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Tools .

Tools. Filters Performances. A filter should maintain the signal integrity. A signal does not exist alone. Signal and noise coexist . Data on a signal without a reference to its noise background are MEANINGLESS. Filters Performances. A few performances worth to consider:

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Tools .

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  1. Tools. ESINSA

  2. Filters Performances • A filter should maintain the signal integrity. • A signal does not exist alone. • Signal and noise coexist. • Data on a signal without a reference to its noise background are MEANINGLESS. ESINSA

  3. Filters Performances • A few performances worth to consider: • Transfer function, Impulse and Step Responses, • Total Signal to Noise Ratio (TSNR), Idle Channel Noise (ICN), • Total Harmonic Distortion (THD), • Group Delay, • Gain tracking, Frequency tracking, • Dynamic range, • Non Linear Behavior, • Power efficiency, etc.. ESINSA

  4. Tools • The preferred way is to evaluate the filters performances is • to simulate in the TIME DOMAIN,to analyze in TIME and FREQUENCY DOMAINS. • Electrical Simulations: SPICE, .. • System Simulations: C, VHDL, .. • Mathematica, MatLab, .. • Dedicated Simulators: SwitCap, .. ESINSA

  5. How to simulate? • Digital Filters are the simplest to simulate. • Analog Filters in the sampled domain are also easy to simulate, if the sampling is rigorously periodic. Jitter is causing a mathematical nightmare. • Analog Filters in the continuous time domain are tricky to simulate. • Master the sampling techniques. • Be an expert in FFT and data windowing. • Be a guru of the decimation and interpolation. ESINSA

  6. Test Signals. ESINSA

  7. Non Linearities In principle, linear theory does not apply. For fairly linear circuits (*), we will suppose it applies! (*) signal not ‘too’ large! No transfer function exists in a non linear circuit. Nothing is granted. The test signals are important. ESINSA

  8. Test Signals All partners must agree on the test conditions! Several test signals are often used. Sinewave, step and impulse are the most classical and described in theorical books. We will see that other test signals are useful. A test signal should exercise an IC in such a way that the user should have no surprise in the real applications with real signals. Tough. ESINSA

  9. a b d c A Few Test Signals (time) ESINSA

  10. dB dB dB dB Same Test Signals (frequency) ESINSA

  11. a a a a Same Test Signals (histogram) ESINSA

  12. Pseudo RandomUniformly DistributedNoise Pseudo RandomNormally DistributedNoise Pseudo RandomCoherent PeriodicNoise CoherentSinewave Same Test Signals ESINSA

  13. Sinewave. 0 dB ref = 1.0V RMS 1.5 1 0.5 1.000 V peak-3.010 dB RMS 0 -0.5 -1 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 ESINSA current time

  14. 0 -6.030042 dB ?? dB -20 Signal -40 -60 -80 Signal leakage -100 -120 -140 -160 -180 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 freq (FFT) 0 dB ref = 1.0V RMS ESINSA

  15. -6.030042 dB 1230 1240 (FFT Zoom) 0 dB ref = 1.0V RMS 0 dB -20 Signal = -3.010 dB -40 -60 Signal leakage -80 FFT resolution = 1Hz -100 -120 Window resolution? -140 -160 1200 1210 1220 1250 1260 ESINSA freq

  16. 1.5 1 0.5 0 -0.5 -1 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 current time Gaussian Noise 0 dB ref = 1.0V RMS 1.000 V RMS 0.000 dB RMS (Bandwidth 500.0 kHz) ESINSA

  17. -45 dB -50 -55 -60 -65 -70 -75 -80 -85 -90 -95 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 freq (FFT) 0 dB ref = 1.0V RMS Power [0..5kHz] = -20.011dB ESINSA

  18. FFT resolution = 1Hz (FFT Zoom) 0 dB ref = 1.0V RMS -45 dB -50 -55 -60 -65 -70 -75 -80 Power [0..5kHz] = -20.011dB -85 -90 1200 1210 1220 1230 1240 1250 1260 ESINSA freq

  19. 0 dB -20 -40 -60 -80 -100 -120 0 500 1000 1500 2000 2500 3000 freq Lesson learned: Document! 0 dB reference? Windowing? FFT Resolution? ESINSA

  20. TSNR and THD • Sinewave at input, FFT on output. • Evaluate at the output: • the power of the fundamentalthe power of the harmonicsthe power of the noise • SNR is the ratio between signal and noise • TSNR is the ratio between signal and (noise + harmonics) • THD is the ratio between signal and harmonics ESINSA

  21. TSNR and THD Method 1: Frequency Domain Analysis Method 2: Time Domain Analysis ESINSA

  22. Example 1.0 V peak Sinewave @ 1234.5 Hz 1.0 V RMS normally distributed noise, BW=500kHz Fsampling = 1.0 MHz Evaluation on 1 000 000 points ESINSA

  23. 0 dB -10 -20 -30 -40 -50 -60 -70 -80 -90 -100 -110 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 freq TSNR [ method 1 ] 0 dB ref = 1.0V RMS ESINSA

  24. TSNR [ method 1 ] And the result is… Power of Fundamental: -2.999184 dB - 3 dB Power of Noise [0..5 kHz]: -20.09885 dB -20 dB TSNR [0..5 kHz]: 17.09967 dB 17 dB ESINSA

