EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 1
Shunt-Peaking (1)
By connecting an inductor in series with the load resistor (series connection in shunt with output), more current is used, for a longer time, to charge the load capacitance.
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 2
Properties of Shunt-Peaking
€
ωr2
=1
LCL
1−CLR2
L
⎛
⎝ ⎜
⎞
⎠ ⎟
Resonant frequency:
No resonance for
€
LCLR2
< 1
CL
X Re s
Im s
L = 0: pole at s = −1/RC
X O
L ≠ 0: zero at s = −R/L additional pole at s ≈ −(1/CR + R/L)
€
Z(s) = R ⋅1+ s L
R1+ sCLR + s2LCL
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Z( jω) = R ⋅1+ jω L
R1−ω2LCL( ) + jωCLR
Frequency response:
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 3
€
L = 0BW = 6.3 GHz
€
LCLR2
= 0.3
L = 1.8 nH BW = 9.4 GHz
€
LCLR2
= 0.6
L = 3.7 nH BW = 14.3 GHz
Shunt-Peaking -- AC Response
Use of shunt-peaking increases small-signal bandwidth
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CL = 38 fFR = 400 Ω
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 4
Shunt Peaking − Transient Response (1)
Step Response:
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L = 0td = 13.4 ps
L = 1.8 nH td = 8.5 ps
L = 3.7 nH td = 6.7 ps
Pulse Response (Δtin = 50 ps):
L = 3.7 nH Δtout = 50.8 ps ISI = 16 mUI
L = 1.8 nH Δtout = 50.0 ps ISI = 0 mUI
L = 0 Δtout = 48.7 ps ISI = 26 mUI
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 5
Other Advantages of Shunt-Peaking
• CML load is passive & linear
• Can be shown to be very robust in the presence of parasitic series resistance and shunt capacitance ⇒ inductors can be placed far away from other CML circuit elements.
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 6
long metal lines
Effect of Shunt-Peaking Inductor Parasitics (1)
• Series resistance RP simply adds to R
• Shunt capacitance CP resonates with L …
L L
R R
CL CL CL CL
L L
R R
RP RP
CP CP
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 7
€
LCLR2
= 0
€
LCLR2
= 0.3
€
LCLR2
= 0.6
€
LCLR2
= 0
€
LCLR2
= 0.3
€
LCLR2
= 0.6
Moderate amount of parasitic capacitance has similar effect to slightly larger inductor.
Disadvantages of using passive inductors: • Consume huge die area • Difficult to design & model
Effect of Shunt-Peaking Inductor Parasitics (2)
€
CP = 0
€
CP = 0.2CL
ISI (UI) vs. input pulse width
ISI (UI) vs. input pulse width
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 8
Multi-layer Inductors (1)
metal 6
metal 5 d
Distance d between two metal layers is much smaller than lateral distances (e.g., w, l, s)
metal 6
metal 5
d
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 9
€
φ1
φ2
⎛
⎝ ⎜
⎞
⎠ ⎟ =
L1 MM L2
⎡
⎣ ⎢
⎤
⎦ ⎥
i1i2
⎛
⎝ ⎜ ⎞
⎠ ⎟
L1 L2 φ1 φ2
+
_
+
_
i1 i2
2-port representation of coupled inductors:
€
M = k L1L2
Passivity constraint: 1≤k
For metal geometries close to each other, k is close to unity.
series connection of coupled inductors:
L1 L2
i1
i2
M
φ1
+
_ φ2
+
_
€
φseries =φ1 +φ2 = (L1 + M)i1 + (L2 + M)i2
€
iseries = i1 = i 2
€
Lseries =φseries
iseries
= L1 + L2 + 2M
€
⇒
For L1 = L2 = L, we have:
€
Lseries = 2L + 2M = 2L(1+ k) ≈ 4LIn general, for n layers we have:
€
Lseries ≈ n2L
Multi-layer inductors are more appropriate for shunt-peaking than resonant structures due to additional contact resistance.
Multi-layer Inductors (2)
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 10
Ci
Cj
For more details, see:
A. Zolfaghari, A. Chan & B. Razavi, “Stacked inductors and transformers in CMOS technology,” IEEE Journal of Solid-State Circuits, vol. 36, April 2001, pp. 620-628.
