Distortion Analysis T S. 2 N for all k not defined above. THEOREM?: If N P is an integer and x(t) is band limited to f MAX, then

Transcription

1 EE 505 Lecture 6 Spectral Analysis in Spectre - Standard transient analysis - Strobe period transient analysis Addressing Spectral Analysis Challenges Problem Awareness Windowing Post-processing

2 . Review from last lecture. Distortion Analysis T 0 T S THEOREM?: If N P is an integer and x(t) is band limited to f MAX, then 2 Am Χ mnp 1 0 m h N and Χ k for all k not defined above where f = 1/T, Χ k N k 1 is the DFT of the sequence x kt S 0 f N f MAX = 2 N P, and h = Int f MAX f N 1 k 0

3 . Review from last lecture. Spectral Response (expressed in db) (Actually Stem plots but points connected in plotting program) Note Magnitude is Symmetric wrt f SAMPLE f AXIS f SIGNAL n 1 N P

4 . Review from last lecture. Spectral Response with Non-coherent Sampling (zoomed in around fundamental)

5 . Review from last lecture. Observations Modest change in sampling window of out of 20 periods (.0005%) results in a small error in both fundamental and harmonic More importantly, substantial raise in the computational noise floor!!! (from over - 300dB to only -80dB) Errors at about the 13-bit level!

6 . Review from last lecture. Effects of High-Frequency Spectral Components

7 . Review from last lecture. Observations Aliasing will occur if the band-limited part of the hypothesis for using the DFT is not satisfied Modest aliasing will cause high frequency components that may or may not appear at a harmonic frequency More egregious aliasing can introduce components near or on top of fundamental and lower-order harmonics Important to avoid aliasing if the DFT is used for spectral characterization

8 Spectre Limitations in Spectral Analysis Thanks to Xilu Wang for simulation results Normal Transient Analysis Strobe Period Timing Coherent Sampling

9 Simulation Conditions V(t)=sin(2*π*50t) 11 periods Coherent Sampling Number of Samples: Type of Samples: Standard Sweep Strobe Period Sweep

10 512 Samples with Standard Sweep V(t)=sin(2*π*50t) 11 periods Coherent Sampling

11 For reference: Results obtained with MatLab for N=512

12 Mag (volts) 512 Samples with Standard Sweep Time (index)

13 Mag (volts) 512 Samples with Standard Sweep Time (index)

14 512 Samples with Standard Sweep

15 512 Samples with Standard Sweep

16 512 Samples with Standard Sweep Note dramatic increase in noise floor Note what appear to be some harmonic terms extending above noise floor

17 MatLab comparison: 512 Samples with Standard Sweep Spectre Results MatLab Results

18 512 Samples with Standard Sweep

19 512 Samples with Standard Sweep Note presence of odd harmonics in spectrum

20 512 Samples with Standard Sweep

21 512 Samples with Strobe Period Sweep V(t)=sin(2*π*50t) 11 periods Coherent Sampling

22 Mag (volts) 512 Samples with Strobe Period Time (index)

23 Mag (volts) 512 Samples with Strobe Period Time (index)

24 512 Samples with Strobe Period

25 512 Samples with Strobe Period

26 MatLab comparison: 512 Samples with Strobe Period Sweep Spectre Results MatLab Results

27 512 Samples with Strobe Period

28 512 Samples with Strobe Period

29 4096 Samples with Standard Sweep V(t)=sin(2*π*50t) 11 periods Coherent Sampling

30 For reference: Results obtained with MatLab for N=4096

31 Mag (volts) 4096 Samples with Standard Sweep Time (index)

32 Mag (volts) 4096 Samples with Standard Sweep Time (index)

33 4096 Samples with Standard Sweep

34 4096 Samples with Standard Sweep

35 Comparison 4096 Samples with Standard Sweep Spectre MatLab

36 4096 Samples with Standard Sweep

37 4096 Samples with Standard Sweep Note presence of odd harmonics in spectrum

38 4096 Samples with Standard Sweep

39 4096 Samples with Strobe Period Sweep V(t)=sin(2*π*50t) 11 periods Coherent Sampling

