topics in ic design t-coil - seoul national university
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Topics in IC Design
T-Coil
Deog-Kyoon Jeong
School of Electrical and Computer Engineering
Seoul National University
2020 Fall
(Compliment to Hyungrok Do)
Introduction
โข Inductors produce peaking, thereby giving
bandwidth extension.
โข T-coil (Tee-Coil) produces even more bandwidth
extension by giving negative inductance.
ยฉ 2020 DK Jeong Topics in IC Design 2
Dot conventionSame direction : k > 0
Opposite direction : k < 0
๐ = ๐ค ๐๐๐๐|k| โค 1
|k| = 1 when inductors share all of
their magnetic flux.
Introduction
โข Introduced by Ginzton in 1948 as part of distributed
amplifier.
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[0] Ginzton, Proc IRE, 1948
T-Coil
โข Common Source Amplifier
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๐๐๐ ๐ฉ = ฮค๐ ๐๐ ๐น๐ซ๐ช๐ณ
Without T-Coil, 1
1 + ๐ ๐ ๐ท๐ถ๐ฟ
With T-Coil,
[1] B. Razavi, ISSC Magazine, 2015
โข When two zeros in the numerator are cancelled by two of the four
poles in the denominator, the second-order transfer function is
obtained.
โข Given RD and CL, what are CB, L, and M, assuming L1 = L2 = L
(symmetric T-Coil)?
โข Four equations must be satisfied with five variables (CB, L, M,
, ๐๐). Out of numerous solutions, what is the best transfer
function that maximizes the bandwidth?
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Symmetric T-Coil
๐4๐๐2 = ๐2
๐3๐๐2 = ๐22๐๐ + ๐1
๐2๐๐2 = ๐2๐๐
2 + ๐12๐๐ + 1
๐1๐๐2 = ๐1๐๐
2 + 2๐๐
Symmetric T-Coil
โข Let k=M/L and simplify 4 equations.
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2
2
1 1
4 1
12
1
2
1
1
2 1
B
L
L B
D
n
L
D L D
L
C k
C k
k LkC C
k R
k LC
R C k L R
k LC
2
2
2
2
2
22
2 2
1 44
4 1
4 1
16
16
D L
LB
n
D L
R CL
k
CC
R C
โข Then, determine that maximizes the bw.
[1] B. Razavi, ISSC Magazine, 2015
Symmetric T-Coil
โข With the following 2nd order transfer function,
โข 3-dB BW with T-Coil is
which is maximized when .
โข Then
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22 2 2 2
,
22
2 2
2 2
1 2 1 2 1
161 2 1 2 1
BW T Coil n
D LR C
,
3
12 2
2.828
BW T Coil n
D L
dB
R C
[1] B. Razavi, ISSC Magazine, 2015
โข The maximum bandwidth solution is
๐ฟ =3
8๐ ๐ท2๐ถ๐ฟ , ๐ =
1
3๐ฟ, ๐ถ๐ต =
1
8๐ถ๐ฟ, ๐๐=2 2/๐ ๐ท๐ถ๐ฟ
which extends the bandwidth by 2.828.
Topics in IC Design 8
Symmetric T-Coil
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BWER=2.828
โข What are its input impedances Zin1 and Zin2?
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Features of Symmetric T-Coil
Zin1
Under the maximum bandwidth
condition,
Zin1 = RD
Zin2 =
T-Coil is transparent.
CL is not seen.
Can be used for return loss (RL)
minimization.
Zin2
โข What is the transfer function to the resistor node?
Topics in IC Design 10
Features of Symmetric T-Coil
VR
โข Under the maximum bandwidth
condition,
โข All-pass function with infinite
bandwidth!
โข Extra phase delay could be a
problem.
๐๐ ๐๐๐
๐ = โ๐๐๐ ๐ท๐ 2 โ 2๐๐๐ + ๐๐
2
๐ 2 + 2๐๐๐ + ๐๐2
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โโ ๐ = โ2 arctan[2๐๐๐
๐๐2 โ ๐2
]
โข With one less constraint (L1L2), more freedom for
design is utilized to extend the bandwidth at the cost
of higher design complexity.
โข Given RD and CL, what are CB, L1, L2 , and M?
โข Four equations must be satisfied with five variables
(CB, L1, L2 , M, ๐๐, and = ฮค๐ ๐). Out of numerous
solutions, what is the best transfer function that
maximizes the bandwidth, ๐๐๐ ๐ฉ,๐ปโ๐ช๐๐๐?
Topics in IC Design 11
Asymmetric T-Coil
๐4๐๐2 = ๐2
๐3๐๐2 = ๐22๐๐ + ๐1
๐2๐๐2 = ๐2๐๐
2 + ๐12๐๐ + 1
๐1๐๐2 = ๐1๐๐
2 + 2๐๐
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Asymmetric T-Coil
โข No closed-form analytical solution was found.
