6.776 High Speed Communication Circuits and Systems Lecture 12 Low Noise Amplifiers
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6.776 High Speed Communication Circuits and Systems Lecture 12 Low Noise Amplifiers Massachusetts Institute of Technology March 15, 2005 Copyright © 2005 by Hae-Seung Lee and Michael H. Perrott Narrowband LNA Design for Wireless Systems Zin From Antenna and Bandpass Filter PC board trace To Mixer Package Interface Zo LNA Design Issues - Noise Figure – impacts receiver sensitivity - Linearity (IIP3) – impacts receiver blocking performance - Gain – high gain reduces impact of noise from components that follow the LNA (such as the mixer) - Power match – want Z = Z (usually = 50 Ohms) - Power – want low power dissipation - Bandwidth – need to pass the entire RF band for the intended radio application (i.e., all of the relevant channels) - Sensitivity to process/temp variations – need to make it in o manufacturable in high volume H.-S. Lee & M.H. Perrott MIT OCW Our Focus in This Lecture Zin From Antenna and Bandpass Filter PC board trace Zo To Mixer Package Interface LNA Designing for low Noise Figure Achieving a good power match Hints at getting good IIP3 Impact of power dissipation on design Tradeoff in gain versus bandwidth H.-S. Lee & M.H. Perrott MIT OCW Direct Input Termination of CS Amplifier For power match, terminate the input of CS amplifier Voltage gain is halved Termination resistor adds thermal noise More appropriate for broadband than narrowband (maybe) H.-S. Lee & M.H. Perrott MIT OCW Noise Factor (Low Frequency) Noise factor at low frequencies (thus ignoring gate current noise) looking at short-circuit output current Noise factor too high even at low frequencies. Generally not an acceptable circuit for LNA H.-S. Lee & M.H. Perrott MIT OCW Common-Gate Amplifier Offers the possibility of power match without an explicit termination resistor For power match, make At low frequencies, it can be shown Better than the CS, but noise factor degrades significantly at high frequencies H.-S. Lee & M.H. Perrott MIT OCW Noise Factor Analysis of CG Amp (Low Freq.) Equivalent Circuit H.-S. Lee & M.H. Perrott MIT OCW Noise Factor Calculation Noise factor at low frequencies (thus ignoring gate current noise) looking at short-circuit output current First calculate the output noise due to the source resistance only (en) using voltage divider: The next step is finding the total output noise due to en and id. We can use superposition as before. H.-S. Lee & M.H. Perrott MIT OCW Noise Factor Calculation, Continued First, let’s compute output noise due to id only. We’ll need to use the instantaneous value of id for now: The instantaneous value of the output noise due to id The mean-square value of the output noise due to id H.-S. Lee & M.H. Perrott MIT OCW Noise Factor of CG Amplifier For power match, 1/gm=Rs This may be o.k. for broadband amplifiers. For narrowband amplifiers, we can improve the noise factor considerably while maintaining power match: inductors! H.-S. Lee & M.H. Perrott MIT OCW Inductor Degenerated CS Amp Source inout Rs ens Lg Zgs Cgs gmvgs indg Ldeg Source Rs vgs Iout Lg M1 vin Ldeg Vbias Same as amp in Lecture 10 except for inductor degeneration - Note that noise analysis in Tom Lee’s book does not include inductor degeneration (i.e., Table 12.1 (11.1)) H.-S. Lee & M.H. Perrott MIT OCW Recall Small Signal Model for Noise Calculations iout D Iout G D G S Zg Zg Zgs vgs Cgs gmvgs indg Zdeg S Zdeg H.-S. Lee & M.H. Perrott MIT OCW Key Assumption: Design for Power Match Zin Iout Lg vin Rs Vbias M1 Ldeg Real =RT Input impedance (from Lec 9) Set to achieve pure resistance = Rs at frequency ωo Adding Lg gives additional degree of freedom to set ωo and RT independently H.-S. Lee & M.H. Perrott MIT OCW Key Assumption: Design for Power Match Zin Iout Lg vin Vbias Rs M1 Ldeg The total impedance of the RLC circuit (including the source resistance) Thus Q is then H.