z = 2( ) Z1
e
e
e 2v =
e
l
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ECE 451 – Jose Schutt‐Aine 21
coaxial line
Zg
Zg
stepgenerator
Vb
Vf line 1
line 2
IT
VTI2 reference plane floating
+-
I1
tdr e d e dV = a (t,0)+a (t,0)- a (t,0)-a (t,0) f bV V
tdr ( ,0) ( ,0)I = e d
e d
a t a tZ Z
tdr
( ,0) ( ,0)I =- e de d
a t a tZ Z
ae(t,0) = 0, VtdrItdr
= 2Zd
dd
1 1 2l, v = 2 1
dd g
d
Z Z
Odd Mode
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ECE 451 – Jose Schutt‐Aine 22
EXTRACT INDUCTANCE AND CAPACITANCE COEFFICIENTS
s1L = + 2
e d
e d
Z Zv v
1s
e e
CZ v
m 1L = - 2
e d
e d
Z Zv v
m 1 1 1C = - 2 e e d dZ v Z v
d s eZ < Z < Z
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ECE 451 – Jose Schutt‐Aine 23
20
40
60
80
100
120
4 6 8 10 12 14 16 18Spacing (mils)
Even-Mode Impedanceh=3 milsh=5 milsh=7 mils
h=10 milsh=14 mils
h=21 mils
Ze(
)
Measured even-mode impedance
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ECE 451 – Jose Schutt‐Aine 24
20
25
30
35
40
45
50
4 6 8 10 12 14 16 18Spacing (mils)
Odd-Mode Impedanceh=3 mils
h=5 mils
h=7 mils
h=10 mils
h=14 mils
h=21 mils
Zd
(
)
Measured odd-mode impedance
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ECE 451 – Jose Schutt‐Aine 25
0.158
0.16
0.162
0.164
0.166
0.168
0.17
4 6 8 10 12 14 16 18Spacing (mils)
Even-Mode velocityh=3 mils
h=5 mils
h=7 mils
h=10 mils
h=14 mils
h=21 mils
v e(m
/ns)
Measured even-mode velocity
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ECE 451 – Jose Schutt‐Aine 26
0.175
0.18
0.185
0.19
0.195
0.2
0.205
0.21
4 6 8 10 12 14 16 18Spacing (mils)
Odd-Mode Velocity
h=3 milsh=5 mils
h=7 mils
h=10 milsh=14 milsh=21 mils
vd(
m/n
s)
Measured odd-mode velocity
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ECE 451 – Jose Schutt‐Aine 27
0
50
100
150
200
250
4 6 8 10 12 14 16 18Spacing (mils)
Mutual Inductance h=3 milsh=5 mils
h=7 mils
h=10 mils
h=14 mils
h=21 mils
Lm
(nH
/m)
Measured mutual inductance
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ECE 451 – Jose Schutt‐Aine 28
10
15
20
25
30
35
40
4 6 8 10 12 14 16 18Spacing (mils)
Mutual Capacitance h=3 milsh=5 mils
h=7 milsh=10 mils
h=14 mils
h=21 mils
Cm
(pF/
m)
Measured mutual capacitance
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ECE 451 – Jose Schutt‐Aine 29
40
50
60
70
80
90
100
110
10 20 30 40 50
Typical Even & Odd Mode Impedances
ZevenZodd
Zeve
n, Z
odd
(Ohm
s)
Distance (mils)
Even & Odd Mode Impedances
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ECE 451 – Jose Schutt‐Aine 30
Microstrip : Inhomogeneous structure, odd and even-mode velocities must have different values.
Stripline : Homogeneous configuration, odd and even-mode velocities have approximately the same values.
