M.H. Perrott
High Speed Communication Circuits and SystemsLecture 6
Enhancement Techniques for Broadband Amplifiers,Narrowband Amplifiers
Michael H. PerrottFebruary 20, 2004
Copyright © 2004 by Michael H. PerrottAll rights reserved.
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M.H. PerrottM.H. Perrott
Resistor Loaded Amplifier (Unsilicided Poly)
We decided this was the fastest non-enhanced amplifier- Can we go faster? (i.e., can we enhance its bandwidth?)
We will look at the following- Reduction of Miller effect on Cgd- Shunt, series, and zero peaking- Distributed amplification
M1
RL
vout
M2
Cfixed
Id
Vbias
vin
Ctot = Cdb1+CRL/2 + Cgs2+KCov2 + Cfixed
Miller multiplication factor(+Cov1)
1
voutvin
f
slope = -20 dB/dec
gm12πCtot
gm1RL
2πRLCtot
1
Vdd
2
M.H. PerrottM.H. Perrott
Cgd is quite significant compared to Cgs- In 0.18 CMOS, Cgd is about 45% the value of Cgs
Input capacitance calculation
- For 0.18 CMOS, gain of 3, input cap is almost tripled over Cgs!
M1
RL
vout
CL
Id
Vbias
vin
CgdZin
Rs
Cgs
Miller Effect on Cgd Is Significant
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M.H. PerrottM.H. Perrott
Reduction of Cgd Impact Using a Cascode Device
The cascode device lowers the gain seen by Cgd of M1
- For 0.18m CMOS and gain of 3, impact of Cgd is reduced by 30%:
Issue: cascoding lowers achievable voltage swing
M1
RL vout
CL
Vbias
vin
CgdZin
Rs
Cgs
Vbias2M2
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M.H. PerrottM.H. Perrott
Source-Coupled Amplifier
Remove impact of Miller effect by sending signal through source node rather than drain node- Cgd not Miller multiplied AND impact of Cgs cut in half!
The bad news- Signal has to go through source node (Csb significant)- Power consumption doubled
M1
Vbias
vin
Cgd
Rs
M2
RL
Cgd
2Ibias
voutZin
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M.H. PerrottM.H. Perrott
Neutralization
Consider canceling the effect of Cgd- Choose CN = Cgd- Charging of Cgd now provided by CN
Benefit: Impact of Cgd removed Issues:- How do we create the inverting amplifier?- What happens if CN is not precisely matched to Cgd?
M1
RL
vout
CL
Id
Vbias
vin
CgdZin
Rs
Cgs
-1CN
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M.H. PerrottM.H. Perrott
Practical Implementation of Neutralization
Leverage differential signaling to create an inverted signal Only issue left is matching CN to Cgd- Often use lateral metal caps for CN (or CMOS transistor)- If CN too low, residual influence of Cgd- If CN too high, input impedance has inductive component
Causes peaking in frequency response Often evaluate acceptable level of peaking using eye diagrams
M1
RL
Vbias
vin
Cgd
Rs
CN
M2
RL
Cgd
2Ibias
CN
-vin
Rs
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M.H. PerrottM.H. Perrott
Shunt-peaked Amplifier
Use inductor in load to extend bandwidth- Often implemented as a spiral inductor We can view impact of inductor in both time and
frequency- In frequency: peaking of frequency response- In time: delay of changing current in RL
Issue – can we extend bandwidth without significant peaking?
M1
RL
vout
M2
Cfixed
Id
Vbias
vin
Vdd
Ld
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M.H. PerrottM.H. Perrott
Shunt-peaked Amplifier - Analysis
Expression for gain
Parameterize with
- Corresponds to ratio of RC to LR time constants
M1
RL
vout
M2
Cfixed
Id
Vbias
vin
Vdd
Ld
RL
Ld
Ctotiin=gmvin
vout
Small Signal ModelZout
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M.H. PerrottM.H. Perrott
The Impact of Choosing Different Values of m – Part 1
Parameterized gain expression
Comparison of new and old 3 dB frequencies
Want to solve for w2/w1
RL
Ld
Ctotiin=gmvin
vout
Small Signal ModelZout
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M.H. PerrottM.H. Perrott
The Impact of Choosing Different Values of m – Part 2
From previous slide, we have
After much algebra
We see that m directly sets the amount of bandwidth extension!- Once m is chosen, inductor value is
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M.H. PerrottM.H. Perrott
Plot of Bandwidth Extension Versus m
0 1 2 3 4 5 6 7 8 9 101.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Bandwidth Extension (w2/w
1) Versus m
w1/w
2
m
Highest extension: w2/w1 = 1.85 at m ≈ 1.41- However, peaking occurs!