-S. Lee & M.H. Perrott Rs MIT OCW Process and Topology Parameters for Noise Calculation Source inout Rs ens Lg Zgs vgs Cgs gmvgs indg Ldeg Process parameters Circuit topology parameters Zg and Zdeg - For 0.18µ CMOS, we will assume the following H.-S. Lee & M.H. Perrott MIT OCW Calculation of Zgs Source inout Rs ens Lg Zgs vgs Cgs gmvgs indg Ldeg H.-S. Lee & M.H. Perrott MIT OCW Calculation of η Source inout Rs ens Lg Zgs vgs Cgs gmvgs indg Ldeg = Rs H.-S. Lee & M.H. Perrott MIT OCW Calculation of Zgsw By definition Calculation H.-S. Lee & M.H. Perrott MIT OCW Calculation of Output Current Noise Step 3: Plug in values to noise expression for indg H.-S. Lee & M.H. Perrott MIT OCW Compare Noise With and Without Inductor Degeneration Source inout Rs ens Lg Zgs vgs Cgs gmvgs indg Ldeg From Lecture 10, we derived for Ldeg = 0, ωo2 = 1/(LgCgs) We now have for (gm/Cgs)Ldeg = Rs, ωo2 = 1/((Lg + Ldeg)Cgs) H.-S. Lee & M.H. Perrott MIT OCW Derive Noise Factor for Inductor Degenerated Amp Source inout Rs ens Lg Zgs vgs Cgs gmvgs indg Ldeg Recall the alternate expression for Noise Factor derived in Lecture 11 We now know the output noise due to the transistor noise - We need to determine the output noise due to the source resistance H.-S. Lee & M.H. Perrott MIT OCW Output Noise Due to Source Resistance Source inout Rs ens Lg Zin Zgs vgs Cgs gmvgs indg Ldeg H.-S. Lee & M.H. Perrott MIT OCW Noise Factor for Inductor Degenerated Amplifier Noise Factor scaling coefficient H.-S. Lee & M.H. Perrott MIT OCW Noise Factor Scaling Coefficient Versus Q Noise Factor Scaling Coefficient Versus Q for 0.18 µ NMOS Device 7 Achievable values as a function of Q under the constraints that 1 = wo (Lg+Ldeg)Cgs gm L = Rs Cgs deg Noise Factor Scaling Coefficient 6.5 6 5.5 5 4.5 c = -j0 4 3.5 3 2.5 1 Note: 1 Q= 2RswoCgs c = -j0.55 c = -j1 1.5 H.-S. Lee & M.H. Perrott 2 2.5 3 Q 3.5 4 4.5 5 MIT OCW Noise Factor Comparison Inductor Degenerated CS Noise Factor scaling coefficient Non degenerated (From Lecture 10) Noise Factor scaling coefficient H.-S. Lee & M.H. Perrott MIT OCW Noise Factor Scaling Coefficient Comparison Noise Factor Scaling Coefficient Versus Q for 0.18 µ NMOS Device Noise Factor Scaling Coefficient Versus Q for 0.18 µ NMOS Device 7 8 Achievable values as a function of Q under the constraints that 1 = wo (Lg+Ldeg)Cgs gm L = Rs Cgs deg 6 5.5 5 7 Noise Factor Scaling Coefficient Noise Factor Scaling Coefficient 6.5 4.5 c = -j0 4 3.5 3 2.5 1 Note: 1 Q= 2RswoCgs c = -j0.55 6 c = -j0 c = -j0.55 5 Achievable values as a function of Q under the constraint that 1 = wo LgCgs c = -j1 c = -j0 4 c = -j0.55 3 Minimum across all values of Q and 1 Note: curves meet if we approximate Q2+1 Q2 2 1 1.5 2 2.5 3 Q 3.5 4 With degeneration H.-S. Lee & M.H. Perrott 4.5 5 0 1 2 3 c = -j1 LgCgs c = -j1 4 5 6 7 8 9 10 Q Without degeneration MIT OCW Achievable Noise Figure in 0.18µ with Power Match Suppose we desire to build a narrowband LNA with center frequency of 1.8 GHz in 0.18µ CMOS (c=-j0.55) - From Hspice – at V gs = 1 V with NMOS (W=1.8µ, L=0.18µ) measured gm =871 µS, Cgs = 2.9 fF - Looking at previous curve, with Q ≈ 1.4 we achieve a Noise Factor scaling coefficient ≈ 3.25 H.-S. Lee & M.H. Perrott MIT OCW Component Values for Minimum NF with Power Match Assume Rs = 50 Ohms, Q = 1.4, fo = 1.8 GHz, ft = 47.8 GHz -C -L -L gs calculated as deg g calculated as calculated as H.-S. Lee & M.H. Perrott MIT OCW Id Vgs M1 1.8µ W = L 0.18µ gm and gdo (milliAmps/Volts) and Vgs (Volts) Have We Chosen a Good Bias Point? (Vgs = 1V) 4.5 Vgs , gm , and gdo versus Current Density for 0.18µ NMOS Chosen bias point is Vgs = 1 V 4 3.5 3 2.5 Lower power Higher power Higher ft Lower ft Lower IIP3 Higher IIP3 gdo gdo Lower g Higher g m m gdo 2 Vgs 1.5 gm 1 0.5 0 0 100 200 300 400 500 600 700 Current Density (microAmps/micron) Note: IIP3 is also a function of Q H.-S. Lee & M.H. Perrott MIT OCW Calculation of Bias Current for Example Design Calculate current density from previous plot Calculate W from HSpice simulation (assume L=0.18 µm) - Could also compute this based on C ox value Calculate bias current - Problem: this is not low power!! H.-S. Lee & M.H. Perrott MIT OCW
