# 16.8 Problems

## Review Questions

- What is PCM?
- Define the term resolution.
- What is quantization?
- What is an alias, and how is it produced? How is an alias avoided?
- Define Nyquist frequency, and discuss the importance of this parameter.
- Explain how a summing amplifier may be used to create a digital-to-analog converter.
- Explain the difference between integral nonlinearity and differential nonlinearity.
- What is a smoothing (reconstruction) filter?
- What is the purpose of a track-and-hold amplifier?
- Detail the differences between flash conversion and the successive approximation technique. Where would each type be used? What are their limitations?
- Give several examples of possible DSP functions.

## Problems

### Analysis Problems

- Determine the number of quantization steps for a 10-bit system.
- A 14-bit converter produces a maximum peak-to-peak output of 2.5 V. What is the step size?
- Determine the dynamic range of the converters in Problems 1 and 2.
- We wish to resolve a 1 V peak-to-peak signal to at least 1 mV. What is the minimum allowable number of bits in the converted data?
- We wish to create analog signals using an arbitrary waveform generator. If we send out digital words at the rate of 50 kHz, what is the maximum allowable conversion speed for the DAC?
- Assume that we are trying to digitize ultrasonic signals lying between 25 kHz and 45 kHz.
- What is the Nyquist frequency?
- What is the minimum acceptable sampling rate?

- 7. Determine the maximum allowable conversion time for the ADC of Problem 6.
- 8. Given a 14-bit ADC,
- Determine the number of comparators required for the flash technique.
- Determine the number of comparisons required if the successive approximation technique is used.

- Assume that a single 16-bit ADC is connected to an embedded computer. The sampling rate is 10 kHz. Determine the data rate in bytes per second.
- Referring to Problem 9, if the computing device has 350 k bytes of RAM available for data storage, how much time does this represent?
- DAT (digital audio tape) recorders normally use a 16 bit representation with a sampling rate of 48 kHz. If the unit is used to record a performance of Stravinsky’s “Rite of Spring” (35 minutes total), what is the required storage capacity in bytes?
- If the data is transferred serially from the DAT of Problem 11 to a digital signal processing IC in real time, what is the width of each individual pulse?
- A 12-bit 2-microsecond DAC is used as part of a discrete successive approximation analog-to-digital converter. Assuming that logic delays and signal settling times are negligible, determine:
- The minimum time allowable between sample points.
- The maximum input signal frequency without aliasing.

- A 6-bit video DA converter produces a maximum output swing of approximately 1.25 V (unipolar). Determine the output voltage for the following digital input words.
- 000001
- 100000
- 111111
- 011101

- A 10-bit instrumentation DAC produces an output of 16 mV with an input of 0000000100. Determine:
- The step size
- The maximum output signal.

- An 8-bit ADC produces a full scale output of 11111111 with a 2 V input signal. Determine the output word given the following inputs. (Assume that this converter rounds to the nearest output value and is unipolar.)
- 100 mV
- 10 𝜇μV
- 0 V
- 1.259 V

- Assume that comparator/logic delays, amplifier settling times, and other factors require 400 ns total in a particular IC fabrication technique. If this technology is used to create AD converters, determine the maximum conversion time for the following 8-bit converters:
- Flash
- Successive approximation
- Staircase/Ramp type

### Design Problems

- We wish to digitize human voice signals. The maximum input frequency is to be limited to 3 kHz and resolution to better than 0.5% of the maximum input value is required.
- Draw a block diagram of the complete system.
- Determine the minimum bit requirement.
- Determine the minimum sampling rate if the Nyquist rate is set to 25% greater than the theoretical minimum.
- Determine the anti-alias filter tuning frequency.
- Determine the preferred conversion technique.
- Determine which of the ICs presented in the chapter is best suited for this system.

- We wish to design a system capable of digitizing complex signals with a spectrum ranging from DC to 400 kHz. Accuracy must be at least 0.2% of full scale.
- Draw a block diagram of the complete system.
- Determine the minimum bit requirement.
- Determine the minimum sampling rate if the Nyquist rate is set to 20% greater than the theoretical minimum.
- Determine the anti-alias filter tuning frequency.
- Determine the preferred conversion technique.
- Determine which of the ICs presented in the chapter is best suited for this system.

- Write a computer algorithm that can be used to “flip” digital data back to front. (i.e., play it backwards).
- Write a computer algorithm that will determine the maximum peak value of the digital data.
- Write a computer algorithm that will determine the RMS value of the digital data.