6.776 High Speed Communication Circuits and Systems Lecture 9

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6.776
High Speed Communication Circuits and Systems
Lecture 9
Enhancement Techniques for Broadband Amplifiers,
Narrowband Amplifiers
Massachusetts Institute of Technology
March 3, 2005
Copyright © 2005 by Hae-Seung Lee and Michael H.
Perrott
Shunt-Series Peaking
ƒ
ƒ
ƒ
Series inductors isolate load capacitance from M1:
delays charging of load capacitance
Trades delay for bandwidth
L1, L2, L3 can be implemented by 2 coupled inductors
with coupling coefficient of k
H.-S. Lee & M.H. Perrott
MIT OCW
T-Coil Bandwidth Enhancement
Vdd
RL
Vdd
RL
L2
CB
L1
L3
vin
Vbias
M1
Id L2
k
vout
Cfixed
L1
vout
vin
M2
Vbias
M1
Cfixed
M2
ƒ
Uses coupled inductors to realize T inductor network
ƒ
is much less than
the capacitance being driven at the output load
CB provides parallel resonance to improve bandwidth further
See Chap. 9 (Ch. 8, 1st ed.) of Tom Lee’s book pp 279-282 (187191)
- Works best if capacitance at drain of M
1
H.-S. Lee & M.H. Perrott
MIT OCW
T-Coil Continued
ƒ
The self inductance L (with the other winding opencircuited) must be
ƒ
The bridging capacitance
ƒ
Coupling coefficient
k=1/3 for Butterworth response
k=1/2 for maximally flat delay (linear phase)
Bandwidth extension: approximately 2.8 (Butterworth)
- 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
- Also see "Circuit Techniques for a 40 Gb/s Transmitter in 0.13um CMOS",
J. Kim, et. al. ISSCC 2005, Paper 8.1
H.-S. Lee & M.H. Perrott
MIT OCW
Bandwidth Enhancement With ft Doublers
I1 I2
M1
2Ibias
ƒ
A MOS transistor has ft calculated as
ƒ
ft doubler amplifiers attempt to
increase the ratio of
transconductance to capacitance
M2
vin
Vbias
ƒ
We can make the argument that differential amplifiers
are ft doublers
- Capacitance seen by V
- Difference in current:
in
ƒ
for single-ended input:
Transconductance to Cap ratio is doubled:
H.-S. Lee & M.H. Perrott
MIT OCW
Creating a Single-Ended Output
Io
I1 I2
M1
M2
vin
M1
vin
Vbias
2Ibias
ƒ
ƒ
ƒ
M2
Vbias
Ibias
Ibias
Input voltage is again dropped across two transistors
- Ratio given by voltage divider in capacitance
ƒ 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 C
gs
of M1
Currents of each device add to ideally yield ratio:
H.-S. Lee & M.H. Perrott
MIT OCW
Creating the Bias for M2
M1
M2
vin
Vbias
ƒ
M1
M1
vin
2Ibias
Io
Io
I1 I2
M2
Vbias
Ibias
Ibias
vin
Vbias
M2
M3
Ibias
Use current mirror for bias (Battjes ft doubler)
- Inspired by bipolar circuits (see Tom Lee’s book, pp288290 (197-199))
ƒ
Need to set Vbias such that current through M1 has the
desired current of Ibias
- The current through M
2
H.-S. Lee & M.H. Perrott
will ideally match that of M1
MIT OCW
Problems of ft Doubler in Modern CMOS RF Circuits
ƒ
Problems:
Works if Cgs dominates capacitance , but in modern
CMOS, this is not the case (for example, Cgd=0.45Cgs in
0.18 µ CMOS)
achievable bias voltage across M1 (and M2) is severely
reducedby 2x!) (thereby reducing effective ft of device)
Input capacitance degrades due to Cgs, Cdb of M3: at most
1.5x improvement in transconductance/capacitance ratio
-
Assuming zero Cdb:
H.-S. Lee & M.H. Perrott
MIT OCW
Increasing Gain-Bandwidth Product Through Cascading
vin
Amp
Amp
Cfixed
vin
ƒ
A
1 + s/wo
Amp
vout
Cfixed
A
1 + s/wo
vout
A
1 + s/wo
We can significantly increase the gain of an amplifier
by cascading n stages
- Issue – bandwidth degrades, but by how much?
