Quantization Error 10 Bit
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Quantization Error Example
Advanced Search 22nd June 2005,16:25 #1 KrisUK Newbie level 4 Join Date May 2005 Posts 7 Helped 0 / 0 Points 1,398 Level 8 How quantization error in pcm 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 conclusion it is the max voltage divided
Quantization Error In A/d Converter
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 represent both positive and negative values, then the LSB weighting is how to reduce quantization error 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 Member level 1 Join Date Dec 2004 Posts 458 Helped 17 / 17 Points 3,856 Level 14 Quantization Error assuming you're using round-
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
Quantization Error Percentage
for signals coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, dB
Quantization Error Ppt
1 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 quantization error in dsp 64 0.01563 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 http://www.edaboard.com/thread40731.html 32768 0.00003 92 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 http://www.skillbank.co.uk/SignalConversion/snr.htm input voltage is measured by 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 t
changing over time. There are three samples shown on the figure. The process of sampling the data is not instantaneous, so each http://engineeronadisk.com/V2/book_PLC/engineeronadisk-156.html sample has a start and stop time. The time required to acquire the http://www.embedded.com/design/configurable-systems/4025078/Understanding-analog-to-digital-converter-specifications sample is called the sampling time. A/D converters can only acquire a limited number of samples per second. The time between samples is called the sampling period T, and the inverse of the sampling period is the sampling frequency (also called sampling rate). The sampling time is often much smaller quantization error than the sampling period. The sampling frequency is specified when buying hardware, but for a PLC a maximum sampling rate might be 20Hz. Figure 21.2 Sampling an Analog Voltage A more realistic drawing of sampled data is shown in Figure 21.3 Parameters for an A/D Conversion. This data is noisier, and even between the start and end of the data sample there quantization error in is a significant change in the voltage value. The data value sampled will be somewhere between the voltage at the start and end of the sample. The maximum (Vmax) and minimum (Vmin) voltages are a function of the control hardware. These are often specified when purchasing hardware, but reasonable ranges are; 0V to 5V 0V to 10V -5V to 5V -10V to 10V The number of bits of the A/D converter is the number of bits in the result word. If the A/D converter is 8 bit then the result can read up to 256 different voltage levels. Most A/D converters have 12 bits, 16 bit converters are used for precision measurements. Figure 21.3 Parameters for an A/D Conversion The parameters defined in Figure 21.3 Parameters for an A/D Conversion can be used to calculate values for A/D converters. These equations are summarized in Figure 21.4 A/D Converter Equations. Equation 1 relates the number of bits of an A/D converter to the resolution. In a normal A/D converter the minimum range value, Rmin, is zero, however some devices will provide 2's compliment negative numbers for negative volt
& SoCs Operating Systems Power Optimization Programming Languages & Tools Prototyping & Development Real-time & Performance Real-world Applications Safety & Security System Integration Essentials & Education Products News Source Code Library Webinars Courses Tech Papers Community Insights Forums Events Archives ESP / ESD Magazine Newsletters Videos Collections About Us About Embedded Contact Us Newsletters Advertising Editorial Contributions Site Map Home> Configurable Systems Development Centers > Design How-To Understanding analog to digital converter specifications Len Staller February 24, 2005 Tweet Save to My Library Follow Comments Len StallerFebruary 24, 2005 Confused by analog-to-digital converter specifications? Here's a primer to help you decipher them and make the right decisions for your project. Although manufacturers use common terms to describe analog-to-digital converters (ADCs), the way ADC makers specify the performance of ADCs in data sheets can be confusing, especially for a newcomers. But to select the correct ADC for an application, it's essential to understand the specifications. This guide will help engineers to better understand the specifications commonly posted in manufacturers' data sheets that describe the performance of successive approximation register (SAR) ADCs. ABCs of ADCs ADCs convert an analog signal input to a digital output code. ADC measurements deviate from the ideal due to variations in the manufacturing process common to all integrated circuits (ICs) and through various sources of inaccuracy in the analog-to-digital conversion process. The ADC performance specifications will quantify the errors that are caused by the ADC itself. ADC performance specifications are generally categorized in two ways: DC accuracy and dynamic performance. Most applications use ADCs to measure a relatively static, DC-like signal (for example, a temperature sensor or strain-gauge voltage) or a dynamic signal (such as processing of a voice signal or tone detection). The application determines which specifications the designer will consider the most important. For example, a DTMF decoder samples a telephone signal to determine which button is depressed on a touchtone keypad. Here, the concern is the measurement of a signal's power (at a given set of frequencies) among other tones and noise generated by ADC measurement errors. In this design, the engineer will be most concerned with dynamic performance specifications such as signal-to-noise ratio and harmonic distortion. In another e