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Analog-to-digital converter

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From Molecupedia, the encyclopedia of very small things
Circuit that turns a voltage into a number

An analog-to-digital converter (ADC) measures a voltage at set instants and reports each measurement as an integer. It is the last link of the analog front end of a nanopore instrument: the current through the pore becomes a voltage in a transimpedance amplifier, a filter limits its bandwidth, and the converter turns what is left into the samples that a computer can store. The number of bits sets the smallest step the instrument can see, the sampling rate sets how fast the voltage can change before the record misses it, and the input range sets the largest current.

Resolution and quantization noise

A converter with N bits divides its input range into 2N steps. The step, one least-significant bit (LSB), is the range divided by 2N. Rounding the input to the nearest step makes an error of up to half a step, and for an input that moves across many steps the rms of that error is the step divided by √12, about 0.29 LSB. For an ideal converter measuring a full-scale sine wave the ratio of signal to this noise, over the band from zero to half the sampling rate, is 6.02N + 1.76 dB, or 98 dB for 16 bits.[1] Real converters add their own noise, and the effective number of bits (ENOB) is the number of bits an ideal converter would need to match what the real one delivers.

Whether the step matters depends on the gain in front of it. The data sheet of the Axopatch 200B gives a scaled output of 1 mV per picoampere in patch mode, multiplied by an output gain of 0.5 to 500 and swinging ±10 V, and the data sheet of the Axon Digidata 1550B digitizer lists 16 bits over ±10 V, which is 305 µV a step, with eight channels sampled together at up to 500 kHz.[2][3]

The output gain of an Axopatch 200B read by a 16-bit digitizer of ±10 V[2][3]
Output gain Scaled output One count Full scale
1 1 mV/pA 0.305 pA ±10 nA
10 10 mV/pA 0.0305 pA ±1 nA
100 100 mV/pA 0.00305 pA ±100 pA

The headstage's largest noise in patch mode is 0.130 pA rms in 0.1 to 10 kHz, so at a gain of 1 one count is more than twice the noise, and at a gain of 10 it is a quarter of it. Choosing the output gain chooses how many counts the noise spans.

Architectures

File:SAR conversion steps.svg A flash converter compares the input with every possible level at once, using 2N − 1 comparators; it is the fastest design and the most expensive in area and power.[1] A successive-approximation (SAR) converter uses one comparator and an internal converter in the other direction, a digital-to-analog converter, and finds the answer by binary search: it freezes the input, sets the internal converter to half of full scale, asks whether the input is above or below, keeps or drops that bit, and halves the interval, so that a conversion of N bits takes N comparisons.[4] For a 4-bit converter and an input at 0.69 of full scale the trial values are 0.5, 0.75, 0.625 and 0.6875, kept, rejected, kept and kept, which is the code 1011 and the value 0.6875.

A delta-sigma converter trades speed for resolution. A quantizer of one or a few bits runs at many times the rate wanted, inside a feedback loop that pushes the quantization noise to high frequencies, and a digital filter removes it and reduces the rate, which leaves high resolution at low bandwidth.[1] Its output is the output of a digital filter, so it lags the input by the delay of the filter, where a SAR converter returns a value for one instant. The AD4000, a SAR converter, has 16 bits and a maximum rate of 2 million samples a second.[5]

Sampling and aliasing

File:Aliasing 70 kHz at 100 kSps.svg Sampling at fs records a signal faithfully only if it contains nothing above fs/2, the Nyquist frequency, a condition that goes back to Nyquist's analysis of telegraph transmission in 1928 and Shannon's theorem of 1949.[6][7] Anything above it folds down into the band below. At 100 kilosamples a second a component at 70 kHz appears at 30 kHz, and nothing in the record tells it from a real one. The remedy is a low-pass filter ahead of the converter, and since real filters cut off gradually, the sampling rate is set several times above the cutoff.

Filters and sampling rates in nanopore recordings
Study Filter Sampling rate Cutoff as a fraction of the rate
Kasianowicz and colleagues, 1996 Bessel, below 3/8 of the rate Typically 64 kS/s, 16-bit board Below 0.375[8]
Smeets and colleagues, 2008 Eight-pole Bessel, 49.9 kHz 250 or 500 kS/s 0.20 or 0.10[9]
Kwok and colleagues, 2014 Four-pole Bessel, 100 kHz 250 kS/s 0.40[10]

Folding adds noise as well. Power above the Nyquist frequency lands in the band below it, so the sampled noise is that of everything that reaches the converter.

In nanopore instruments

A commercial sequencer samples slowly because a motor protein slows the strand to a few hundred bases a second. For the chemistry of 2018 the maker reported a speed of 450 bases a second and a sampling frequency of 4 kHz, which is about nine samples for each base the strand advances.[11] The PromethION 24 sequencer has up to 3,000 channels active on each of its 24 flow cells, and the maker puts its maximum output at 360 million samples a second, which implies 5 kHz a channel.[12] DNA crosses a solid-state pore at 10 to 1,000 ns per base, and a group that recorded such events reached a bandwidth of 1 MHz.[13] The EDR4 amplifier on Molecular Reality's live stream samples at 200 kHz, one value every 5 µs.[14]