€
Leffective ≈ 4L
€
Ceffective ≈13
Ci +1
12Cj
Effective Capacitance:
Multi-layer Inductors (3)
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 11
metal 6 only 100µ x 100µ w = 4; s = 2; n = 4 L=2.0 nH R=6.9 Ω
metal 6 over metal 4 46µ x 46µ w = 4; s = 2; n = 2.5 L=2.0 nH R=12.5 Ω
+
Multi-layer Inductors (4)
Area comparison:
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 12
Active Inductors (1)
Rgyr
+
_ v1
i1
+
_
v2
i2
Ideal gyrator:
€
v2 = Rgyr i1v1 = −Rgyr i2
Impedance inversion:
Rgyr
+
_ vin
iin
C
€
Zin = Rgyr2 sC( )
Port 1 exhibits inductance when port 2 is connected to a capacitance.
€
v1v2
⎛
⎝ ⎜
⎞
⎠ ⎟ =
0 −Rgyr
Rgyr 0
⎡
⎣ ⎢
⎤
⎦ ⎥
i1i2
⎛
⎝ ⎜ ⎞
⎠ ⎟
Matrix representation (Z-parameters):
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 13
Active Inductors (2)
RG
+
_
v1 i1
+
_ v2
i2
i1 applied with port 2 open-circuited:
i2 applied with port 1 open-circuited:
€
v2 =1
gm
i1
€
v1 = − RG −1
gm
⎛
⎝ ⎜
⎞
⎠ ⎟ i2
(Assume RG gm > 1)
€
v1v2
⎛
⎝ ⎜
⎞
⎠ ⎟ =
1 gm − RG −1 gm( )1 gm 1 gm
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
i1i2
⎛
⎝ ⎜ ⎞
⎠ ⎟
Complete Z-parameters (lossy/active gyrator):
Consider common-drain configuration:
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 14
€
v1v2
⎛
⎝ ⎜
⎞
⎠ ⎟ =
1 gm 1 gm −RG
1 gm 1 gm
⎡
⎣ ⎢
⎤
⎦ ⎥
i1i2
⎛
⎝ ⎜ ⎞
⎠ ⎟
+
_
vin
Active Inductors (3)
Interpretation of non-ideal matrix entries:
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 15
€
Zsource =1
gm
1+ sCgsRG
1+ sCgs gm
⎡
⎣ ⎢
⎤
⎦ ⎥
At low frequencies (Cgs open) ⇒ Zsource = 1/gm
At high frequencies (Cgs short) ⇒ Zsource = RG
Active Inductors (4)
Impedance at port 1 with port 2 terminated with transistor Cgs:
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 16
€
ω
€
gm
Cgs
€
1CgsRG
€
1gm
€
RG
€
Zsource
€
Leff ≈CgsRG
gm
=RG
ωT
€
gmRG > 1
Equivalent circuit:
+
_
vin
€
1gm
€
RG −1
gm
€
Cgs ⋅RG
gm
Active Inductors (5)
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 17
€
Av =gm 1
gm 2
=W1
W2
For shunt peaking:
€
L ≈ 0.3CLR2
€
CgsRG
gm2
= 0.3 CL
gm22
€
gm 2RG = 0.3 CL
Cgs
Low-frequency gain:
CML Buffer with Active Inductor Load
€
WL
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
=40.18
€
WL
⎛
⎝ ⎜
⎞
⎠ ⎟
2
=2.50.18
€
ISS = 400µA
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 18
Active Inductor AC Response
RG = 4k
RG = 2k
RG = 0
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 19
Active Inductor Transient Response (1)
RG = 0 PW = 97ps
RG = 5k PW = 100 ps
RG = 10k PW = 104 ps
Differential signals:
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 20
Active Inductor Transient Response (2)
Problem: n-channel load shifts output by Vt. Vsb > 0; body effects exacerbates this effect..
Single-ended input
Single-ended outputs
Single-ended signals:
EECS 270C / Winter 2013 Prof. M. Green / U.C. Irvine 21
Alternate topology: p-channel load exhibits lower Vt (Vbs = 0)
Active Inductor Alternate Topology
differential
single-ended
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