Modal Velocities in Stripline and Microstrip
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ECE 451 – Jose Schutt‐Aine 31
Microstrip vs Stripline
Microstrip (h =8 mils)w = 8 milsr = 4.32Ls = 377 nH/mCs = 82 pF/mLm = 131 nH/mCm = 23 pF/mve = 0.155 m/nsvd = 0.178 m/ns
Stripline (h =16 mils)w = 8 milsr = 4.32Ls = 466 nH/mCs = 86 pF/mLm = 109 nH/mCm = 26 pF/mve = 0.142 m/nsvd = 0.142 m/ns
50
50
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ECE 451 – Jose Schutt‐Aine 32
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Volts
microstrip
C
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Vol
ts
stripline
C
50
50
Microstrip vs Stripline
Sense line response at near end
Probe
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ECE 451 – Jose Schutt‐Aine 33
1( ) e e d dj z j z j z j zv v v v
e e d d
even odd
V z A e B e A e B e
2 ( ) e e d dj z j z j z j zv v v v
e e d d
even odd
V z A e B e A e B e
Zs1
Zs2 ZL2
ZL1line 1
line 2
General Solution for Voltages
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ECE 451 – Jose Schutt‐Aine 34
11 1( ) e e d d
j z j z j z j zv v v v
e e d de d
even odd
I z A e B e A e B eZ Z
21 1( ) e e d d
j z j z j z j zv v v v
e e d de d
even odd
I z A e B e A e B eZ Z
Zs1
Zs2 ZL2
ZL1line 1
line 2
General Solution for Currents
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ECE 451 – Jose Schutt‐Aine 35
odd
even
First reflection
even
even
odd
odd
Second reflection
odd
odd
odd
oddeven
even
even
even
Zs1
Zs2 ZL2
ZL1line 1
line 2
Coupling of Modes (asymmetric load)
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ECE 451 – Jose Schutt‐Aine 36
Coupling of Modes(symmetric load)
Zs
Zs ZL
ZLline 1
line 2
odd
even
First reflection
even
odd
Second reflection
odd
even
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ECE 451 – Jose Schutt‐Aine 37
-0.2
0
0.2
0.4
0.6
0.8
1
Vol
ts
0 5 10 15 20 25 30
Time (ns)
Drive Line at Near End
35 40
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Vol
ts
0 5 10 15 20 25 30
Time (ns)
Sense Line at Near End
35 40
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ECE 451 – Jose Schutt‐Aine 38
1 2 3
31 1 211 12 13
VI V VC C Cz t t t
32 1 221 22 23
VI V VC C Cz t t t
3 31 231 32 33
I VV VC C Cz t t t
31 1 211 12 13
IV I IL L Lz t t t
32 1 221 22 23
IV I IL L Lz t t t
3 31 231 32 33
V II IL L Lz t t t
Three‐Line Microstrip
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ECE 451 – Jose Schutt‐Aine 39
11 13( )V IL Lz t
11 13( )I VC Cz t
Subtract (1c) from (1a) and (2c) from (2a), we get
This defines the Alpha mode with:
1 3V V V 1 3I I I and
The wave impedance of that mode is:
11 13
11 13
L LZC C
and the velocity is 11 13 11 13
1uL L C C
Three‐Line – Alpha Mode
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ECE 451 – Jose Schutt‐Aine 40
In order to determine the next mode, assume that
1 2 3V V V V
1 2 3I I I I
31 211 21 31 12 22 32 13 23 33V II IL L L L L L L L Lz t t t
31 211 21 31 12 22 32 13 23 33I VV VC C C C C C C C Cz t t t
By reciprocity L32 = L23, L21 = L12, L13 = L31
By symmetry, L12 = L23
Also by approximation, L22 L11, L11+L13 L11
Three‐Line – Modal Decomposition
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ECE 451 – Jose Schutt‐Aine 41
31 211 12 13 12 112V II IL L L L Lz t t t
In order to balance the right-hand side into I, we need to have
12 11 2 11 12 13 2 11 12 22L L I L L L I L L I 2
12 122L L
or 2
Therefore the other two modes are defined as
The Beta mode with
Three‐Line – Modal Decomposition
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ECE 451 – Jose Schutt‐Aine 42
The Beta mode with
1 2 32V V V V
1 2 32I I I I
The characteristic impedance of the Beta mode is:
11 12 13
11 12 13
22
L L LZC C C
and propagation velocity of the Beta mode is
11 12 13 11 12 131
2 2u
L L L C C C
Three‐Line – Beta Mode
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ECE 451 – Jose Schutt‐Aine 43
The Delta mode is defined such that
1 2 32V V V V
1 2 32I I I I
The characteristic impedance of the Delta mode is
11 12 13
11 12 13
22
L L LZC C C
The propagation velocity of the Delta mode is:
11 12 13 11 12 131
2 2u
L L L C C C
Three‐Line – Delta Mode
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ECE 451 – Jose Schutt‐Aine 44
1 0 1
1 2 1
1 2 1
E
1 2 3
Alpha modeBeta mode*
Delta mode*
Symmetric 3‐Line Microstrip
In summary: we have 3 modes for the 3-line system
*neglecting coupling between nonadjacent lines
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ECE 451 – Jose Schutt‐Aine 45
1 2 3
r = 4.3
113 17 5( / ) 16 53 16
5 17 113C pF m
346 162 67( / ) 152 683 152
67 162 346L nH m
0.45 0.12 0.450.5 0 0.50.45 0.87 0.45
E
0.44 0.49 0.440.5 0 0.50.10 0.88 0.10
H
Coplanar Waveguide
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ECE 451 – Jose Schutt‐Aine 46
73 0 0( ) 0 48 0
0 0 94mZ
56 23 8( ) 22 119 22
8 23 56cZ
0.15 0 0( / ) 0 0.17 0
0 0 0.18pv m ns
1 2 3
r = 4.3
Coplanar Waveguide
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ECE 451 – Jose Schutt‐Aine 47
WS' S'WS
rh
2Sk
S W
( ) : Complete Elliptic Integral of the first kindK k
'( ) ( ')K k K k
2 1/ 2' (1 )k k
30 '( ) (ohm)( )1
2
ocpr
K kZK k
1/ 22
1cp rv c
Coplanar Waveguide
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ECE 451 – Jose Schutt‐Aine 48
S WW
rh
120 '( ) (ohm)( )1
2
ocsr
K kZK k
Coplanar Strips
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ECE 451 – Jose Schutt‐Aine 49
Characteristic Microstrip Coplanar Wguide Coplanar strips
eff* ~6.5 ~5 ~5
Power handling High Medium Medium
Radiation loss Low Medium Medium
Unloaded Q High Medium Low or High
Dispersion Small Medium Medium
Mounting (shunt) Hard Easy Easy
Mounting (series) Easy Easy Easy
* Assuming r=10 and h=0.025 inch
Qualitative Comparison
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ECE 451 – Jose Schutt‐Aine 50
2p
h
w
dielectric
ground
signal strip
V Transmission Line
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ECE 451 – Jose Schutt‐Aine 51
0
50
100
150
200
250
0 0.1 0.2 0.3 0.4 0.5 0.6w/h
CHARACTERISTIC IMPEDANCE
30º37.5º45º52.5º
60ºMicrostrip
0.7 0.8 0.9 1
Zo (o
hms)
Calculated values of the characteristic impedance for a single-line v-strip structure as a function of width-to-height ratio w/h. The relative dielectric constant is r = 2.55.