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M.H. PerrottM.H. Perrott
Plot of Transfer Function Versus m
Maximum bandwidth: m = 1.41 (extension = 1.85)
Maximally flat response: m = 2.41 (extension = 1.72)
Best phase response: m = 3.1 (extension = 1.6)
No peaking: m = infinity
Eye diagrams often used to evaluate best m
1/100 1/10 1 10 100-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
Nor
mal
ized
Gai
n (d
B)
Normalized Frequency (Hz)
Normalized Gain for Shunt Peaked Amplifier For Different m Values
m=1.41m=2.41
m=3.1m=infinity
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M.H. PerrottM.H. Perrott
Zero-peaked Common Source Amplifier
Inductors are expensive with respect to die area We can instead achieve bandwidth extension with
capacitor- Idea: degenerate gain at low frequencies, remove degeneration at higher frequencies (i.e., create a zero)
Issues:- Must increase RL to keep same gain (lowers pole)- Lowers achievable gate voltage bias (lowers device ft)
M1
RL
vout
M2
Cfixed
Id
Vbias
vin
Vdd
Rs Cs
voutvin
f
gmRL
2πCtotRL
1
2πCsRs
1
1+gmRs
zero
overallresponse
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M.H. PerrottM.H. Perrott
Back to Inductors – Shunt and Series Peaking
Combine shunt peaking with a series inductor- Bandwidth extension by converting to a second order
filter response Can be designed for proper peaking
Increases delay of amplifier
M1
RL
vout
M2
Cfixed
Id
Vbias
vin
Vdd
L1
L2
voutvin
f
gmRL
2πCtotRL
1
-40 dB/dec-20 dB/dec
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M.H. PerrottM.H. Perrott
T-Coil Bandwidth Enhancement
Uses coupled inductors to realize T inductor network- Works best if capacitance at drain of M1 is much less than
the capacitance being driven at the output load See Chap. 8 of Tom Lee’s book (pp 187-191) for analysis See S. Galal, B. Ravazi, “10 Gb/s Limiting Amplifier and
Laser/Modulator Driver in 0.18u CMOS”, ISSCC 2003, pp 188-189 and “Broadband ESD Protection …”, pp. 182-183
M1
RL
vout
M2
Cfixed
Id
Vbias
vin
Vdd
L1
L2L3
M1
vout
M2
CfixedVbias
vin
L2
L1
CB
k
RL
Vdd
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M.H. PerrottM.H. Perrott
Bandwidth Enhancement With ft Doublers
A MOS transistor has ft calculated as
ft doubler amplifiers attempt to increase the ratio of transconductance to capacitance
M1 M2
2Ibias
I1 I2
Vbias
vin
We can make the argument that differential amplifiers are ft doublers- Capacitance seen by Vin for single-ended input:- Difference in current:
Transconductance to Cap ratio is doubled:
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M.H. PerrottM.H. Perrott
Creating a Single-Ended Output
Input voltage is again dropped across two transistors- Ratio given by voltage divider in capacitance
Ideally is ½ of input voltage on Cgs of each device Input voltage source sees the series combination of
the capacitances of each device- Ideally sees ½ of the Cgs of M1
Currents of each device add to ideally yield ratio:
M1 M2
2Ibias
I1 I2
Vbias
vinM1
M2
Ibias
Io
Vbias
vin
Ibias
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M.H. PerrottM.H. Perrott
Creating the Bias for M2
Use current mirror for bias- Inspired by bipolar circuits (see Tom Lee’s book, page 198)
Need to set Vbias such that current through M1 has the desired current of Ibias- The current through M2 will ideally match that of M1
Problem: achievable bias voltage across M1 (and M2) is severely reduced (thereby reducing effective ft of device)- Do ft doublers have an advantage in CMOS?