  25. TSNR [ method 2 ] Sinewave at input, Linear Curve Fitting on output. Output signal must be prefiltered as it is not possible to limit otherwise the bandwidth of analysis. • Residue0 = Signal • with k = 0..HFitk = rk * Sin[k  t + k] • Residuek+1 = Residuek - Fitk • Fundamental = r1 • Harmonics = Sqrt[(r2)2 + .. + (rH)2] • Noise = Power_of[ResidueH+1] ESINSA

  26. TSNR [ method 2 ] 4 output 3 2 1 0 -1 -2 -3 -4 0 0.0005 0.001 0.0015 0.002 0.0025 ESINSA time

  27. 4 output best Fit 3 2 1 0 -1 -2 -3 -4 0 0.0005 0.001 0.0015 0.002 0.0025 time TSNR [ method 2 ] ESINSA

  28. TSNR [ method 2 ] And the result is… TSNR [0..500 kHz]: -2.999201 dB -3 dB OK! Data are not filtered! ESINSA

  29. THD [ method 2 ] 1.0 V peak Sinewave @ 1234.5 Hz 0.2 V peak Sinewave @ 2469.0 Hz 1.0 V RMS normally distributed noise, BW=500kHz Fsampling = 1.0 MHz Evaluation on 100 000 points ESINSA time

  30. 5 output 4 3 2 1 0 -1 -2 -3 -4 -5 0 0.0005 0.001 0.0015 0.002 0.0025 THD [ method 2 ] ESINSA time

  31. 5 output residue 4 best fit 3 2 1 0 -1 -2 -3 -4 -5 0 0.0005 0.001 0.0015 0.002 0.0025 time THD [ method 2 ] ESINSA

  32. 5 output fundamental 4 harmonics 2 3 2 1 0 -1 -2 -3 -4 -5 0 0.0005 0.001 0.0015 0.002 0.0025 time THD [ method 2 ] ESINSA

  33. THD [ method 2 ] And the result is… SNR: -3.082609 dB -3 dB SDR: 13.95151 dB 14 dB THD: 4 % ESINSA

  34. Dynamic Range Running the TSNR analysis for a set of sinewaves with various amplitudes allows to determine the dynamic range. An example on a Sigma-Delta Converter. ESINSA

  35. Dynamic Range Analog Sigma Delta Modulator 120 tsnr 100 140 dB 80 120 dB 100 dB 60 80 dB 60 dB 40 40 dB 20 20 dB 0 -80 -70 -60 -50 -40 -30 -20 -10 0 ESINSA Amplitude (output)

  36. Transfer Function • White noise at input, FFT on input and output, RMS Average! • avg[FFT( in) . FFT(out)*] • TF = ------------------------- • avg[FFT( in) . FFT( in)*] • for a ‘fairly’ linear circuit. ESINSA

  37. Biquadratic Filter, statistical study, Sigma = 0.05 10 mag 0 -10 -20 -30 -40 -50 -60 -70 1000 10000 100000 1e+006 freq Transfer Function ESINSA

  38. Impulse Response • White noise at input, FFT on input and output, RMS Average! • Iresp = IFFT(TF) • for a ‘fairly’ linear circuit. ESINSA

  39. Impulse Response Nyquist FIR Filter, 365 coefficients 0.07 impulse response 0.06 FIR coefficients ... h[174] 0.037855 h[175] 0.044183 h[176] 0.050129 h[177] 0.055516 h[178] 0.060176 h[179] 0.063964 h[180] 0.066760 h[181] 0.068475 h[182] 0.069052 h[183] 0.068475 h[184] 0.066760 h[185] 0.063964 h[186] 0.060176 h[187] 0.055516 h[188] 0.050129 h[189] 0.044183 h[190] 0.037855 ... 0.05 0.04 0.03 0.02 0.01 0 -0.01 -0.02 0 5e-005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004 time ESINSA

  40. Step Response • Step Response is the integral of the Impulse Response. • for a ‘fairly’ linear circuit. ESINSA

  41. Nyquist FIR Filter, 365 coefficients 1.2 step response 1 0.8 0.6 0.4 0.2 0 -0.2 0 5e-005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004 time Step Response ESINSA

  42. Remark on FFT (1) • How the FFT of a sinewave behaves • when the number of sampling points changes? • when the sampling frequency changes? 1.0 V peak Sinewave @ 5432.1 Hz a. Fs = 1.0 MHz, N = 100 000 points b. Fs = 1.0 MHz, N = 200 000 points c. Fs = 2.0 MHz, N = 100 000 points d. Fs = 2.0 MHz, N = 200 000 points ESINSA

  43. 0 dB ref = 1.0V RMS 0 A = 1 MHz, 100 000 pts B = 1 MHz, 200 000 pts -20 C = 2 MHz, 100 000 pts D = 2 MHz, 200 000 pts -40 -60 -80 C -100 -120 A,D B -140 -160 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 freq Remark on FFT (2) ESINSA

  44. Remark on FFT (3) • How the FFT of a sinewave behaves when • the number of samples changes? • the sampling frequency changes? • It depends on the FREQUENCY RESOLUTION of the FFT. • Sampling Frequency • Frequency Resolution = ------------------ • Number of Samples ESINSA

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