Digital to Analog Converters I
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1 Advanced Analog Building Blocks 2 Digital to Analog Converters I Albert Comerma (PI) (comerma@physi.uni-heidelberg.de) Course web WiSe 2017
2 DAC parameters DACs parameters DACs non ideal effects DACs performance measurement N = number of bits V ref Full scale, V FS LSB = V FS /2 N b i = 0 or 1 V out = V FS N 1 i=0 b i = 2 N 1 LSB N 1 Note: for b i = 1, V out = V FS LSB V FS i=0 b i 2 i N c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 1 / 18
3 Ideal output DACs parameters DACs non ideal effects DACs performance measurement c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 2 / 18
4 DAC offset error DACs parameters DACs non ideal effects DACs performance measurement c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 3 / 18
5 DAC gain error DACs parameters DACs non ideal effects DACs performance measurement c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 4 / 18
6 Monotonicity DACs parameters DACs non ideal effects DACs performance measurement Ideally DACs should be monotonic c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 5 / 18
7 Saturation DACs parameters DACs non ideal effects DACs performance measurement Saturation on extreme values, usually close to power rails. c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 6 / 18
8 Differential Non Linearity, DNL DACs parameters DACs non ideal effects DACs performance measurement Deviation of an output step from 1 LSB: DNL i = i stepsize LSB LSB, Extremes are taken i.e.: DNL = ±0.5LSBs c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 7 / 18
9 Integral Non Linearity, INL DACs parameters DACs non ideal effects DACs performance measurement Deviation of an output from ideal value, Cumulative sum of DNL: INL i = i j=0 DNL j c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 8 / 18
10 Idea of DAC performance DACs parameters DACs non ideal effects DACs performance measurement DNL < INL DNL > INL In reality always obtain a mix + offset + gain errors + saturation. Different methods to calculate INL: Typically after removing offset and gain errors. c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 9 / 18
11 Examples: DACs parameters DACs non ideal effects DACs performance measurement 6 bit DAC 8 bit DAC c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 10 / 18
12 DACs classification Resistor string DACs Current steering DACs Segmented DACs DACs classification based on frequency domain performance. Nyquist rate DACs (Flash): Analog output samples are generated at the system sampling frequency Resistor string DAC Current steering DAC Thermometric Binary-weighted Segmented DAC Oversampling DACs: Analog output samples are generated at much higher frequencies than the system sampling frequency c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 11 / 18
13 Resistor string DACs Resistor string DACs Current steering DACs Segmented DACs All possible analog voltages are generated. Desired voltage is connected to the output. Monotonic. Good DNL/INL. Limitations: Speed limited by output RC. Large resistors needed for low power. Good matching for Rs. c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 12 / 18
14 Resistor string DACs - tree Resistor string DACs Current steering DACs Segmented DACs Reduced parasitic capacitance. Decoder not needed. c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 13 / 18
15 Thermometric DACs Resistor string DACs Current steering DACs Segmented DACs Thermometric code, one bit changes. Based on repetition of exact blocks (unity element). Binary to Thermometric decoder needed: Dec b 2 b 1 b 0 d 7 d 6 d 5 d 4 d 3 d 2 d 1 d c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 14 / 18
16 Current steering DAC, thermometric Resistor string DACs Current steering DACs Segmented DACs Fast and monotonic (by construction), good DNL. c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 15 / 18
17 Current steering DAC, binary weighted Resistor string DACs Current steering DACs Segmented DACs Current switching, simple and fast. INL and DNL depends on matching, not inherently monotonic. c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 16 / 18
18 Current steering DAC, R2R Resistor string DACs Current steering DACs Segmented DACs Reduced component spread due to the R-2R ratio. c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 17 / 18
19 Segmented DACs Resistor string DACs Current steering DACs Segmented DACs Combination of previous architectures; c comerma@physi.uni-heidelberg.de Advances Analog Building Blocks 2: DACs 18 / 18
20 Practice: simulate and compare different binary weighed DACs Use as a reference the following schematic, based on current binary weighted DAC. For a few µa bias current and 7bit resolution check DNL/INL on simulation. Perform a montecarlo simulation on DAC behaviour. Try to estimate area for an equivalent R2R version.
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