M1 M2
2Ibias
I1 I2
Vbias
vinM1
M2
Ibias
Io
Vbias
vin
Ibias
M1
M2
Io
Vbias
vin
IbiasM3
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M.H. PerrottM.H. Perrott
Increasing Gain-Bandwidth Product Through Cascading
We can significantly increase the gain of an amplifier by cascading n stages
- Issue – bandwidth degrades, but by how much?
Amp Amp
Cfixed
Amp
Cfixed
A1 + s/wo
A1 + s/wo
A1 + s/wo
vin vout
vin vout
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M.H. PerrottM.H. Perrott
Analytical Derivation of Overall Bandwidth
The overall 3-db bandwidth of the amplifier is where
- w1 is the overall bandwidth- A and wo are the gain and bandwidth of each section
- Bandwidth decreases much slower than gain increases! Overall gain bandwidth product of amp can be increased!
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M.H. PerrottM.H. Perrott
Transfer Function for Cascaded Sections
1/100 1/10 1 10 100-80
-70
-60
-50
-40
-30
-20
-10
0
Nor
mal
ized
Gai
n (d
B)
Normalized Frequency (Hz)
Normalized Transfer Function for Cascaded Sections
n=1
n=2
n=3
n=4
-3
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M.H. PerrottM.H. Perrott
Choosing the Optimal Number of Stages
To first order, there is a constant gain-bandwidth product for each stage
- Increasing the bandwidth of each stage requires that we lower its gain- Can make up for lost gain by cascading more stages
We found that the overall bandwidth is calculated as
Assume that we want to achieve gain G with n stages
From this, optimum gain ≈ sqrt(e) = 1.65- See Tom Lee’s book, pp 207-211
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M.H. PerrottM.H. Perrott
Achievable Bandwidth Versus G and n
0 5 10 15 20 25 300
0.05
0.1
0.15
0.2
0.25
Achievable Bandwidth (Normalized to f )t Versus Gain (G) and Number of Stages (n)
n
w1/
wt
0.3
A=1.65
A=3
G=10
G=100
G=1000
Optimum gain per stage is about 1.65- Note than gain
per stage derived from plot as
- Maximum is fairly soft, though
Can dramatically lower power (and improve noise) by using larger gain per stage
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M.H. PerrottM.H. Perrott
Motivation for Distributed Amplifiers
We achieve higher gain for a given load resistance by increasing the device size (i.e., increase gm)- Increased capacitance lowers bandwidth
We therefore get a relatively constant gain-bandwidth product We know that transmission lines have (ideally) infinite
bandwidth, but can be modeled as LC networks- Can we lump device capacitances into transmission line?
M1 M2 M3
vout
vin
Rs=Z0
RL=Z0
Cin CinCin
Cout Cout Cout
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M.H. PerrottM.H. Perrott
Distributing the Input Capacitance
Lump input capacitance into LC network corresponding to a transmission line- Signal ideally sees a real impedance rather than an RC
lowpass- Often implemented as lumped networks such as T-coils- We can now trade delay (rather than bandwidth) for gain
Issue: outputs are delayed from each other
M1 M2 M3
Zo Zo Zo Zo
vout
RL=Z0
delay
vin
Rs=Z0
RL=Z0
Cout Cout Cout
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M.H. PerrottM.H. Perrott
Distributing the Output Capacitance
Delay the outputs same amount as the inputs- Now the signals match up- We have also distributed the output capacitance!
Benefit – high bandwidth Negatives – high power, poorer noise performance,
expensive in terms of chip area- Each transistor gain is adding rather than multiplying!
M1
Zo Zo Zo Zo
M2 M3
Zo Zo Zo Zo
RL=Z0
vout
RL=Z0
delay
delay
vin
Rs=Z0
RL=Z0
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M.H. PerrottM.H. Perrott
Narrowband Amplifiers
For wireless systems, we are interested in conditioning and amplifying the signal over a narrow frequency range centered at a high frequency- Allows us to apply narrowband transformers to create
matching networks Can we take advantage of this fact when designing
the amplifier?
