Calculating Maximum Quantization Error
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Data Conversion Website Quantization Error and Signal - to - Noise Ratio calculations The signal to noise ratio of a quantized signal is 2+6*(no of bits), as shown in the following table. Resolution and Signal to Noise Ratio for signals how to calculate quantization error in adc coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, dB 1 quantization error formula 2 0.5 8 2 4 0.25 14 3 8 0.125 20 4 16 0.0625 26 5 32 0.03125 32 6 64 0.01563 quantization error equation 38 7 128 0.00781 44 8 256 0.00391 50 9 512 0.00195 56 10 1024 0.00098 62 11 2048 0.00048 68 12 4096 0.00024 74 13 8192 0.00012 80 14 16384 0.00006 86 15 32768 0.00003 92 quantization error example 16 65536 0.00001 98 These values are for a signal matched to the full-scale range of the converter. If a signal with a range of 5V is measured by an 8 bit ADC with a range of 10V then only 7 bits are effectively in use, and a signal to noise ratio of 44 rather than 50 will apply. Proof: Suppose that the instantaneous value of the input voltage is measured by
Quantization Error In A/d Converter
an ADC with a Full Scale Range of Vfs volts, and a resolution of n bits. The real value can change through a range of q = Vfs / 2n volts without a change in measured value occurring. The value of the measured signal is Vm = Vs - e, where Vm is the measured value, Vs is the actual value, and e is the error. The maximum value of error in the measured signal is emax = (1/2)(Vfs / 2n) or emax = q/2 since q = Vfs / 2n The RMS value of quantization error voltage is whence The Signal to Noise Ratio (SNR) is defined as It is normally quoted on a logarithmic scale, in deciBels ( dB ). or The RMS signal voltage is then The error, or quantization noise signal is Thus the signal - to - noise ratio in dB. is since Vfs = 2n q, then which simplifies to N.B. This equation is true only if the input signal is exactly matched to the Full Scale Range of the converter. For signals whose amplitude is less than the FSR the Signal - to - Noise Ratio will be reduced. Download a .pdf file of the analysis of quantization error and signal to noise ratio
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Quantization Error In Pcm
system? LinkBack LinkBack URL About LinkBacks Thread Tools Show Printable Version Download This Thread Subscribe to quantization error definition this Thread… Search Thread Advanced Search 22nd June 2005,16:25 #1 KrisUK Newbie level 4 Join Date May 2005 Posts 7 Helped 0 / 0 quantization error percentage Points 1,398 Level 8 How do I solve quantization errors in ADC system? How do I work out quantization error in a ADC system? I looked around on different sites from a recommendation from another user and came to the http://www.skillbank.co.uk/SignalConversion/snr.htm conclusion it is the max voltage divided by the number of bits. Is this correct? Thank you. 22nd June 2005,16:25 22nd June 2005,16:52 #2 Kral Advanced Member level 4 Join Date Mar 2005 Location USA Posts 1,326 Helped 278 / 278 Points 11,626 Level 25 Re: Quantization Error The weighting of the LSB is equal to the (Reference Voltage)/2^n, where n is the number of bits. The Quantization error = 1/2 LSB. If the ADC is bipolar (can http://www.edaboard.com/thread40731.html represent both positive and negative values, then the LSB weighting is 2X the above value. The quantization error is still 1/2 LSB. The total error includes the quantization error plus scale factor (gain) error, non-linearity errors. Regards, Jon 22nd June 2005,17:22 #3 banh Advanced Member level 1 Join Date Dec 2004 Posts 458 Helped 17 / 17 Points 3,856 Level 14 Quantization Error quantization error/noise is the difference between the actual sampled value and the quantized value. 2 cases: if the the actual sampled value is between 2 quantized levels -> it will either be rounded off or truncated. rounding -> take the nearest quantized level. truncated -> take the level below it. hence: the error is - rounding off: - truncated where Q is the resolution. Last edited by BlackMamba; 27th August 2010 at 12:44. 22nd June 2005,17:22 22nd June 2005,18:42 #4 KrisUK Newbie level 4 Join Date May 2005 Posts 7 Helped 0 / 0 Points 1,398 Level 8 Re: Quantization Error Well, say I had a 3 bit ADC with a max of 8V; what would the max quantization error be? Would it be 8/8 = 1V ? Or say a 10 bit ADC with a max of 5V: 5/1024 = 0.0048828125V (or 4.88mV) ? I don't really need to know the theory behind it, just how to work it out for an exam I've got coming up. 22nd June 2005,18:49 #5 banh Advanced M
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