โข So, first assume L1=L, L2=bL, M= mL, with constraint
of the coupling coefficient
Topics in IC Design 12
๐ =๐
๐ฟ1๐ฟ2=
๐
๐< 1
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[3] S.C.D.Roy, IETE Journal of Research, 2016
Asymmetric T-Coil
โข b=1 (Symmetric T-Coil)
โข b=1, m=0.333 (k=0.333), ๐ณ = ๐. ๐๐๐๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = ๐. ๐๐๐๐ช๐ณ, ๐๐= 2. ๐๐๐/๐น๐ซ๐ช๐ณ
โข b<1, what are m(k), ๐ณ, ๐ช๐ฉ, ๐๐? (using Mathematica)
Topics in IC Design 13
b=1.0, m= 0.333 (k=0.333), ๐ณ = 0.375๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = 0.1250๐ช๐ณ, ๐๐= 2.828/๐น๐ซ๐ช๐ณ
b=0.9, m= 0.378 (k=0.398), ๐ณ = 0.406๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = 0.1074๐ช๐ณ, ๐๐= 2.939/๐น๐ซ๐ช๐ณ
b=0.8, m= 0.412 (k=0.460), ๐ณ = 0.44๐๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = 0.091๐๐ช๐ณ, ๐๐= 3.062/๐น๐ซ๐ช๐ณ
b=0.7, m= 0.436 (k=0.521), ๐ณ = 0.49๐๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = 0.077๐๐ช๐ณ, ๐๐= 3.202/๐น๐ซ๐ช๐ณ
b=0.6, m= 0.449 (k=0.580), ๐ณ = 0.55๐๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = 0.063๐๐ช๐ณ, ๐๐= 3.367/๐น๐ซ๐ช๐ณ
b=0.5, m= 0.451 (k=0.638), ๐ณ = 0.635๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = 0.051๐๐ช๐ณ, ๐๐= 3.572/๐น๐ซ๐ช๐ณ
b=0.4, m= 0.440 (k=0.696), ๐ณ = 0.751๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = 0.0396๐ช๐ณ, ๐๐= 3.838/๐น๐ซ๐ช๐ณ
b=0.3, m= 0.414 (k=0.756), ๐ณ = 0.93๐๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = 0.0284๐ช๐ณ, ๐๐= 4.215/๐น๐ซ๐ช๐ณ
b=0.2, m= 0.366 (k=0.818), ๐ณ = 1.25๐๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = 0.017๐๐ช๐ณ, ๐๐= 4.828/๐น๐ซ๐ช๐ณ
b=0.1, m= 0.280 (k=0.886), ๐ณ = 2.02๐๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ = 0.007๐๐ช๐ณ, ๐๐= 6.176/๐น๐ซ๐ช๐ณ
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Practical Implementation
โข Coupling coefficient of greater than 0.7 is not
practical with on-chip spiral inductor.
โข So, b=0.4, m= 0.440 (k=0.696), ๐ณ = 0.751๐น๐ซ๐๐ช๐ณ, ๐ช๐ฉ =
0.0396๐ช๐ณ, ๐๐= 3.838/๐น๐ซ๐ช๐ณ is the practical limit.
Topics in IC Design 14ยฉ 2020 DK Jeong
[3] S.C.D.Roy, IETE Journal of Research, 2016
Output at Resistor Load
With asymmetric T-coil and =ฮค๐ ๐,
1) transfer function to RD?
2) impedance seen from either
side of the T-Coil?
Zin1 = ?
Zin2 = ?
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VR
Zin1
Zin2
๐ฝ๐น๐ฝ๐๐
๐ = ?
T-Coil Design Flow
โข Design flow
โ For given CL and RD, determine L1, L2, k, and CB.
โ Design T-coil in a 3-D EM tool and extract S-parameter or circuit model.
โ Perform circuit simulation including parasitic resistance and capacitance.
โข Parasitic RC
โ If using top metal, a 100 pH of inductor has series resistance of 5 ~ 10 .
โ Natural bridge capacitance is known to be 10 ~ 30 fF.
โข Realistic limitation
โ k canโt be over +0.7 in the chip.
โ Self-resonance limits large k and L.