40 Mag (volts) 4096 Samples with Strobe Period Time (index)

41 Mag (volts) 4096 Samples with Strobe Period Time (index)

42 4096 Samples with Strobe Period

43 4096 Samples with Strobe Period

44 Comparison 4096 Samples with Strobe Period Sweep Spectre MatLab

45 4096 Samples with Strobe Period

46 4096 Samples with Strobe Period

47 Mag (volts) Superimposed Standard/Strobe Sweep Time (index)

48 Mag (volts) Superimposed Standard/Strobe Sweep Time (index)

49 Mag (volts) Difference Standard/Strobe Sweep Time (index)

50 Mag (volts) Difference Standard/Strobe Sweep Time (index)

51 Difference Standard/Strobe Sweep Mag (volts)

52 Mag (volts) Difference Standard/Strobe Sweep Time (index)

53 Addressing Spectral Analysis Challenges Problem Awareness Windowing and Filtering Post-processing

54 Problem Awareness T THEOREM If N P is an integer and x(t) is band limited to f MAX, then f = 1/T, T S 2 Am Χ mnp 1 0 m h-1 and Χ k 0 for all k not defined N N 1 N 1 above where Χ k is the DFT of the sequence x kt k 0 S k 0 f N f MAX = 2 N P, and h = Int Hypothesis is critical Even minor violation of the premise can have dramatic effects Validation of all tools is essential Learn what to expect f MAX f

55 Filtering - a strategy to address the aliasing problem A lowpass filter is often used to enforce the band-limited requirement if not naturally band limited Lowpass filter often passive Lowpass filter design often not too difficult Minimum sampling frequency often termed the Nyquist rage.

56 Considerations for Spectral Characterization Tool Validation FFT Length Importance of Satisfying Hypothesis - NP is an integer - Band-limited excitation Windowing

57 Windowing - a strategy to address the problem of requiring precisely an integral number of periods to use the DFT for Spectral analysis? Windowing is sometimes used Windowing is sometimes misused

58 Windowing Windowing is the weighting of the time domain function to maintain continuity at the end points of the sample window Well-studied window functions: Rectangular (also with appended zeros) Triangular Hamming Hanning Blackman

59 Rectangular Window Sometimes termed a boxcar window Uniform weight Can append zeros Without appending zeros equivalent to no window

60 Rectangular Window Assume f SIG =50Hz V IN sin( t) 0. 5sin( 2 t) ω 2πf SIG Consider N P =20.1 N=512

61 Rectangular Window

62 Spectral Response with Non-coherent sampling (zoomed in around fundamental)

63 Rectangular Window Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through

64 Rectangular Window Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through Energy spread over several frequency components

65 Rectangular Window (with appended zeros)

66 Triangular Window

67 Triangular Window

68 Spectral Response with Non-Coherent Sampling and Windowing (zoomed in around fundamental)

69 Triangular Window

70 Triangular Window Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through

71 Hamming Window

72 Hamming Window

73 Spectral Response with Non-Coherent Sampling and Windowing (zoomed in around fundamental)

74 Comparison with Rectangular Window

75 Hamming Window Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through

76 Hanning Window

77 Hanning Window

78 Spectral Response with Non-Coherent Sampling and Windowing (zoomed in around fundamental)

79 Comparison with Rectangular Window

80 Hanning Window Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through

81 Comparison of 4 windows

82 Comparison of 4 windows

83 Preliminary Observations about Windows Provide separation of spectral components Energy can be accumulated around spectral components Simple to apply Some windows work much better than others But windows do not provide dramatic improvement and

84 Comparison of 4 windows when sampling hypothesis are satisfied

85 Comparison of 4 windows

86 Preliminary Observations about Windows Provide separation of spectral components Energy can be accumulated around spectral components Simple to apply Some windows work much better than others But windows do not provide dramatic improvement and can significantly degrade performance if sampling hypothesis are met

87 Addressing Spectral Analysis Challenges Problem Awareness Windowing and Filtering Post-processing

88 Post-processing Method of circumventing the coherent sampling problem Can also be used for addressing spectral purity problem for test signal generation x kt S N 1 k 0 Post-Processor Χ k N 1 k 0 Non-coherent Easily implemented in MATLAB Will be considered in the laboratory Removes fundamental from samples and replaces with coherent fundamental before taking DFT

89 Post-processing x kt S N 1 k 0 Post-Processor Χ k N 1 k 0 Non-coherent Χ SG N k 1 k 0 Easily implemented in MATLAB Will be considered in the laboratory Removes fundamental from samples and replaces with coherent fundamental before taking DFT Removes spectral impurity of input test signal generator when testing data converters

90 Issues of Concern for Spectral Analysis An integral number of periods is critical for spectral analysis Not easy to satisfy this requirement in the laboratory Windowing can help but can hurt as well Out of band energy can be reflected back into bands of interest Characterization of CAD tool environment is essential Spectral Characterization of high-resolution data converters requires particularly critical consideration to avoid simulations or measurements from masking real performance

91 End of Lecture 6