# Applications

Here are some examples of problems where one must choose an appropriate analog to digital converter. Don't peek at the answers 'til you've jousted with the problem for a while. In some cases, hints are provided as "mouseovers." Answers used ADCs available in June, 2009.

1. Video digitization

Goal: decide what ADC to use with a CMOS array in a cell phone camera.

Analysis of the problem: An example high speed CMOS sensing chip is Cypress Electronics LUPA-1300. The full 48 page chip specification is on-line. Useful information extracted from the specification:

1280×1024 pixels, each 14 μm square.

Full well capacity: 62500 electrons.

Output at 60,000 electrons: 1 V.

Typical quantum efficiency across the visible spectrum: 10%.

Dark current and read noise: 45 e-/pixel

Recommended clock speed (pixel read rate): 40 MHz

Output read by 16 parallel amplifer channels (so each channel only looks at an 80×1024 subarray).

Questions and choices:

1. How many bits of resolution are justified?
2. How many conversions per second must each ADC perform?
3. What type of ADC do you recommend be employed?
4. For a SINGLE READ CYCLE, what is the signal-to-noise ratio of an intensity measurement?
5. If we average all the data for 1 s, what is the precision of the mean of the measurement? Recall that the standard deviation of the mean is t s/N1/2 with N the number of data averaged. Use t for 95% confidence (you can find t tables on the web).

2. Chronopotentiometry or Chronoamperometry

Goal: decide what ADC to use in building a general electroanalytical instrument that can do either chronopotentiometry or chronoamperometry. While we could also look at the needed DAC and analog circuits to control current or potential, that is NOT part of this problem.

Analysis of the problem: In chronopotentiometry, one monitors the potential on an electrode through which current is constant (possibly including i=0). In chronoamperometry, one monitors the current at an electrode which is maintained at a constant potential vs. a reference potential. The electrochemical standard potential ranges from + 3.03 V (for 1/2 F2 + e- + H+ ↔ HF) to
- 2.923 V (for Cs+ + e- ↔ Cs). Currents may range from ~ 1 pA to ~ 1 A, 12 orders of magnitude.

Questions and choices:

1. To measure potential in chronopotentiometry, would you choose a unipolar or bipolar ADC? What potential range would you choose (look on the web to find an example of an ADC that has this range)? How many bits would it have?
2. To measure current in chronocoulometry, would you choose a unipolar or bipolar ADC?
3. Converting current to voltage will be essential. What voltage output range would you choose? If you use a current-to-voltage converter with a 1 MΩ resistor so that output is 1V/μA, what is the highest current that can be digitized?
4. An operational amplifier typically has noise of 10 nV Hz-1/2. If this is the dominant noise source, what is the fastest 16 bit ADC you need to carry out the measurements you chose in question 3? Is this a sensible answer?
5. Is it always the case that amplifier noise constrains ADC resolution for chronoamperometry? If not, list other possible limiting factors.
6. Finally, if you want to perform chronoamperometry with data collection at 100 kHz (Nyquist frequency 50 kHz), choose an ADC resolution that is appropriate and a converter type that is appropriate (again, look on the web to choose an ADC that meets your specifications).

3. Charge-coupled Array Detector

A charge-coupled array detector is to be used for obtaining atomic emission spectra. What readout ADC is appropriate?

Analysis of the problem: Because of the wide dynamic range required for analysis of trace components in the presence of high matrix concentrations, scientific CCDs tend to use large pixels, deep full-well depths, and slow readouts. An example is the E2V Technologies CCD42-90 (note: this is a PDF file even if the file name doesn't include the .pdf suffix). Superficially, it's not hugely different from the CMOS array example previously:

2048×4608 pixels, each 13.5 μm square.

Full well capacity: 100,000 electrons.

Output at 100,000 electrons: 0.45 V.

Typical quantum efficiency across the visible spectrum: 80%.

Dark current and read noise: 3 e-/pixel + 1 e-/pixel/hr if cooled to -100°C

Recommended clock speed (pixel read rate): 50 kHz - 3 MHz

Output read by 2 amplifer channels (so reading the entire array requires 95 s = 1 min, 35 s if each pixel is read at optimum frequency).

Questions and choices:

1. Given the recommended readout time, what is the "optimum frequency" for readout?
2. How many conversions per second must each ADC perform?
3. How many bits of resolution are justified?
4. What type of ADC do you recommend be employed?
5. For a SINGLE READ CYCLE, what is the signal-to-noise ratio of an intensity measurement?
6. Comparing this CCD to the CMOS detector in Problem 1, give an example of a measurement problem where the CCD is preferable, and an example of a measurement problem where the CMOS detector is preferable.

4. Flame Ionization Detector

For the flame ionization detector (FID)in a GC, what ADC should one choose?

Analysis of the problem: When biased appropriately and when support gases are clean, the background current for the FID is about 1 pA. Peak widths are commonly ~ 1 s, so signals need to be digitized at at least 10 Hz. Maximum useful current before nonlinearity sets in is about 1 μA.

Questions and choices:

1. List the possible types of ADCs that are good for signal averaging at the speeds required.
2. If the background current is 1 pA and one integrates for 0.1 s, what is the best possible (shot noise limited) standard deviation of the background? What is the shot noise limit for current detection (3 times standard deviation of the background)? Thus, what is the dynamic range required for the ADC?
3. Suggest an appropriate ADC for this situation.

5. Electron Capture Detector

For the electron capture detector in a gas chromatograph, what ADC should one choose?

Analysis of the problem: In an electron capture detector, either photoionization or β decay of 63Ni causes sustained ionization of a sensitizer, typically CH4. A current is sustained by imposing an electric field on the detector. The presence of a compound that can capture electrons (typically a halogen-containing molecule) lowers the mobility of the electrons, requiring a higher field to maintain constant current. Thus, the departure of a voltage from its quiescent value signals the presence of analyte. Instantaneous concentration is proportional to (V - V0) over a wide concentration range, with typical response ~ 1000 V s pg-1 for the highly electronegative compound CCl4. That is, a 100 fg sample in a GC peak would produce a peak with an area of 100 V s. If the peak were 1 s wide, the voltage change would be 100 V. If the peak stretched to 2 s, the voltage excursion would be 50 V. For CCl4, the dynamic range is from ~ 3 fg to ~ 200 pg for common GC parameters. See H. Cai, S. D. Stearns, and W. E. Wentworth, "Pulsed Discharge Electron Capture Detector Operating in the Constant-Current Mode by Means of Feedback dc Bias Voltage," Anal. Chem. 70, 3770-3776 (1998) for details.

Questions and choices:

1. What is the quantity that needs to be digitized here?
2. How does this differ from other situations in these exercises?
3. If you had to choose one of the ADC approaches discussed in this set of modules to digitize the detector signal, what would it be and why?
4. Can you devise an approach to digitization that is a variation on the methods we have discussed that might work more easily than the scheme you chose in question 3?

Next