V‐Line Characteristic Impedance
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ECE 451 – Jose Schutt‐Aine 52
1.8
1.85
1.9
1.95
2
2.05
2.1
2.15
2.2
0 0.1 0.2 0.3 0.4 0.5 0.6
w/h
EFFECTIVE PERMITTIVITY
30º
37.5º
45º
52.5º
60º
Microstrip
0.7 0.8 0.9 1
Effe
ctiv
e R
elat
ive
Die
lect
ric C
onst
ant
Calculated values of the effective relative dielectric constant for a single-line v-strip structure as a function of width-to-height ratio w/h. The relative dielectric constant is r = 2.55
V‐Line – Effective Permittivity
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ECE 451 – Jose Schutt‐Aine 53
h
y
x
Region 2
Region 3
Region 4
Region 6
Region 1
Region 5
2pw
dielectricground surface
signal strip
s
Three‐Line – V Transmission Line
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ECE 451 – Jose Schutt‐Aine 54
74.00 -0.97 -0.23C (pF/m) = -0.97 74.07 -0.97
-0.23 -0.97 74.00
425.84 20.35 7.00L (nH/m) = 20.36 422.85 20.36
7.00 20.35 425.84
52.49 -5.90 -0.57C (pF/m) = -5.90 53.27 -5.90
-0.57 -5.90 52.49
609.74 113.46 41.79L (nH/m) = 113.54 607.67 113.54
41.79 113.46 609.74
Microstrip V-line
Comparison of the inductance and capacitance matricesbetween a three-line v-line and microstrip structures. The parameters are p/h = 0.8 mils, w/h = 0.6 and r = 4.0.
h
y
x
Region 2
Region 3
Region 4
Region 6
Region 1
Region 5
2pw
dielectricground surface
signal strip
s1 2 3
V‐Line and Microstrip
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ECE 451 – Jose Schutt‐Aine 55
0
50
100
150
200
250
300
350
0 0.2 0.4 0.6 0.8 1 1.2s/h
Mutual Inductance
V-linemicrostrip
Lm
(nH
/m)
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1 1.2s/h
Mutual Capacitance
V-linemicrostrip
C m(p
F/m
)
Plot of mutual inductance (top) and mutual capacitance (bottom) versus spacing-to-height ratiofor v-line and microstrip configurations. The parameters are w/h = 0.24, r = 4.0.
V‐Line: Coupling Coefficients
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ECE 451 – Jose Schutt‐Aine 56
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1 1.2s/h
Coupling Coefficient
V-linemicrostrip
Kv
Plot of the coupling coefficient versus spacing-to-height ratio for v-line and microstrip configurations. The parameters are w/h = 0.24, r = 4.0.
V‐Line vs Microstrip: Coupling Coefficients
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ECE 451 – Jose Schutt‐Aine 57
0.5
0.6
0.7
0.8
0.9
1
1 3 5 7 9 11 13 15 17
microstrip
V-60
V-30
Frequency (GHz)
Linea
r Atte
nua ti
on
Propagation Function
2p
h
w
dielectric
ground
signal strip
Advantages of V Line* Higher bandwidth
* Lower crosstalk
* Better transition
ground reference
ground reference
dielectr
ic
substra
te
signal strip
Advantages of V‐Line
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ECE 451 – Jose Schutt‐Aine 58
-8
-7
-6
-5
-4
-3
-2
-1
0
0 5 10 15 20 25
Insertion Loss
VlineMicrostrip20
*log1
0*|S
21|
Frequency (GHz)
V‐Line vs Microstrip: Insertion Loss