Quantization Error Calculation In Adc
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In electronics, an analog-to-digital converter (ADC, A/D, A–D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light
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entering a digital camera, into a digital signal. An ADC may also quantization error example provide an isolated measurement such as an electronic device that converts an input analog voltage or current
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to a digital number proportional to the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, how to reduce quantization error but there are other possibilities. There are several ADC architectures. Due to the complexity and the need for precisely matched components, all but the most specialized ADCs are implemented as integrated circuits (ICs). A digital-to-analog converter (DAC) performs the reverse function; it converts a digital signal into an analog signal. Contents 1 Explanation 1.1 Resolution 1.1.1 Quantization quantization error in a/d converter error 1.1.2 Dither 1.1.3 Non-linearity 1.2 Jitter 1.3 Sampling rate 1.3.1 Aliasing 1.3.2 Oversampling 1.4 Relative speed and precision 1.5 Sliding scale principle 2 Types 2.1 Direct-conversion 2.2 Successive approximation 2.3 Ramp-compare 2.4 Wilkinson 2.5 Integrating 2.6 Delta-encoded 2.7 Pipeline 2.8 Sigma-delta 2.9 Time-interleaved 2.10 Intermediate FM stage 2.11 Other types 3 Commercial 4 Applications 4.1 Music recording 4.2 Digital signal processing 4.3 Scientific instruments 4.4 Rotary encoder 5 Electrical symbol 6 Testing 7 See also 8 Notes 9 References 10 Further reading 11 External links Explanation[edit] The conversion involves quantization of the input, so it necessarily introduces a small amount of error. Furthermore, instead of continuously performing the conversion, an ADC does the conversion periodically, sampling the input. The result is a sequence of digital values that have been converted from a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal. An ADC is defined by its bandwidth and its signal-to-noise ratio. The bandwidth of an ADC is characterized primarily by its sampling rate. The dynamic
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
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coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, dB 1 quantization error percentage 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
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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 https://en.wikipedia.org/wiki/Analog-to-digital_converter 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 input voltage is measured http://www.skillbank.co.uk/SignalConversion/snr.htm 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 the analysis of quantization error and signal to
In electronics, an analog-to-digital converter (ADC, A/D, A–D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or https://en.wikipedia.org/wiki/Analog-to-digital_converter light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an input analog voltage or current to a digital number proportional to the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional quantization error to the input, but there are other possibilities. There are several ADC architectures. Due to the complexity and the need for precisely matched components, all but the most specialized ADCs are implemented as integrated circuits (ICs). A digital-to-analog converter (DAC) performs the reverse function; it converts a digital signal into an analog signal. Contents 1 Explanation quantization error in 1.1 Resolution 1.1.1 Quantization error 1.1.2 Dither 1.1.3 Non-linearity 1.2 Jitter 1.3 Sampling rate 1.3.1 Aliasing 1.3.2 Oversampling 1.4 Relative speed and precision 1.5 Sliding scale principle 2 Types 2.1 Direct-conversion 2.2 Successive approximation 2.3 Ramp-compare 2.4 Wilkinson 2.5 Integrating 2.6 Delta-encoded 2.7 Pipeline 2.8 Sigma-delta 2.9 Time-interleaved 2.10 Intermediate FM stage 2.11 Other types 3 Commercial 4 Applications 4.1 Music recording 4.2 Digital signal processing 4.3 Scientific instruments 4.4 Rotary encoder 5 Electrical symbol 6 Testing 7 See also 8 Notes 9 References 10 Further reading 11 External links Explanation[edit] The conversion involves quantization of the input, so it necessarily introduces a small amount of error. Furthermore, instead of continuously performing the conversion, an ADC does the conversion periodically, sampling the input. The result is a sequence of digital values that have been converted from a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal. An ADC is defined by its bandwidth and its signal-to-noise ratio. The bandwidth of an ADC is characte