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 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 Uses coupled inductors to realize T inductor network 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 The self inductance L (with the other winding opencircuited) must be The bridging capacitance 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 A MOS transistor has ft calculated as ft doubler amplifiers attempt to increase the ratio of transconductance to capacitance M2 vin Vbias We can make the argument that differential amplifiers are ft doublers - Capacitance seen by V - Difference in current: in 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 M2 Vbias Ibias 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 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 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)) 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 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 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 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 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 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/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) 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 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 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? 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 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 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 Delay the outputs same amount as the inputs 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 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 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 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 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 Amplifier transfer function Note that conductances add in parallel vout Evaluate at s = jω Look at frequencies about resonance: H.-S. Lee & M.H. Perrott MIT OCW Tuned Amp Transfer Function About Resonance (Cont.) From previous slide =0 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 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 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 vout vin Cp Lp Rp vout g mR p 1 R pC p slope = -20 dB/dec wo iin=gmvin w Ztank By definition For parallel tank 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 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 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 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 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 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 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 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 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 L g H.-S. Lee & M.H. Perrott such that resonant frequency = ωo 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 H.-S. Lee & M.H. Perrott Adapted from Japan Radio Co. MIT OCW SAW Filters Piezoelectric substrate LiTaO3 LiNbO3 Quartz Filter 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 1-2mm 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