H.-S. Lee & M.H. Perrott
MIT OCW
Analytical Derivation of Overall Bandwidth
ƒ
The overall 3-db bandwidth of the amplifier is where
- w is the overall bandwidth
- A and w are the gain and bandwidth of each section
1
o
- Bandwidth decreases much slower than gain increases
ƒ Overall gain bandwidth product of amp can be increased
H.-S. Lee & M.H. Perrott
MIT OCW
Transfer Function for Cascaded Sections
Normalized Transfer Function for Cascaded Sections
0
-3
-10
n=1
Normalized Gain (dB)
-20
-30
n=2
-40
-50
n=3
-60
-70
-80
1/100
H.-S. Lee & M.H. Perrott
n=4
1/10
1
Normalized Frequency (Hz)
10
100
MIT OCW
Choosing the Optimal Number of Stages
ƒ
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
ƒ
We found that the overall bandwidth is calculated as
ƒ
Assume that we want to achieve gain G with n stages
ƒ
From this, optimum gain/stage ≈ sqrt(e) = 1.65
See Tom Lee’s book, pp 299-302 (207-211,1
H.-S. Lee & M.H. Perrott
st
ed.)
MIT OCW
Achievable Bandwidth Versus G and n
Achievable Bandwidth (Normalized to ω
f tu)
Versus Gain (G) and Number of Stages (n)
ƒ
0.3
- Note than gain
per stage derived
from plot as
0.25
G=10
0.2
G=100
w1/wt
ω1
ωu
0.15
- Maximum is fairly
G=1000
ƒ
A=1.65
0.1
A=3
0.05
0
Optimum gain per
stage is about 1.65
0
5
10
H.-S. Lee & M.H. Perrott
15
n
20
25
soft, though
Can dramatically
lower power (and
improve noise) by
using larger gain
per stage
30
MIT OCW
Motivation for Distributed Amplifiers
RL=Z0
vout
M1
Rs=Z0
Cin
M2
Cin
Cout
Cout
Cout
M3
Cin
vin
ƒ
We achieve higher gain for a given load resistance by
increasing the device size (i.e., increase gm)
- Increased capacitance lowers bandwidth
ƒ We therefore get a relatively constant gain-bandwidth product
ƒ
We know that transmission lines have (ideally) infinite
bandwidth, but can be modeled as LC networks
- Can we lump device capacitances into transmission line?
H.-S. Lee & M.H. Perrott
MIT OCW
Distributing the Input Capacitance
RL=Z0
vout
delay
Rs=Z0
Zo
Cout
Cout
Cout
M1
M2
M3
Zo
Zo
Zo
vin
ƒ
RL=Z0
Lump input capacitance into LC network corresponding
to a transmission line
- Signal ideally sees Z =R rather than an RC lowpass
- Often implemented as lumped networks such as T-coils
- We can now trade delay (rather than bandwidth) for gain
o
ƒ
L
Issue: outputs are delayed from each other
H.-S. Lee & M.H. Perrott
MIT OCW
Distributing the Output Capacitance
delay
RL=Z0
RL=Z0
Zo
delay
Rs=Z0
vin
Zo
Zo
Zo
Zo
M1
M2
M3
Zo
Zo
Zo
vout
RL=Z0
ƒ
Delay the outputs same amount as the inputs
ƒ
ƒ
Benefit – high bandwidth
Negatives – high power, poorer noise performance,
expensive in terms of chip area
- Now the signals match up
- We have also distributed the output capacitance
Each transistor gain is adding rather than multiplying!
H.-S. Lee & M.H. Perrott
MIT OCW
Narrowband Amplifiers
package
die
Connector
Controlled Impedance
PCB trace
Matching
Network
Driving
Source
Z1
On-Chip
Delay = x
Characteristic Impedance = Zo
Transmission Line
Vin
ƒ
L1
Matching
Network
Amp
C1
C2
RL
Vout
VL
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
ƒ
Can we take advantage of this fact when designing
the amplifier?
H.-S. Lee & M.H. Perrott
MIT OCW
Tuned Amplifiers
Vdd
LT
RL
vout
CL
vin
Rs
M1
Vbias
ƒ
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
ƒ
To see this and other design issues, we must look
closer at the parallel resonant circuit
H.-S. Lee & M.H. Perrott
MIT OCW
Tuned Amp Transfer Function About Resonance
Cp
iin=gmvin
Lp Rp
Ztank
ƒ
Amplifier transfer function
ƒ
Note that conductances
add in parallel
vout
ƒ
Evaluate at s = jω
ƒ
Look at frequencies about resonance:
H.-S. Lee & M.H. Perrott
MIT OCW
Tuned Amp Transfer Function About Resonance (Cont.)
