# Analog-to-Digital Conversion

## Digital Circuits

• #### Question 1

The circuit shown here is a four-bit analog-to-digital converter (ADC). Specifically, it is a flash converter, so named because of its high speed: Explain why we must use a priority encoder to encode the comparator outputs into a four-bit binary code, and not a regular encoder. What problem(s) would we have if we were to use a non-priority encoder in this ADC circuit?

• #### Question 2

Predict how the operation of this “flash” analog-to-digital converter (ADC) circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults): Resistor R16 fails open:
Resistor R1 fails open:
Comparator U13 output fails low:
Solder bridge (short) across resistor R14:

For each of these conditions, explain why the resulting effects will occur.

• #### Question 3

This “flash” ADC circuit has a problem. The output code jumps from 0000 to 1111 with just the slightest amount of input voltage (Vin). In fact, the only time it outputs 0000 is when the input terminal is slightly negative with reference to ground: Identify at least two possible component faults that could cause this problem, and explain your reasoning in how you made the identifications.

• #### Question 4

 Don’t just sit there! Build something!!

Learning to analyze digital circuits requires much study and practice. Typically, students practice by working through lots of sample problems and checking their answers against those provided by the textbook or the instructor. While this is good, there is a much better way.

You will learn much more by actually building and analyzing real circuits, letting your test equipment provide the “answers” instead of a book or another person. For successful circuit-building exercises, follow these steps:

1. Draw the schematic diagram for the digital circuit to be analyzed.
2. Carefully build this circuit on a breadboard or other convenient medium.
3. Check the accuracy of the circuit’s construction, following each wire to each connection point, and verifying these elements one-by-one on the diagram.
4. Analyze the circuit, determining all output logic states for given input conditions.
5. Carefully measure those logic states, to verify the accuracy of your analysis.
6. If there are any errors, carefully check your circuit’s construction against the diagram, then carefully re-analyze the circuit and re-measure.

Always be sure that the power supply voltage levels are within specification for the logic circuits you plan to use. If TTL, the power supply must be a 5-volt regulated supply, adjusted to a value as close to 5.0 volts DC as possible.

One way you can save time and reduce the possibility of error is to begin with a very simple circuit and incrementally add components to increase its complexity after each analysis, rather than building a whole new circuit for each practice problem. Another time-saving technique is to re-use the same components in a variety of different circuit configurations. This way, you won’t have to measure any component’s value more than once.

• #### Question 5

A comparator may be thought of as a one-bit analog-to-digital converter: Explain why this description of a comparator is appropriate. What exactly is meant by the term “analog-to-digital converter,” or ADC?

• #### Question 6

Flash analog-to-digital converters are easy to understand, but are not practical for many applications. Identify some of the drawbacks of the “flash” circuit design.

• #### Question 7

Explain the operating principle of this analog-to-digital converter circuit, usually referred to as a tracking converter: • #### Question 8

Explain the operating principle of this analog-to-digital converter circuit, usually referred to as a successive-approximation converter: Note: the successive-approximation register (SAR) is a special type of binary counting circuit which begins counting with the most-significant bit (MSB), then the next-less-significant bit, in order all the way down to the LSB. At that point, it outputs a “high” signal at the “Complete” output terminal. The operation of this register may be likened to the manual process of converting a decimal number to binary by “trial and fit” with the MSB first, through all the successive bits down to the LSB.

• #### Question 9

Explain the operating principle of a single-slope ADC circuit, in your own words.

• #### Question 10

Explain the operating principle of a dual-slope ADC circuit, in your own words.

