high-speed serial interface circuits and systemstera.yonsei.ac.kr/class/2020_2_2/lecture/lecture...
TRANSCRIPT
High-Speed Serial Interface Circuits and Systems
Woo-Young ChoiDept. of Electrical and Electronic Engineering
Yonsei University
Lecture 6: Channels (2)
W.-Y. Choi2High-Speed Serial Interface (2020/2)
Channels (2)
- Channels have frequency-dependent loss
- Channels are transmission lines (R,G,C,L)2
2 ( )( )d V R j L G j C Vdz
w w= + +
2
2 ( )( )d I R j L G j C Idz
w w= + +
Voltage, current waves
Signal integrity degradation due to reflection, crosstalk
W.-Y. Choi3High-Speed Serial Interface (2020/2)
Channels (2)
- S-parameters for channel characterization
-Time-domain analysis?
Step response with TDR (Time-Domain Reflectometer)
W.-Y. Choi4High-Speed Serial Interface (2020/2)
Channels (2)
TDR
– Pulse generator produces step input with very large period.
– Scope measures the pulse shape
PulseGenerator
Scope
Channel Zo
Z L
Boundary#1
Boundary#2
W.-Y. Choi5High-Speed Serial Interface (2020/2)
Channels (2)
– Reflection is generated at boundaries if impedance is discontinuous
– Traveling time for each reflected wave can be different– Channel characteristics can be determined by measuring
reflected waves
Channel2 Z2 Channel3 Z3Channel1 Z1
Z L
Input wave
Reflection1
Reflection2
Reflection3
t1 t2 t3
2 x t12 x (t1 + t2)
2 x (t1 + t2 + t3)
Boundary#1
Boundary#2
Boundary#3
GIF clip: http://en.wikipedia.org/wiki/File:Partial_transmittance.gif
W.-Y. Choi6High-Speed Serial Interface (2020/2)
Channels (2)
V0 ~ R0
RGi) At+= 0t
RG
R0 RL+-
V0
t=0
L
00
01 V
RRRV
G+=+
z
V
Initially, the voltage wave “sees” only R0 => Voltage divider
W.-Y. Choi7High-Speed Serial Interface (2020/2)
Channels (2)
V0
ii) AtuLt = =-
1V
iii) AtuLt 2
= ,12-+ G= VV G
iv) AtuLt 3
= .....,22+- G= VV L
( )total tV =¥ =
R0 RL+-
t=0
L
RG
No TL effect:All the wave characteristics have died out!
1 1 2 2 ...V V V V+ - + -+ + + +
( )2 2 2 3 21 1 ...L L G L G L G L GV += +G +G G +G G +G G +G G +
01 0
0
1 1 1 1
L L
L G G L G
RV VR R
+ æ ö æ ö æ ö+ G +G= =ç ÷ ç ÷ ç ÷-G G + -G Gè ø è ø è ø
2 2 2 21 [(1 ...) (1 ...)]L G L G L L G L GV += +G G +G G + +G +G G +G G +
0L
L G
R VR R
æ ö= ç ÷+è ø
,1+G VL
0
0
RRRR
L
L
+-
=GL
0
0
RRRR
G
GG +
-=G
W.-Y. Choi8High-Speed Serial Interface (2020/2)
Channels (2)
R0 RL+-
V0
t=0
L
Example) 00 2,3 RRRR GL ==RG
31
3 ,
21
42
0
0
0
0
0
0
0
0 ==+-
=G==+-
=GRR
RRRR
RR
RRRR
G
GG
L
LL
0)( 53VV ttot =¥=
W.-Y. Choi9High-Speed Serial Interface (2020/2)