ƒ
From previous slide
=0
ƒ
Simplifies to RC circuit for bandwidth calculation
vout
vin
Cp
Lp Rp
vout
g mR p
1
R pC p
slope =
-20 dB/dec
wo
iin=gmvin
w
Ztank
H.-S. Lee & M.H. Perrott
1
Rp2Cp
1
Rp2Cp
MIT OCW
Comparison between Low-Pass and Band-Pass
low-pass
amplifier
band-pass
(tuned)
amplifier
H.-S. Lee & M.H. Perrott
MIT OCW
Comparison between Low-Pass and Band-Pass
ƒ
ƒ
ƒ
ƒ
Tuned amplifier characteristic is a frequency
translated version of the low-pass amplifier
The band-pass bandwidth is equal to the low-pass
bandwidth (the band-pass shape is 2x narrower but
upper and lower sidebands give the same bandwidth
as LP)
We are tuning out the effect of capacitor (parallel LC
looks like an open circuit at resonance, so C doesn’t
load the amplifier)
This is often called low-pass to band-pass transform
in filter design:
- Replace C with parallel LC tank
- Replace L with series LC tank
H.-S. Lee & M.H. Perrott
MIT OCW
Gain-Bandwidth Product for Tuned Amplifiers
vout
vin
Cp
Lp Rp
vout
g mR p
1
R pC p
slope =
-20 dB/dec
wo
iin=gmvin
w
Ztank
1
Rp2Cp
1
Rp2Cp
ƒ
The gain-bandwidth product:
ƒ
The above expression is just like the low-pass and
independent of center frequency!
- In practice, we need to operate at a frequency less than
the ft of the device
H.-S. Lee & M.H. Perrott
MIT OCW
The Issue of Q
vout
vin
Cp
Lp Rp
vout
g mR p
1
R pC p
slope =
-20 dB/dec
wo
iin=gmvin
w
Ztank
ƒ
By definition
ƒ
For parallel tank
ƒ
Comparing to above:
H.-S. Lee & M.H. Perrott
1
Rp2Cp
1
Rp2Cp
MIT OCW
Design of Tuned Amplifiers
vout
vin
Cp
Lp Rp
g mR p
vout
1
R pC p
slope =
-20 dB/dec
wo
iin=gmvin
ƒ
w
Ztank
1
Rp2Cp
1
Rp2Cp
Three key parameters
- Gain = g R
- Center frequency = ω
- Q = ω /BW
Impact of high Q
- Benefit: allows achievement of high gain with low power
- Problem: makes circuit sensitive to process/temp
m
p
o
ƒ
o
variations
H.-S. Lee & M.H. Perrott
MIT OCW
Issue: Cgd Can Cause Undesired Oscillation
Vdd
LT
RL
vout
CL
Zin C
gd
vin
Vbias
ƒ
M1
Rs
Cgs
At frequencies below resonance, tank looks inductive
Negative
Resistance!
H.-S. Lee & M.H. Perrott
MIT OCW
Use Cascode Device to Remove Impact of Cgd
Vdd
LT
RL
vout
Vbias2
M2
Zin C
gd
vin
ƒ
M1
Rs
Vbias
CL
Cgs
At frequencies above and below resonance
Purely
Capacitive!
H.-S. Lee & M.H. Perrott
MIT OCW
Neutralization in Tuned Amplifier
Recall the neutralization for broadband amplifier
RL
CN
-1
Zin
vin
Vbias
Id
Cgd
M1
Rs
vout
CL
Cgs
For narrowband amplifier, the inverting signal can
be generated by a tapped transformer
H.-S. Lee & M.H. Perrott
MIT OCW
Neutralization with Tapped Transformer
Problems: Area and quality of on chip transformer
The neutralization cap CN must be matched to Cgd
H.-S. Lee & M.H. Perrott
MIT OCW
Differential Neutralization for Narrow Band Amplifier
ƒ
ƒ
Same principle as differential neutralization in broadband
amp
Only issue left is matching CN to Cgd
- Often use lateral metal caps for C
H.-S. Lee & M.H. Perrott
N
(or CMOS transistor)
MIT OCW
Superregenerative Amplifier
quench
Vin is sampled at the rate fc (in actual implementation fc may
be input level dependent)
The sampled output voltage
Can be used for both broadband and narrowband – we’ll do a simple
analysis for broadband amp.
