Upload
lydia-charles
View
270
Download
5
Embed Size (px)
Citation preview
中華大學 通訊系 1
Transmission Line Effects in High Speed Digital PCBs
中華大學 通訊系 田慶誠[email protected] 5186030
中華大學 通訊系 4
Lumped v.s. Distributed Circuit
Definitions of lumped element
(1) Input current amplitude = Output current amplitude
(2) Input current phase = Output current phase
中華大學 通訊系 8
Digital Interconnection Rules
數位工程師的 Rule of thumb Signal path can be treated as:
A lumped element, if Tr > 6 Td (Short ckt, series resistor, shunt capacitor)
A lumped model, if 2.5 < Tr/Td < 6 (Series inductor with shunt capacitor)
A distributed model, if Tr < 2.5 Td (Transmission Line or multi-section LC model)
中華大學 通訊系 12
Example of High-Speed IC Interconnection
CMOS On-chip 1mm interconnection Vp= 0.5c = 150mm/ns Td=1mm/Vp = 0.067ns Rule of Thumb only worked as:
Tr > 6Td= 0.04ns FCLK < (8Tr) -1 = 3GHz
Inductance extraction now is very important !!
中華大學 通訊系 13
Example of High-Speed IC Interconnection
10mm interconnection between IC’s Vp= 0.6c =180mm/ns Td= 10mm/Vp = 0.056ns Rule of Thumb only worked as:
Tr > 6Td= 0.33ns FCLK < (8Tr) -1 = 375 MHz
Distributed analysis now is very important !!
中華大學 通訊系 16
Period v.s. Travel Time
Period T = 1/freq Td= L/(freq*) VBB’(t) is different from VAA’(t)
中華大學 通訊系 17
Period v.s. Travel Time
類比工程師的 Rule of thumb Signal path can be treated as:
A lumped element, if Td < T/100 (Short ckt, series resistor, shunt capacitor)
A lumped model, if T/100 < Td < T/20 (Series inductor with shunt capacitor)
A distributed model, if Td > T/20 (Transmission Line or multi-section LC model)
中華大學 通訊系 18
Trace v.s. Wavelength
類比工程師的 Rule of thumb Signal path can be treated as:
A lumped element, if L < /100 (Short ckt, series resistor, shunt capacitor)
A lumped model, if /100 < L < /20 (Series inductor with shunt capacitor)
A distributed model, if L > /20 (Transmission Line or multi-section LC model)
中華大學 通訊系 19
Example of Radio-Frequency Interconnection
For 1GHz RF signal in PCB circuits Vp= 0.6c =180mm/ns = Vp/freq =180mm Rule of Thumb only worked as:
Td < T/100 = 0.01ns L < /100 = 1.8mm = 71 mil
Distributed analysis is needed for RF PCB design !!
中華大學 通訊系 21
Component size v.s. Wavelength
Definitions of lumped element (1) Input current amplitude
= Output current amplitude (2) Input current phase
= Output current phase Only at 100MHz, 2cm resistor can be treat
ed as a lumped resistor !
中華大學 通訊系 23
Resistor Capacitor Inductor
Definitions of lumped element (1) Input current amplitude
= Output current amplitude (2) Input current phase
= Output current phase
Basic Lumped Elements
中華大學 通訊系 24
Capacitor
Time domain : Ic= C (dVc/dt)
t= 0-, Vc=0
(a) t= 0+, Vc can be finite value?Ic= infinity !! impossible!!@#
(b) t=0+, Vc= 0, Short circuit for instant
(c) Ballastor for impulse voltage
Frequency domain : ic= jC vc
中華大學 通訊系 25
Inductor
Time domain : VL= L (dIL/dt)
t= 0-, IL=0
(a) t= 0+, IL can be finite value?
VL = infinity !! impossible!!@#
(b) t=0+, IL= 0, Open circuit for instant
(c) Ballastor for impulse current
Frequency domain : vL= jL iL
中華大學 通訊系 26
Practical Capacitor
With Parasitic Resistor Rs and Inductor Ls
RS LSC
|ZC|
Freq (log)
Capacitive
Inductive
中華大學 通訊系 27
Practical Inductor
With Parasitic Resistor Rp and Capacitor Cp
RP
L
CP
|YC|
Freq (log)
Capacitive
Inductive
中華大學 通訊系 32
Transmission Line Parameters
R: Resistance per unit length (/m) Due to conductor loss
L: Inductance per unit length (H/m) C: Capacitance per unit length (F/m) G: Conductance per unit length (S/m)
Due to dielectric loss
中華大學 通訊系 35
Transmission Line Equations
Kirchhoff’s voltage law
t
tzILtzIR
z
tzV
z
tzVtzzVt
tzIzLtzIzRtzVtzzV
z
),(),(
),(),(),(
),(),(),(),(
lim0
),()(),(
tzIt
LRz
tzV
?!0zas
中華大學 通訊系 36
Transmission Line Equations
Kirchhoff’s current law
t
tzVCtzVG
z
tzI
z
tzItzzIt
tzVzCtzVzGtzItzzI
z
),(),(
),(),(),(
),(),(),(),(
lim0
),()(),(
tzVt
CGz
tzI
?!0zas
中華大學 通訊系 37
Wave Equations for Lossless Line
For a lossless line, R= 0 and G= 0
t
VC
z
I
t
IL
z
V
2
2
22
2
2
2
2
2
22
2
2
2 11
t
I
vt
ILC
z
I
t
V
vt
VLC
z
V
PP
)/(1
smvelocityphaseLC
vp
中華大學 通訊系 38
Traveling-Wave solutions
V+:voltage wave traveling in +z direction V-:voltage wave traveling in -z direction
)()(),(PP v
ztV
v
ztVtzV
中華大學 通訊系 40
Characteristic Impedance
)]()([1
),(
)()(),(
0 PP
PP
v
ztV
v
ztV
ZtzI
v
ztI
v
ztItzI
C
L
I
V
I
VZ
0
Using PSPICE to simulate 100MHz sinusoidal wave propagating in 40cm RG-58/U coaxial cable by lumped model.
RG-58/U cableZ0=50v= 2x108m/sL= 250nH/mC= 100pF/m=2m @100MHzl= 40cm=0.2 @100MHzDelay= 2ns
Ideal LineIdeal Line
中華大學 通訊系 46
Transmission line lumped model使用重點
(1) Z0, 在工程的眼光下,可近似成 Z</20 。
(2) 若要以 Lumped model 建立傳輸線電路的模型,例如 IC Pakage interconnection lines 等,必須先知道傳輸信號所佔頻寬中的最大頻率 Fmax。
(3) 波長 min= 波速 v / Fmax。
(4) Transmission lines 超過 min/20 就必須做適當的切割,分別建立獨立的 Lumped model 。
中華大學 通訊系 49
Skin Effect
For low frequency
For high frequency Skin depth
)/(1
mA
R
A
)/(1
)(1
mfw
R
mf
中華大學 通訊系 53
Potentially DangerousParasitic Transmission Lines
Parallel plates TL for TEM wave
Slab waveguide for surface wave