6.776 high speed communication circuits and systems lecture 9 … · 2020-01-04 · -now the...
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6.776High Speed Communication Circuits and Systems
Lecture 9Enhancement Techniques for Broadband Amplifiers,
Narrowband Amplifiers
Massachusetts Institute of TechnologyMarch 3, 2005
Copyright © 2005 by Hae-Seung Lee and Michael H. Perrott
H.-S. Lee & M.H. Perrott MIT OCW
Shunt-Series Peaking
Series inductors isolate load capacitance from M1: delays charging of load capacitanceTrades delay for bandwidthL1, 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
M1
RL
vout
M2
Cfixed
Id
Vbias
vin
Vdd
L1
L2L3
M1
vout
M2
CfixedVbias
vin
L2
L1
CB
k
RL
Vdd
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 loadCB provides parallel resonance to improve bandwidth further See Chap. 9 (Ch. 8, 1st ed.) of Tom Lee’s book pp 279-282 (187-191)
H.-S. Lee & M.H. Perrott MIT OCW
T-Coil Continued
The self inductance L (with the other winding open-circuited) must be
The bridging capacitance
Coupling coefficientk=1/3 for Butterworth responsek=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
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:
H.-S. Lee & M.H. Perrott MIT OCW
Creating a Single-Ended Output
M1 M2
2Ibias
I1 I2
Vbias
vinM1
M2
Ibias
Io
Vbias
vin
Ibias
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 deviceInput 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:
H.-S. Lee & M.H. Perrott MIT OCW
Creating the Bias for M2
M1 M2
2Ibias
I1 I2
Vbias
vinM1
M2
Ibias
Io
Vbias
vin
Ibias
M1
M2
Io
Vbias
vin
IbiasM3
Use current mirror for bias (Battjes ft doubler)- Inspired by bipolar circuits (see Tom Lee’s book, pp288-
290 (197-199))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
H.-S. Lee & M.H. Perrott MIT OCW
Problems of ft Doubler in Modern CMOS RF Circuits
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
Amp Amp
Cfixed
Amp
Cfixed
A1 + s/wo
A1 + s/wo
A1 + s/wo
vin vout
vin vout
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
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 increasesOverall gain bandwidth product of amp can be increased
H.-S. Lee & M.H. Perrott MIT OCW
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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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 stagesWe found that the overall bandwidth is calculated as
Assume that we want to achieve gain G with n stages
From this, optimum gain/stage ≈ sqrt(e) = 1.65- See Tom Lee’s book, pp 299-302 (207-211,1st ed.)
H.-S. Lee & M.H. Perrott MIT OCW
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
ω1ωu
ωu
H.-S. Lee & M.H. Perrott MIT OCW
Motivation for Distributed Amplifiers
M1 M2 M3
vout
vin
Rs=Z0
RL=Z0
Cin CinCin
Cout Cout Cout
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 productWe 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
M1 M2 M3
Zo Zo Zo Zo
vout
RL=Z0
delay
vin
Rs=Z0
RL=Z0
Cout Cout Cout
Lump input capacitance into LC network corresponding to a transmission line- Signal ideally sees Zo=RL 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
H.-S. Lee & M.H. Perrott MIT OCW
Distributing the Output Capacitance
M1
Zo Zo Zo Zo
M2 M3
Zo Zo Zo Zo
RL=Z0
vout
RL=Z0
delay
delay
vin
Rs=Z0
RL=Z0
Delay the outputs same amount as the inputs- Now the signals match up- We have also distributed the output capacitance
Benefit – high bandwidthNegatives – high power, poorer noise performance, expensive in terms of chip area- Each transistor gain is adding rather than multiplying!
H.-S. Lee & M.H. Perrott MIT OCW
Narrowband Amplifiers
VLC1 RL
L1Delay = xCharacteristic Impedance = Zo
Transmission Line
Z1
VinC2
dieConnector
Controlled ImpedancePCB trace
package
On-ChipDrivingSource
AmpVout
MatchingNetwork
MatchingNetwork
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 networksCan we take advantage of this fact when designing the amplifier?
