Lecture 4, Noise. Noise and distortion


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1 Lecture 4, Noise Noise and distortion
2 What did we do last time? Operational amplifiers Circuitlevel aspects Simulation aspects Some terminology Some practical concerns Limited current Limited bandwidth etc 113 of 34
3 What will we do today? Noise Circuit noise Thermal noise Flicker noise Distortion What sets the (non)linearity in our CMOS devices? 114 of 34
4 The "741 amplifier" Texas instruments opa what is the bandwidth? opa what is the DC gain? Analog Devices AD854x  what is the DC gain, or what is the openloop bandwidth? 115 of 34
5 Operational amplifier architectures Leftovers Examples Telescopic Twostage Foldedcascode Currentmirror Essentially just cascaded stages of different kinds 116 of 34
6 Telescopic OTA Stack many cascodes on top of eachother and use gainboosting, etc. Omitted, since it is not applicable for modern processes. The swing is eaten up. 117 of 34
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9 Foldedcascode OP/OTA V b,1 V b, V out, p V b,3 CL V b,4 M3 M4 M6 M9 M 11 M7 V i n,n M1 M V in,p V b,5 M5 M8 M 10 V b, V out, n V b,3 CL V b,4 10 of 34
10 OP/OTA Compilation Cookbook recipes Handouts with stepbystep explanation of the design of OP/OTAs NN_LN_opampHandsouts_A.pdf Compensation techniques NN_LN_opampCompensationTable_A.pdf 11 of 34
11 Amplifier classes Not really covered in this course. Different classes, such as Class A, B, AB, C, D, E, F, G, H, I, K, S, T, Z, etc. Class A Essentially the commonsource stage Class AB Essentially a pushpull configured class A 1 of 34
12 Noise Any circuit has noise and you, as a designer, have to reduce it or minimize the impact of it "A disturbance, especially a random and persistent disturbance, that obscures or reduces the clarity of a signal." Consequences We need to use stochastic variables and power spectral densities, expectation values, etc. We need to make certain assumptions (models) of our noise sources in order to calculate 13 of 34
13 Superfunction and spectral densitites Power spectral density (PSD) Superfunction S 0 f = Ai f S i f Total noise V tot = v n f df Brickwall noise p1 V =v 0 4 tot n 14 of 34
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15 Flicker noise, 1/fnoise, pink noise Resistor bias v k and i = R v n v= n W L f n Transistor S f 1 C ox W L f KF 1 v = and i d = g m v n C ox W L f g KF 4kT gm log f 16 of 34
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19 Noise compiled in one example, cont'd The general transfer function to the output is given by V n, out f = gn gp v f G n f v f G p f s C L g p g n Insert the values mn V n, out f =4 k T mp g g g mn g mp s g p g n g p g n 1 CL g mn g mp =4 k T g p g n s g p g n 1 CL 130 of 34
20 Noise compiled in one example, cont'd Use the brickwall approach p1 V = V f =V 0 4 g mn g mp g p g n k T g mn g mp V n, tot =4 k T = CL g p g n g p g n 4C L n, tot n, out n, out Conclude V n, tot g mp kt = A0 1 CL g mn kt/c noise! 131 of 34
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22 The commonsource example Inputreferred noise V n,i n [ f = 4 k T g mn g mp g p g n s 1 g p g n CL [ ] ] s 1 g p g n CL g mn g p g n g mp 4kT = 1 g mn g mn 133 of 34
23 What does this mean? Bias transistor should be made with low transconductance! Visible from the formula Gain transistors should be made with high transconductance! Visible from the formula Gain should be distributed between multiple stages (Friis) Left as an exercise 134 of 34
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25 Example from "741" opamp OPA336N (Texas Instruments) Input Voltage Noise, f = 0.1 to 10 Hz Input Voltage Noise Density, f = 1 khz Current Noise Density, f = 1 khz 3 μvpp (e n ) (i n ) 40 nv/ Hz 30 fa/ Hz 136 of 34
26 Example from "741" opamp 137 of 34