VLC1 RL
L1Delay = xCharacteristic Impedance = Zo
Transmission Line
Z1
VinC2
dieConnector
Controlled ImpedancePCB trace
package
On-ChipDrivingSource
AmpVout
MatchingNetwork
MatchingNetwork
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M.H. PerrottM.H. Perrott
Tuned Amplifiers
Put inductor in parallel across RL to create bandpass filter- It will turn out that the gain-bandwidth product is
roughly conserved regardless of the center frequency! Assumes that center frequency (in Hz) << ft
To see this and other design issues, we must look closer at the parallel resonant circuit
M1
vout
CL
Vbias
vinRs
Vdd
LT RL
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M.H. PerrottM.H. Perrott
Tuned Amp Transfer Function About Resonance
Evaluate at s = jw
Look at frequencies about resonance:
RpLpCp
iin=gmvinZtank
vout
Amplifier transfer function
Note that conductances add in parallel
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M.H. PerrottM.H. Perrott
Tuned Amp Transfer Function About Resonance (Cont.)
From previous slide
Simplifies to RC circuit for bandwidth calculation!
=0
RpLpCp
iin=gmvinZtank
vout
voutvin
w
slope =-20 dB/dec
gmRp
Rp2Cp
1
wo
Rp2Cp
1
RpCp
1
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M.H. PerrottM.H. Perrott
Gain-Bandwidth Product for Tuned Amplifiers
The gain-bandwidth product:
The above expression is independent of center frequency!- In practice, we need to operate at a frequency less than
the ft of the device
RpLpCp
iin=gmvinZtank
vout
voutvin
w
slope =-20 dB/dec
gmRp
Rp2Cp
1
wo
Rp2Cp
1
RpCp
1
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M.H. PerrottM.H. Perrott
By definition
For parallel tank (see Tom Lee’s book, pp 88-89)
Comparing to above:
The Issue of Q
RpLpCp
iin=gmvinZtank
vout
voutvin
w
slope =-20 dB/dec
gmRp
Rp2Cp
1
wo
Rp2Cp
1
RpCp
1
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M.H. PerrottM.H. Perrott
Three key parameters- Gain = gmRp- Center frequency = wo- Q = wo/BW Impact of high Q - Benefit: allows achievement of high gain with low power- Problem: makes circuit sensitive to process/temp
variations
Design of Tuned Amplifiers
RpLpCp
iin=gmvinZtank
vout
voutvin
w
slope =-20 dB/dec
gmRp
Rp2Cp
1
wo
Rp2Cp
1
RpCp
1
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M.H. PerrottM.H. Perrott
Issue: Cgd Can Cause Undesired Oscillation
At frequencies below resonance, tank looks inductive
M1
vout
CL
Vbias
vin
CgdZin
Rs
Cgs
Vdd
LT RL
NegativeResistance!
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M.H. PerrottM.H. Perrott
Use Cascode Device to Remove Impact of Cgd
At frequencies above and below resonance
M1
vout
CL
Vbias
vin
CgdZin
Rs
Cgs
Vbias2M2
Vdd
LT RL
PurelyCapacitive!
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M.H. PerrottM.H. Perrott
Active Real Impedance Generator
Input impedance:
Zin
Av(s)VoutVin
Av(s) = -Aoe-jΦ
Cf
Resistive component!37
M.H. PerrottM.H. Perrott
This Principle Can Be Applied To Impedance Matching
We will see that it’s advantageous to make Zin real without using resistors- For the above circuit (ignoring Cgd)
M1
Vbias
vinRs
Ls
ZinIout
Ls
vgs gmvgsCgsItest Vtest
Looks like series resonant circuit!38
M.H. PerrottM.H. Perrott
Use A Series Inductor to Tune Resonant Frequency
Calculate input impedance with added inductor
Often want purely resistive component at frequency wo- Choose Lg such that resonant frequency = wo
M1
Vbias
vinRs
Ls
ZinIout
M1
Vbias
vinRs
Ls
ZinIout
Lg
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