H.-S. Lee & M.H. Perrott MIT OCW
Tuned Amplifiers
M1
vout
CL
Vbias
vinRs
Vdd
LT RL
Put inductor in parallel across RL to create bandpassfilter- It will turn out that the gain-bandwidth product is
roughly conserved regardless of the center frequencyTo 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
Evaluate at s = jω
Look at frequencies about resonance:
RpLpCp
iin=gmvinZtank
vout
Amplifier transfer function
Note that conductancesadd in parallel
H.-S. Lee & M.H. Perrott MIT OCW
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
H.-S. Lee & M.H. Perrott MIT OCW
Comparison between Low-Pass and Band-Pass
low-passamplifier
band-pass(tuned)
amplifier
H.-S. Lee & M.H. Perrott MIT OCW
Comparison between Low-Pass and Band-Pass
Tuned amplifier characteristic is a frequency translated version of the low-pass amplifierThe 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
RpLpCp
iin=gmvinZtank
vout
voutvin
w
slope =-20 dB/dec
gmRp
Rp2Cp
1
wo
Rp2Cp
1
RpCp
1
The gain-bandwidth product:
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
RpLpCp
iin=gmvinZtank
vout
voutvin
w
slope =-20 dB/dec
gmRp
Rp2Cp
1
wo
Rp2Cp
1
RpCp
1
By definition
For parallel tank
Comparing to above:
H.-S. Lee & M.H. Perrott MIT OCW
Design of Tuned Amplifiers
RpLpCp
iin=gmvinZtank
vout
voutvin
w
slope =-20 dB/dec
gmRp
Rp2Cp
1
wo
Rp2Cp
1
RpCp
1
Three key parameters- Gain = gmRp- Center frequency = ωo- Q = ωo/BW
Impact of high Q - Benefit: allows achievement of high gain with low power- Problem: makes circuit sensitive to process/temp
variations
H.-S. Lee & M.H. Perrott MIT OCW
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!
H.-S. Lee & M.H. Perrott MIT OCW
Use Cascode Device to Remove Impact of Cgd
M1
vout
CL
Vbias
vin
CgdZin
Rs
Cgs
Vbias2M2
Vdd
LT RL
At frequencies above and below resonance
PurelyCapacitive!
H.-S. Lee & M.H. Perrott MIT OCW
Neutralization in Tuned Amplifier
Recall the neutralization for broadband amplifier
For narrowband amplifier, the inverting signal can be generated by a tapped transformer
M1
RL
vout
CL
Id
Vbias
vin
CgdZin
Rs
Cgs
-1CN
H.-S. Lee & M.H. Perrott MIT OCW
Neutralization with Tapped Transformer
Problems: Area and quality of on chip transformerThe neutralization cap CN must be matched to Cgd
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Differential Neutralization for Narrow Band Amplifier
Same principle as differential neutralization in broadband ampOnly issue left is matching CN to Cgd- Often use lateral metal caps for CN (or CMOS transistor)
H.-S. Lee & M.H. Perrott 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
Nyquist theorem
Gain calculation
Trades bandwidth only logarithmically with gain!
H.-S. Lee & M.H. Perrott MIT OCW
Superregenerative Amplifier Example (Narrowband)
RB: DC bias resistorLC, C1: Tuning LCC2 : positive feedbackLE: 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
Input admittance:
Zin
Av(s)VoutVin
Av(s) = -Aoe-jΦ
Cf
Resistive component!
H.-S. Lee & M.H. Perrott MIT OCW
This Principle Can Be Applied To Impedance Matching
M1
Vbias
vinRs
Ls
ZinIout
We will see that it’s advantageous to make Zin real without using resistors- For the above circuit (ignoring Cgd)
Ls
vgs gmvgsCgsItest Vtest
Looks like series resonant circuit!
H.-S. Lee & M.H. Perrott MIT OCW
Use A Series Inductor to Tune Resonant Frequency
M1
Vbias
vinRs
Ls
ZinIout
M1
Vbias
vinRs
Ls
ZinIout
Lg
Calculate input impedance with added inductor (in order to choose resonance freq. and input resistance separately)
Often want purely resistive component at frequency ωo- Choose Lg such that resonant frequency = ωo
H.-S. Lee & M.H. Perrott MIT OCW
Narrowband Alternative to LC
On-chip inductors take up considerable die area and have relatively poor Q. Is there any other alternatives?
- 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
SAW filters use piezoelectric substrate to generate surface acoustic wave
electrodes
input output
piezoelectric substrate
λ Adapted from Japan Radio Co.
H.-S. Lee & M.H. Perrott MIT OCW
SAW Filters
Piezoelectric substrate- LiTaO3- LiNbO3- QuartzFilter Structures- Longitudinal Filter- Transversal Filter- Ladder Filter
Saw filters have high selectivity and low insertion loss (down to a fraction of % fractional bandwidth, ~2dB insertion loss
Wide range of enter frequency (few 100 kHz-GHz)
At 1-2 GHz, the dimensions of SAW filters are 1-2mmFor more information on SAW filters look over www.njr.com
H.-S. Lee & M.H. Perrott MIT OCW
SAW Filters in Mobile Phones
ANT
RX
RF Amp
Ant. SW
IF Amp
Buff Amp
IF Detection
OSC(1)
OSC(2)
Buff Amp
Buff Amp Power Amp
TX
BPF
BPFBPF
BPF Mixer
Mixer
Figure by MIT OCW.
Adapted from Japan Radio Co.
H.-S. Lee & M.H. Perrott MIT OCW
SAW Filter Example
JRC NSVS754 2.4 GHz RF SAW Filter Charactersitic
Inse
rtion
Los
s [d
B]
Frequency [MHz]24502200 2700
5045
4035
302520
1510
50
109
87
654
3210
Figure by MIT OCW.
Adapted from Japan Radio Co.