H.-S. Lee & M.H. Perrott
MIT OCW
Superregenerative Amplifier
Gain calculation
Nyquist theorem
Trades bandwidth only logarithmically with gain!
H.-S. Lee & M.H. Perrott
MIT OCW
Superregenerative Amplifier Example (Narrowband)
RB: DC bias resistor
LC, C1: Tuning LC
C2 : positive feedback
LE: RF choke (large inductance)
•When the RF amplitude becomes large, it is rectified at the emitter of Q1
•This raises the DC potential at the emitter Q1 eventually turning it off
•The RF oscillation dies (quenched), and the DC potential at emitter of Q1
returns
•Amplitude of oscillation grows again due to positive feedback
H.-S. Lee & M.H. Perrott
MIT OCW
Active Real Impedance Generator
Zin
Vin
ƒ
Cf
Av(s)
Vout
Av(s) = -Aoe-jΦ
Input admittance:
Resistive component!
H.-S. Lee & M.H. Perrott
MIT OCW
This Principle Can Be Applied To Impedance Matching
Zin
Iout
vin
M1
Rs
Ls
Vbias
ƒ
We will see that it’s advantageous to make Zin real
without using resistors
- For the above circuit (ignoring C
gd)
Itest
Vtest C
gs
vgs
gmvgs
Ls
H.-S. Lee & M.H. Perrott
Looks like series resonant circuit!
MIT OCW
Use A Series Inductor to Tune Resonant Frequency
Zin
Zin
Iout
Iout
Lg
vin
M1
Rs
vin
Ls
Vbias
Rs
Vbias
M1
Ls
ƒ
Calculate input impedance with added inductor (in
order to choose resonance freq. and input resistance
separately)
ƒ
Often want purely resistive component at frequency ωo
- Choose L
g
H.-S. Lee & M.H. Perrott
such that resonant frequency = ωo
MIT OCW
Narrowband Alternative to LC
ƒ
On-chip inductors take up considerable die area and have
relatively poor Q. Is there any other alternatives?
ƒ
Use quarter-wavelength transmission line (waveguide) resonator?
In Lecture 5 we found the λ/4 waveguide with shorted load behave much like
a parallel LC circuit, while with open load it behaves like a series LC
The problem is the dimension. For 900MHz mobile phone frequency, λ/4 in
free space is 3.25 inches!
With high permittivity dielectric material (ceramic), the size can be reduced
to a reasonable dimensions. With εr=10, the length of waveguide is only
about inch.
Different configurations of filters can be built by combining sections of
series and parallel LC equivalents
More appropriate at frequencies over GHz
SAW (Surface Acoustic Wave) filters are another popular
alternative
H.-S. Lee & M.H. Perrott
MIT OCW
SAW Filters
ƒ
SAW filters use piezoelectric substrate to generate surface
acoustic wave
electrodes
input
output
piezoelectric
substrate
λ
H.-S. Lee & M.H. Perrott
Adapted from Japan Radio Co.
MIT OCW
SAW Filters
ƒ
ƒ
Piezoelectric substrate
LiTaO3
LiNbO3
Quartz
Filter Structures
Longitudinal Filter
Transversal Filter
Ladder Filter
-
ƒ
Saw filters have high selectivity and low insertion loss (down to
a fraction of % fractional bandwidth, ~2dB insertion loss
ƒ
Wide range of enter frequency (few 100 kHz-GHz)
ƒ
ƒ
At 1-2 GHz, the dimensions of SAW filters are 1-2mm
For more information on SAW filters look over www.njr.com
H.-S. Lee & M.H. Perrott
MIT OCW
SAW Filters in Mobile Phones
BPF
Mixer
BPF
RX
IF Detection
IF Amp
OSC
(1)
RF Amp
Buff Amp
ANT
Ant. SW
Buff Amp
OSC
(2)
BPF
BPF
TX
Mixer
Buff Amp
Power Amp
Figure by MIT OCW.
H.-S. Lee & M.H. Perrott Adapted from Japan Radio Co.
MIT OCW
Insertion Loss [dB]
SAW Filter Example
0
5
0
1
10
2
15
3
20
4
25
5
30
6
35
7
40
8
45
50
9
10
2200
2450
2700
Frequency [MHz]
Figure by MIT OCW.
JRC NSVS754 2.4 GHz RF SAW Filter Charactersitic
H.-S. Lee & M.H. Perrott
Adapted from Japan Radio Co.
MIT OCW
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