# DAC-ADC2 - CHARACTERIZATION OF DIGITAL-ANALOG CONVERTERS...

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CHARACTERIZATION OF DIGITAL-ANALOG CONVERTERS STATIC CHARACTERISTICS OUTPUT-INPUT CHARACTERISTICS Ideal input-output characteristic of a 3-bit DAC

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DEFINATION Resolution of the DAC is equal to the number of bits in the applied digital input word. The full scale (FS): FS = Analog output when all bits are 1 - Analog output all bits are 0 - = - - = N REF N REF REF 2 1 1 V 0 ) 2 V V ( FS Full scale range (FSR) is defined as REF FS lim V N FSR = → = Quantization Noise is the inherent uncertainty in digitizing an analog value with a finite resolution converter.

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MORE DEFINATIONS Dynamic Range (DR) of a DAC is the ratio of the FSR to the smallest difference that can be resolved (i.e. an LSB) N N 2 2 / FSR FSR LSBchange FSR DR = = = or in term of decibels DR(dB) = 6.02N (dB) Signal-to-noise ratio (SNR) for the DAC is the ratio of the full scale value to the rms value of the quantization noise. 12 2 12 5 . 0 1 ) ( 0 2 2 N T FSR LSB dt T t LSB T noise on quantizati rms = - =
Therefore ) 2 12 / FSR ( ) rms ( v SNR N OUT = Maximum SNR(SNR max ) is defined as 2 2 6 ) 2 12 ( FSR ) 2 2 ( FSR ) 2 12 / FSR ( ) rms ( v SNR N N N OUT max max = = = or in terms of decibels ) 2 ( log 20 ) 2 ( log 20 ) 6 ( log 10 2 2 6 log 20 ) dB ( SNR 10 N 10 10 N 10 max - + = = = 7.78dB – 6.02dB + 6.02N dB = 1.76 dB + 6.02N dB

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EVEN MORE DEFINATIONS Effective number of bits (ENOB) can be defined from the above as 02 . 6 76 . 1 SNR ENOB Actual - = where SNR Actual is the actual SNR of the converter.
Comment : The DR is the amplitude range necessary to resolve N bits regardless of the amplitude of the output voltage. However, when referenced to a given output analog signal amplitude, the DR required must include 1.76 dB more to account for the presence of quantization noise. Thus, for a 10-bit DAC, the DR is 60.2 dB and for a full- scale, rms output voltage, the signal must be approximately 62 dB above whatever noise floor is present in the output of the DAC.

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OFFSET AND GAIN ERRORS An offset error is a constant difference between the actual finite resolution characteristic and the infinite resolution characteristic measured at any vertical jump. A gain error is the difference between the slope of an
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## This note was uploaded on 11/07/2009 for the course ELEC ece212 taught by Professor None during the Spring '09 term at York University.

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DAC-ADC2 - CHARACTERIZATION OF DIGITAL-ANALOG CONVERTERS...

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