Channels (2)
R0+-
V0
t=0
L
3R0
2R0
1 1, 2 3L GG = G =
( ) ( ) ' '20' 1
2z zL
LIV z Z Z e eg g-é ù= + + Gë û
( ) ( ) ' '20
0
' 12
z zLL
II z Z Z e eZ
g g-é ù= + -Gë û
( In Lecture 5) current
voltage
W.-Y. Choi10High-Speed Serial Interface (2020/2)
Channels (2)
Z0(=R0)+-
V0
t=0
L
LR0 +
VL--
0
0
LL
L
Z ZZ Z
-G =
+
è only for sinusoidal signals
At+= 0t 1V
+ =
At the inductor,1 1LV V V+ -= +
0 12L LV i R V ++ =
LZ j Lw=
?LZ =
( )Remember ( ) dI tV t Ldt
=
1 1
0 0LV ViR R
+ -
= -
LL
diV Ldt
=0 0
LL
diL R i Vdt
+ =
00 0
0 0
12
R V VR R
=+
0V=
0 0LL
R Vdi idt L L
+ =
(Does not change because no reflection at generator)
W.-Y. Choi11High-Speed Serial Interface (2020/2)
Channels (2)
0 0LL
R Vdi idt L L
+ =
0( )0
0
1Rt TL
LVi eR
- -æ ö= -ç ÷
è ø0( )
0
Rt TLV e
- -=
Z0(=R0)+-
V0
t=0
L
LR0 +
VL--
1V- = 1LV V +-
0( )
01( )2
Rt TLV e
- -= -
(for t , otherwise 0)LLt T iu
³ = = =
LL
diV Ldt
=
We can solve above differential equation and show
1 1LV V V+ -= +
1 1
0 0LV ViR R
+ -
= -
LL
diV Ldt
=
W.-Y. Choi12High-Speed Serial Interface (2020/2)
Channels (2)
Z0(=R0)+-
V0
t=0
L
LR0 +
VL--
When V+ reaches the inductor initially,
Eventually, the inductor becomes short
In-between, inductor voltage changesexponentially with the characteristic time constant R0/L
( )LV t =
( )LV t T= =
( )LV t = ¥ =
2V +0V=
0
0( )
0
Rt TLV e
- -
it sees open circuit
1 ( )V t-1( )LV t V += -
0( )
01( )2
Rt TLV e
- -= - 1( , )V z t
W.-Y. Choi13High-Speed Serial Interface (2020/2)
Channels (2)
Z0(=R0)+-
V0
t=0
L
LR0 +
VL--
current
0
0
VR
0
02VR
voltage
0V
0
2V
W.-Y. Choi14High-Speed Serial Interface (2020/2)
Channels (2)
R0+-
V0
t=0
L
CR0 +
Vc--
Ic dttdVCtI )()( =
+V--
I initially short
eventually open
0
0
0
( )
0
( )0
0
( )
1 1 0
( ) 1
( )
1( ) ( )2
t TR C
L
t TR C
L
t TR C
L
V t V e
Vi t eR
V t V t V V e
--
--
--
- +
æ ö= -ç ÷ç ÷
è ø
=
æ ö= - = -ç ÷ç ÷
è ø
0
( )
0( ) 1t TR C
LV t V e-
-æ ö= -ç ÷ç ÷
è ø
0
( )0
0
( )t TR C
LVi t eR
--
=
0
( )
1 1 01( ) ( )2
t TR C
LV t V t V V e-
-- +
æ ö= - = -ç ÷ç ÷
è ø
W.-Y. Choi15High-Speed Serial Interface (2020/2)
Channels (2)
R0+-
V0
t=0
L
CR0 +
Vc--
Ic
current
1
0
2VR
+
1
0
VR
+
voltage
1V+
W.-Y. Choi16High-Speed Serial Interface (2020/2)
Channels (2)
– TDR can determine characteristic impedance of each segment of channel
– Recent oscilloscope software capable of automatic calculation
W.-Y. Choi17High-Speed Serial Interface (2020/2)
Channels (2)
Homework (Due: 10/19 2pm)Determine TDR waveforms for following channels.