MR1 Nanopore Reader

The open design of the MR1 Nanopore Reader digitizes with a SAR converter of the AD40xx family. The firmware says that a conversion takes about 290 ns, and at 100 kilosamples a second the converter is converting for 3% of each 10 µs.[15] The repository names the part in four ways: the data-acquisition specification gives the AD4000 or AD4002, the bill of materials the AD4000 or the AD4020, the schematic symbol is "AD40xxBRMZ" with the data sheet of the AD4003 family, and the firmware calls its driver "AD40xx".[16][17][18][15] They are different parts. The AD4000 has 16 bits and a pseudo-differential input, the AD4003 has 18 bits and a differential input, and the AD4020 has 20 bits, a differential input and a maximum rate of 1.8 million samples a second.[5] The reference pin of the family takes 2.4 to 5.1 V. The specification gives 2.048 V, and the host software assumes 4.096 V.[19][16][20]

At a full scale of 4.096 V and 16 bits one count is 62.5 µV, which is 6.25 pA behind the 10 MΩ of the drawn amplifier chain. Spread over the band to 50 kHz the quantization noise is 1.8 pA rms, one sixteenth of the 28.8 pA rms that the 1 MΩ feedback resistor of the first stage makes in the same band.[a] Sixteen bits are more than the chain needs. As drawn, nothing ahead of the converter is an anti-aliasing filter; see Analog front end.

The samples reach an ESP32-S3 microcontroller over a serial bus with direct memory access, are packed 64 to a frame of 146 bytes with a header and a checksum, and leave over USB at 1,562.5 frames a second, about 1.83 Mbit/s.[16] For the web display the firmware averages each block of 100 samples, which takes 100 kHz down to 1 kHz and lowers white noise by a factor of 10, worth three bits.[21][15]

See also

Notes

  1. ^ The step is 4.096 V / 216 = 62.5 µV, and the quantization noise is 62.5 µV / √12 = 18 µV, or 1.8 pA through 10 MΩ. The resistor's current noise is √(4kBT/R) = 129 fA/√Hz at 300 K for 1 MΩ, which over 50 kHz is 28.8 pA.

References

  1. ^ a b c Kester, W. (2005). Data Conversion Handbook. Newnes. ISBN 978-0-7506-7841-4.
  2. ^ a b "Axon Axopatch 200B Microelectrode Amplifier (data sheet)". Molecular Devices. July 2012.
  3. ^ a b "Axon Digidata 1550B plus HumSilencer (data sheet)". Molecular Devices.
  4. ^ Kester, W. (January 2006). "MT-021: ADC Architectures II: Successive Approximation ADCs". Analog Devices.
  5. ^ a b "ad4000.c: Analog Devices AD4000 and similar analog-to-digital converters". GitHub. Linux kernel.
  6. ^ Nyquist, H. (1928). "Certain topics in telegraph transmission theory". Transactions of the American Institute of Electrical Engineers 47 (2): 617-644. doi:10.1109/T-AIEE.1928.5055024.
  7. ^ Shannon, C. E. (1949). "Communication in the presence of noise". Proceedings of the IRE 37 (1): 10-21. doi:10.1109/JRPROC.1949.232969.
  8. ^ Kasianowicz, J. J.; Brandin, E.; Branton, D.; Deamer, D. W. (1996). "Characterization of individual polynucleotide molecules using a membrane channel". Proceedings of the National Academy of Sciences 93 (24): 13770-13773. doi:10.1073/pnas.93.24.13770.
  9. ^ Smeets, R. M. M.; Keyser, U. F.; Dekker, N. H.; Dekker, C. (2008). "Noise in solid-state nanopores". Proceedings of the National Academy of Sciences 105 (2): 417-421. doi:10.1073/pnas.0705349105.
  10. ^ Kwok, H.; Briggs, K.; Tabard-Cossa, V. (2014). "Nanopore fabrication by controlled dielectric breakdown". PLOS ONE 9 (3): e92880. doi:10.1371/journal.pone.0092880.
  11. ^ Rang, F. J.; Kloosterman, W. P.; de Ridder, J. (2018). "From squiggle to basepair: computational approaches for improving nanopore sequencing read accuracy". Genome Biology 19: 90. doi:10.1186/s13059-018-1462-9.
  12. ^ "Transforming basecalling in genomic sequencing". Oxford Nanopore Technologies. March 18, 2026.
  13. ^ Rosenstein, J. K.; et al. (2012). "Integrated nanopore sensing platform with sub-microsecond temporal resolution". Nature Methods 9 (5): 487-492. doi:10.1038/nmeth.1932.
  14. ^ "Keltar's Field Guide to Molecular Reality". Molecular Reality Corporation. August 2026.
  15. ^ a b c "adc_ad40xx.cpp". GitHub. Molecular Reality Corporation. October 2026.
  16. ^ a b c "High-Speed Streaming DAQ & External Interfacing Specification". GitHub. Molecular Reality Corporation. October 2026.
  17. ^ "MR1 Nanopore Reader bill of materials". GitHub. Molecular Reality Corporation. October 2026.
  18. ^ "Amplifier.kicad_sch". GitHub. Molecular Reality Corporation. October 2026.
  19. ^ "AD4003: 18-bit, 2 MSPS, differential SAR ADC". Analog Devices. Retrieved October 25, 2026.
  20. ^ "daq_client.py". GitHub. Molecular Reality Corporation. October 2026.
  21. ^ "config.h". GitHub. Molecular Reality Corporation. October 2026.
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