Lecture 4, Noise. Noise and distortion

Transcription

1 Lecture 4, Noise Noise and distortion

2 What did we do last time? Operational amplifiers Circuit-level 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 open-loop bandwidth? 115 of 34

5 Operational amplifier architectures Left-overs Examples Telescopic Two-stage Folded-cascode Current-mirror Essentially just cascaded stages of different kinds 116 of 34

6 Telescopic OTA Stack many cascodes on top of each-other 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 Folded-cascode 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 Hand-outs with step-by-step 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 common-source stage Class AB Essentially a push-pull 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/f-noise, 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 common-source example Input-referred 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 μvp-p (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 unity-gain 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 low-pass 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 Signal-to-noise ratio (SNR) At the output of our system, we will have a certain signal power. The signal-to-noise 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 Frequency-domain measures Spurious-free dynamic range, SFDR Harmonic distortion, HD Signal-to-noise-and-distortion 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, steady-state 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 Even-order terms disappear! 149 of 34

39 Distortion in a common-source Assume a common-source stage with resistive load First-order 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 common-source, 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 input-referred IIP, OIP Common measures of nonlinearity 15 of 34

42 Distortion vs Noise, concludingly High signal power gives high signal-to-noise ratio High signal power gives low signal-to-distortion ratio This means that you need to distribute the gain between the different stages accordingly and trade-off 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 Surface-mounted components PCB Some PCB specifics 155 of 34