ECE 546 – Jose Schutt‐Aine 1 ECE 546 Lecture ‐ 09 Lossy Transmission Lines Spring 2020 Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois [email protected]
ECE 546 – Jose Schutt‐Aine 1
ECE 546 Lecture ‐ 09
Lossy Transmission LinesSpring 2020
Jose E. Schutt-AineElectrical & Computer Engineering
University of [email protected]
ECE 546 – Jose Schutt‐Aine 2
RF SOURCE
Loss in Transmission Lines
Signal amplitude decreases with distance from the source.
ECE 546 – Jose Schutt‐Aine 3
Low Frequency High Frequency Very High Frequency
Skin Effect in Lines
ECE 546 – Jose Schutt‐Aine 4
r
H. A. Wheeler, "Formulas for the skin effect," Proc. IRE, vol. 30, pp. 412-424,1942
Skin Effect in Microstrip
ECE 546 – Jose Schutt‐Aine 5
/ /y jyoJ J e e
/ /
0 1y jy o
oJ wI J we e dy
j
oo o o
JE J E
oo
J DV E D
Current density varies as
Note that the phase of the current density varies as a function of y
The voltage measured over a section of conductor of length D is:
Skin Effect in Microstrip
ECE 546 – Jose Schutt‐Aine 6
11o
skino
jJ DV DZ j fI J w w
1
skin skinDR X fw
The skin effect impedance is
where
Skin Effect in Microstrip
is the bulk resistivity of the conductor
skin skin skinZ R jX
with
Skin effect has reactive (inductive) component
ECE 546 – Jose Schutt‐Aine 7
V I =RI+Lz t
I V= GV Cz t
L
z
C
I
V
+
-
G
R
Telegraphers Equation: Time Domain
Lossy Transmission Line
ECE 546 – Jose Schutt‐Aine 8
Vz
= (R+ jL)I = ZI
Iz
= (G+ jC)V = YV
L
z
C
I
V
+
-
G
R
Telegraphers Equation: Frequency Domain
Lossy Transmission Line
ECE 546 – Jose Schutt‐Aine 9
z
R, L, G, C,
forward wave
backward wave
Lossy Transmission Line
ECE 546 – Jose Schutt‐Aine 10
( ) z j zV z Ae e z j zBe e
1( ) z j z
o
I z Ae eZ
z j zBe e
j R j L G j C o
R j LZ
G j C
z
Zo Z1 Z2
Vsl
Lossy Transmission Line
ECE 546 – Jose Schutt‐Aine 11
‐ Signal attenuation
‐ Dispersion
‐ Rise time degradation-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Vol
ts
0 0.4 0.8 1.2 1.6 2Time (ns)
Far End Response
BoardVLSISubmicronDeep Submicron
( )( ) j R j L G j C
Effects of Losses
ECE 546 – Jose Schutt‐Aine 12
l
Zin
R
C
R : series resistance per unit lengthC : shunt capacitance per unit length
in
coth (1 )2Z =
(1 )2
Rl CRl jR
Rl C jR
inarg(Z ) 45 For very high ,
RC Transmission Line
ECE 546 – Jose Schutt‐Aine 13
l
Zin
R
C
2
2 << RCl
If then
in1 1Z + = +
2 2T
T
Rl RjCl jC
RT = Rl : total resistanceCT = Cl : total capacitance
RC Transmission Line
ECE 546 – Jose Schutt‐Aine 14
Line
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Vol
ts
0 0.4 0.8 1.2 1.6 2Time (ns)
Far End Response
BoardVLSISubmicronDeep Submicron
-0.1
0.175
0.45
0.725
1
0 0.4
Vol
ts
0.8 1.2 1.6 2Time (ns)
Near End Response
BoardVLSISubmicronDeep Submicron
Pulse Characteristics: rise time: 100 ps fall time: 100 ps pulse width: 4ns
Line Characteristics length : 3 mm near end termination: 50 far end termination 65
LogicthresholdLogic
threshold
RC Transmission Line
ECE 546 – Jose Schutt‐Aine 15
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0 0.02 0.04 0.06 0.08 0.1
Category 5/ 100-meter
Simulation
Measurement
S11
Mag
nitu
de
Frequency (GHz)