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28 Noise in OP, example cont'd PSD 1 S n ( f )= j π f RC A nasty transfer function  the noise never reaches zero! Practically The opamp unitygain bandwidth will bandlimit the noise for which we can use the brickwall approach: P tot, op v n, op ωug (0) of 34
29 Noise in OP, example cont'd The noise sources, resistors V s V s 1 1 = = and V r s 1 s RC V r1 s 1 s RC PSD 1 S n ( f )= 1+ j π f RC A lowpass filter response  use the brickwall approach 1/ RC P tot, R v n, R (0) of 34
30 Noise in OP, example cont'd Combined P tot =P tot, R+P tot, op v P tot v n, op n, op ωug 1/ RC (0) + v n, R (0) 4 4 ωug ωug k T 1/ RC (0) +4 k T R =v n, op (0) + C This is the power normalized over 1 Ohm We could define the rms voltage as: v o, rms= P tot v n, op ωug k T (0) + C 141 of 34
31 Noise in OP, example cont'd, values Example: C =1 nf, R=10 kohm, i.e., a bandwidth of f bw 14 khz OPA336: v n, op (0) sqv/hz, and f ug 100 khz P tot = or v o, rms 9.4 uv (compare with the reported 3 uv in the data sheet) 14 of 34
32 Signaltonoise ratio (SNR) At the output of our system, we will have a certain signal power. The signaltonoise ratio (SNR) determines the quality of the system: P sig v s, rms P sig or SNR=10 log 10 or SNR=0 log 10 SNR= P noise v n, rms P noise ( ) ( ) OPA336 example Assume signal swing at output is v rms =1 V. Then the SNR is SNR 0 log10 ( db (approximately 16 bits) ) 143 of 34
33 Distortion Frequencydomain measures Spuriousfree dynamic range, SFDR Harmonic distortion, HD Signaltonoiseanddistortion ratio, SNDR Amplitude domain measures Compression (clipping) Offset 144 of 34
34 Distortion No circuit is fully linear Y = 0 1 X X 3 X 4 X Example X =sin t is the sinusoidal, steadystate signal 1=1, =0.01 are the characteristic coefficients of the system Results in an output as 1 cos ω t Y (t )=sin ω t +α sin ω t =sin ω t +α 145 of 34
35 Distortion, cont'd Results in a DC shift and a distortion term Y= sin t cos t desired DC shift distortion Harmonic distortion 1 1 HD = = =40000, ( α / ) (0.01/ ) i.e., approximately 46 db 146 of 34
36 Frequency domain measures 147 of 34
37 Distortion, fully differential circuits Assume distortion is identical in two branches 3 4 Y p= 0 1 X p X p 3 X p 4 X p 3 and 4 Y n= 0 1 X n X n 3 X n 4 X n Difference Y =Y p Y n= X p X n X p X n Further on, assume input is already OK X p = X n= X 148 of 34
38 Distortion, fully differential, cont'd Results in Y = 1 X p X p X p X p 3 X 3p X p 3 and eventually 3 Y = 1 X X 3 4 Evenorder terms disappear! 149 of 34
39 Distortion in a commonsource Assume a commonsource stage with resistive load Firstorder model I D = V eff RL V out =V DD R I D =V DD R V eff V out Assume a limited input signal (no clipping) V in V eff t =V eff0 V x sin t Form the output V out t =V DD R V eff0 V x sin t V out (t )=V DD R α ( V eff0 +V eff0 V x sin ω t+v x sin ωt ) 150 of 34
40 Distortion in a commonsource, cont'd Continue to rewrite using trigonometrics V x V out (t )=V DD R α V eff0 + V eff0 V x sin ω t + (1 cos ω t ) ( ) Analyze V V x V out (t )=V DD R α V eff0 + x + V V R α sin ω t cos ω t eff0 x DC desired signal distortion 151 of 34
41 Compression analysis Signal power scales "linearly" with amplitude V V x V out (t )=V DD R α V eff0 + x + V V R α sin ω t cos ω t eff0 x desired signal DC distortion Distortion power scales "quadratically" At some point they will meet. Intercept points Output and inputreferred IIP, OIP Common measures of nonlinearity 15 of 34
42 Distortion vs Noise, concludingly High signal power gives high signaltonoise ratio High signal power gives low signaltodistortion ratio This means that you need to distribute the gain between the different stages accordingly and tradeoff between the two. 153 of 34
43 What did we do today? Noise Circuit noise Thermal noise Flicker noise Distortion What sets the (non)linearity in our CMOS devices? 154 of 34
44 What will we do next time? PCB vs silicon What are the differences when scaling up the geometries Components Surfacemounted components PCB Some PCB specifics 155 of 34
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