AnalogtoDigital Conversion
Digital Circuits
The circuit shown here is a fourbit analogtodigital 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 fourbit binary code, and not a regular encoder. What problem(s) would we have if we were to use a nonpriority encoder in this ADC circuit?
Predict how the operation of this “flash” analogtodigital 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 R_{16} fails open:
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 Resistor R_{1} fails open:
 •
 Comparator U_{13} output fails low:
 •
 Solder bridge (short) across resistor R_{14}:
For each of these conditions, explain why the resulting effects will occur.
This “flash” ADC circuit has a problem. The output code jumps from 0000 to 1111 with just the slightest amount of input voltage (V_{in}). 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.
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 änswers” instead of a book or another person. For successful circuitbuilding 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 onebyone 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 reanalyze the circuit and remeasure.
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 5volt 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 timesaving technique is to reuse 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.
Explain the operating principle of this analogtodigital converter circuit, usually referred to as a successiveapproximation converter:

Note: the successiveapproximation register (SAR) is a special type of binary counting circuit which begins counting with the mostsignificant bit (MSB), then the nextlesssignificant 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.
The DeltaSigma or SigmaDelta analogtodigital converter works on the principle of oversampling, whereby a lowresolution ADC repeatedly samples the input signal in a feedback loop. In many cases, the ADC used is nothing more than a comparator (a 1bit 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 pulsedensity modulated (PDM) “bitstream” of 1bit 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:
 •
 V_{in} = 0 volts
 •
 V_{in} = V_{DD}
 •
 V_{in} = V_{ref}
The pulsedensity modulation (PDM) of a 1bit oversampled DeltaSigma modulator circuit may be “decimated” into a multibit 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 sevenbit sample:
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 001001001001001
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 101101101101101
 •
 010010001100010
 •
 010001100010001
 •
 111011101110111
Then, take the same five PDM bitstreams and “decimate” them over a sampling interval of 15 bits.
Suppose an analogdigital converter IC (“chip”) inputs a voltage ranging from 0 to 5 volts DC and converts the magnitude of that voltage into an 8bit binary number. How many discrete ßteps” 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?
Analogtodigital converter circuits (ADC) are usually equipped with analog lowpass filters to precondition 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 prefilters are thus known as antialiasing filters.
Determine which of the following SallenKey active filters is of the correct type to be used as an antialiasing filter:


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 överflows” and ünderflows” at the waveform’s peaks, as though the input waveform is too large (outside of the +5/5 volt ADC chip range). The technician rechecks 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 överrange” 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.
This bargraph 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 bargraph 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 R_{4} failed open:
 •
 Solder bridge (short) past resistor R_{3}:
 •
 Resistor R_{11} failed open:
 •
 Zener diode D_{1} failed shorted:
 •
 Schottky diode D_{2} failed shorted:
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 DeltaSigma analogtodigital converter!
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