-50
-40
-30
-20
-10
0
10
20
30
0 0.02 0.04 0.06 0.08 0.1
Category 5/ 100-meter
Simulation
Measurement
S11
Phas
e (d
eg)
Frequency (GHz)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.02 0.04 0.06 0.08 0.1
Category 5/ 100-meter
Simulation
Measurement
S21
Mag
nitu
de
Frequency (GHz)-200
-150
-100
-50
0
50
100
150
200
0 0.02 0.04 0.06 0.08 0.1
Category 5/ 100-meter
Simulation
Measurement
S21
Phas
e (d
eg)
Frequency (GHz)
100m Category‐5 Cable
Long Cable
ECE 546 – Jose Schutt‐Aine 16
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.05 0.1 0.15 0.2
Category 5/ 1-meter
Simulation
Measurement
S11
Mag
nitu
de
Frequency (GHz)-200
-150
-100
-50
0
50
100
150
0 0.05 0.1 0.15 0.2
Category 5/ 1-meter
Simulation
Measurement
S11
Phas
e (d
eg)
Frequency (GHz)
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0 0.05 0.1 0.15 0.2
Category 5/ 1-meter
Simulation
Measurement
S21
mag
nitu
de
Frequency (GHz)-200
-150
-100
-50
0
50
100
150
200
0 0.05 0.1 0.15 0.2
Category 5/ 1-meter
Simulation
Measurement
S21
phas
e (d
eg)
Frequency (GHz)
Short Cable1m Category‐5 Cable
ECE 546 – Jose Schutt‐Aine 17
0
1
2
3
4
5
6
0 0.02 0.04 0.06 0.08 0.1
Category 5/ 100-meter
Res
ista
nce
(Ohm
s/m
)
Frequency (GHz)
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.02 0.04 0.06 0.08 0.1
Category 5/ 100-meter
Vel
ocity
Rat
io
Frequency (GHz)
Resistance and velocity
Category 5 Cable
ECE 546 – Jose Schutt‐Aine 18
( ) * psR f R f
*r ro rsv v v f
( ) ( )skin skinZ R f j L R j R L
Cable Loss Model
Category 5 100 0.724 -0.165 15.38 0.482 0.224-Ga 100 0.678 1.157 29.03 0.593 0.1Category 3 100 0.705 11.06 12.31 0.473 0.01 SMA 50 0.700 0.113 7.94 0.415 0.2
Zo vro vrs Rs p fmax() (m/ns) (m/ns-GHz) (/m-GHzp) (GHz)
ECE 546 – Jose Schutt‐Aine 19
Lossy TL Simulation
( , ) z j z z j zv t z IFFT Ae e Be e
1( , ) + z j z z j z
o
i t z IFFT Ae e Ae eZ
j R j L G j C o
R j LZ
G j C
• To simulate lossy TL with resistive loadsNo closed form solutionSimplest method is to use IFFT
21 2
( ) 1
sl
TVAe
2
2 lB e A 1
o
o
ZTZ Z
11
1
o
o
Z ZZ Z
22
2
= o
o
Z ZZ Z
For multiconductor transmission lines: see: J. E. Schutt‐Aine and R. Mittra, "Transient analysis of coupled lossytransmission lines with nonlinear terminations," IEEE Trans. Circuit Syst., vol. CAS‐36, pp. 959‐967, July 1989
ECE 546 – Jose Schutt‐Aine 20
cableZs = 50
Vs
open
near end far end
Time‐Domain Simulations
ECE 546 – Jose Schutt‐Aine 21
-0.5
0
0.5
1
1.5
2
0 500 1000 1500 2000
22GA/Cu/4-cond Near End
volts
Time (ns)
-0.5
0
0.5
1
1.5
2
2.5
3
0 500 1000 1500 2000
22GA/Cu/4-cond Far End
volts
Time (ns)
Pulse Propagation (CAT‐5)
ECE 546 – Jose Schutt‐Aine 22
-0.5
0
0.5
1
1.5
2
0 500 1000 1500 2000 2500 3000 3500
MP/CM Shielded Near Endvo
lts
Time (ns)
-0.5
0
0.5
1
1.5
0 500 1000 1500 2000 2500 3000 3500
MP/CM Shielded Far End
volts
Time (ns)
Pulse Propagation (MP/CM)
ECE 546 – Jose Schutt‐Aine 23
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 500 1000 1500 2000
RG174 Near End
volts
Time (ns)
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 500 1000 1500 2000
RG174
volts
Time (ns)
Pulse Propagation (RG174)