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Eye Diagram Optimization
โข Maximally Flat Gain ( = 1/โ2) vs Maximally Flat Phase Delay ( = 1)
โข Minimum Jitter Condition: Minimum phase delay variation
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[4] W Bae, TVLSI, 2017
Asymmetric T-Coil Simulation
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ฮท = 3.04 as expected
Gain:
No T-coil
T-coil 1
T-coil 2
Phase delay:
No T-coil
T-coil 1
T-coil 2
CL = 200 fF, RT = 50
(BW = 15.92 GHz)
ฮถ = 1/โ2, k = 0.45
L = 219 pH, b = 0.815
CB = 18.74 fF
Two T-coils :
1. Maximally flat gain @ k = 0.45
2. Maximally flat phase delay
around 1. (L = 200 pH)
Asymmetric T-Coil Simulation
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CL = 200 fF, RT = 50
(BW = 15.92 GHz)
ฮถ = 1/โ2, k = 0.45
L = 219 pH, b = 0.815
CB = 18.74 fF
Two T-coils :
1. Maximally flat gain @ k = 0.45
2. Maximally flat phase delay
around 1. (L = 200 pH)
No T-coil T-coil 1 T-coil 2
Return Loss Reduction
โข Minimize Return Loss at TX driver and RX receiver.
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โข Effect of Large ESD Capacitance is removed.
[5] M.Kossel, JSSC, 2008
[6] M.S.Keel, EOS/ESD, 2015
TX Optimization
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Cp 200 fF
Ct 50 fF
Ce 100 fF
RT, Z0 50 ฮฉ
No T-coil k = 0.5, L = 200 pH, b = 0.3
Z0CpbLL
Ce
Cc
CtRT
Channel
Vin
Vout
Zout
k = -0.25, L = 250 pH, b = 0.4
56Gb/s eye diagram
Example: ESD Diode Isolation
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[7] J.Kim, ISSCC, 2015
Example: ESD Separation
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[8] C.Y.Lin, IEEE Transactions on Electron Devices. 2013
Example: Double T-Coil
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[9] G.Steffan, ISSCC, 2017
Example: Coil with 4 ports
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[10] J Kim, JSSC, 2019
References
26Topics in IC Designยฉ 2020 DK Jeong
[0] E. Ginzton et. al, โDistributed Amplification,โ Proc. IRE, vol. 36, pp. 956โ969, Aug.
1948.
[1] Razavi, Behzad, "The bridged T-coil [a circuit for all seasons]." IEEE Solid-State
Circuits Magazine 7.4 (2015): 9-13.
[2] Paramesh, Jeyanandh, and David J. Allstot. "Analysis of the bridged T-coil circuit
using the extra-element theorem." IEEE Transactions on Circuits and Systems II:
Express Briefs 53.12 (2006): 1408-1412.
[3] Dutta Roy, Suhash C. "A Theoretical Investigation into the Limits of Bandwidth
Enhancement with the Asymmetrical Bridged T-Coil Network." IETE Journal of
Research 62.3 (2016): 379-386.
[4] Bae, Woorham, Borivoje Nikoliฤ, and Deog-Kyoon Jeong. "Use of phase delay
analysis for evaluating wideband circuits: An alternative to group delay analysis."
IEEE Transactions on Very Large Scale Integration (VLSI) Systems 25.12 (2017):
3543-3547.
[5] Kossel, Marcel, et al. "A T-Coil-Enhanced 8.5 Gb/s High-Swing SST Transmitter in
65 nm Bulk CMOS With โช-16 dB Return Loss Over 10 GHz Bandwidth." IEEE
Journal of Solid-State Circuits 43.12 (2008): 2905-2920.
[6] Keel, Min-Sun, and Elyse Rosenbaum. "CDM-reliable T-coil techniques for high-
speed wireline receivers." 2015 37th Electrical Overstress/Electrostatic Discharge
Symposium (EOS/ESD). IEEE, 2015.
References
27Topics in IC Designยฉ 2020 DK Jeong
[7] Kim, Jihwan, et al. "3.5 A 16-to-40Gb/s quarter-rate NRZ/PAM4 dual-mode
transmitter in 14nm CMOS." 2015 IEEE International Solid-State Circuits
Conference-(ISSCC) Digest of Technical Papers. IEEE, 2015.
[8] Lin, Chun-Yu, Li-Wei Chu, and Ming-Dou Ker. "Robust ESD protection design for
40-Gb/s transceiver in 65-nm CMOS process." IEEE transactions on electron
devices 60.11 (2013): 3625-3631.
[9] Steffan, Giovanni, et al. "6.4 A 64Gb/s PAM-4 transmitter with 4-Tap FFE and 2.26
pJ/b energy efficiency in 28nm CMOS FDSOI." 2017 IEEE International Solid-
State Circuits Conference (ISSCC). IEEE, 2017.
[10] Kim, Jihwan, et al. "A 112 Gb/s PAM-4 56 Gb/s NRZ reconfigurable transmitter
with three-tap FFE in 10-nm FinFET." IEEE Journal of Solid-State Circuits 54.1
(2019): 29-42.