Digital Circuits

Analog-to-Digital Conversion

18 questions By Tony R. Kuphaldt

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Question 16 of 18

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.

Reveal answer

The technician failed to consider the peak voltage of the AC line!

Challenge question: one thing the technician did right in this circuit was use a transformer as the front-end of his signal conditioning network. Explain why this was a smart idea. In other words, why would it possibly be worse to simply use a resistive voltage divider to do all the attenuation, instead of using a step-down transformer to do part of it and a resistive divider to do the rest?

Notes:
The given answer is purposefully minimal, but should contain enough information that anyone familiar with RMS versus peak sinusoidal values should realize what the problem is. There is more than one practical solution for fixing this problem, so be sure to allow time for discussion into the various options.
Question 17 of 18

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:

Reveal answer

Resistor R₄ failed open: LEDs 1 through 3 always off, LEDs 4 through 6 always on (with any substantial input signal amplitude at all).

Solder bridge (short) past resistor R₃: LEDs 2 and 3 always energize at the same time.

Resistor R₁₁ failed open: LED 4 never lights up.

Zener diode D₁ failed shorted: All LEDs light up together with any substantial input signal amplitude at all.

Schottky diode D₂ failed shorted: None of the LEDs ever light up.

Follow-up question: does each comparator source or sink current to its respective LED?

Challenge question: if resistors R₁ through R₇ are all equal value, the response of the bar graph will be linear (twice the signal amplitude results in twice as many LEDs energized). What would have to be changed in this circuit to give the bar graph a logarithmic response, so it registered proportional to a decibel scale rather than a voltage scale?

Notes:
Questions like this help students hone their troubleshooting skills by forcing them to think through the consequences of each possibility. This is an essential step in troubleshooting, and it requires a firm understanding of circuit function.
Question 18 of 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!

Reveal answer

The duty cycle of the switch actuations is in direct proportion to the river’s speed.

Notes:
The purpose of this question is to present an analogy which students may use to grasp the operation of a Delta-Sigma ADC: the idea that a bitstream (PDM) may represent an analog value.