• #### Question 11

The Delta-Sigma or Sigma-Delta analog-to-digital converter works on the principle of oversampling, whereby a low-resolution ADC repeatedly samples the input signal in a feedback loop. In many cases, the ADC used is nothing more than a comparator (a 1-bit ADC!), the output of this ADC subtracted from the input signal and integrated over time in an attempt to achieve a balance near 0 volts at the output of the integrator. The result is a pulse-density modulated (PDM) “bitstream” of 1-bit digital data which may be filtered and decimated (converted to a binary word of multiple bits): Explain what this PDM bitstream would look like for the following input voltage conditions:

Vin = 0 volts
Vin = VDD
Vin = Vref
• #### Question 12

The pulse-density modulation (PDM) of a 1-bit oversampled Delta-Sigma modulator circuit may be “decimated” into a multi-bit binary number simply by counting the number of “1” states in a bitstream of fixed length.

Take for example the following bitstreams. Sample the first seven bits of each stream, and convert the equivalent binary numbers based on the number of “high” bits in each seven-bit sample:

001001001001001
101101101101101
010010001100010
010001100010001
111011101110111

Then, take the same five PDM bitstreams and “decimate” them over a sampling interval of 15 bits.

• #### Question 13

Suppose an analog-digital converter IC (“chip”) inputs a voltage ranging from 0 to 5 volts DC and converts the magnitude of that voltage into an 8-bit binary number. How many discrete “steps” are there in the output as the converter circuit resolves the input voltage from one end of its range (0 volts) to the other (5 volts)? How much voltage does each of these steps represent?

• #### Question 14

One of the idiosyncrasies of analog-to-digital conversion is a phenomenon known as aliasing. It happens when an ADC attempts to digitize a waveform with too high of a frequency.

Explain what aliasing is, how it happens, and what may be done to prevent it from happening to an ADC circuit.

• #### Question 15

Analog-to-digital converter circuits (ADC) are usually equipped with analog low-pass filters to pre-condition the signal prior to digitization. This prevents signals with frequencies greater than the sampling rate from being seen by the ADC, causing a detrimental effect called aliasing. These analog pre-filters are thus known as anti-aliasing filters.

Determine which of the following Sallen-Key active filters is of the correct type to be used as an anti-aliasing filter:  • #### Question 16

Suppose a particular ADC has an input voltage range of 5 volts to -5 volts, and therefore is suitable for digitizing AC input signals. A technician wants to use this ADC to digitize AC line voltage (120 volts RMS), and builds the following conditioning circuit to safely connect the ADC to the AC line: Unfortunately, this ADC is not able to fully sample the AC waveform when tested. It “overflows” and “underflows” at the waveform’s peaks, as though the input waveform is too large (outside of the 5/-5 volt ADC chip range). The technician re-checks his calculations, but still thinks the voltage division ratio provided by the potential transformer and resistor network should be sufficient for this task.

What is wrong with this circuit? Why does it “over-range” at the waveform peaks instead of sampling the 120 volt waveform with range to spare? Then, once having identified the problem, recommend a solution to fix the problem.

• #### Question 17

This bar graph driver circuit takes an audio input signal and displays the amplitude as a moving “bar” of lights. The stronger the amplitude of the signal, the more LEDs energize in the bar graph display. Predict how the operation of this circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults): Resistor R4 failed open:
Solder bridge (short) past resistor R3:
Resistor R11 failed open:
Zener diode D1 failed shorted:
Schottky diode D2 failed shorted:
• #### Question 18

Examine this vertical (“bird’s eye”) view of a boat resisting a river’s current: Suppose the driver of this boat does not own an anchor, and furthermore that the only form of propulsion is an electric “trolling” motor with an on/off switch (no variable speed control). With the right combination of switch actuations (on, off, on, off), it should be possible for the boat to maintain its position relative to the riverbanks, against the flow of water.

Now, if we know the boat is actually holding position in the middle of the river, by trolling motor power alone, the pattern of on/off switch actuations should tell us something about the speed of the river. Perform a couple of “thought experiments” where you imagine what the driver of the boat would have to do with the motor’s on/off switch to maintain position against a fast current, versus against a slow current. What relationship do you see between the switch actuations and the speed of the current?

Note: once you understand this question, you will be better prepared to grasp the operation of a Delta-Sigma analog-to-digital converter! 