write a report

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Experiment 9

Analog/Digital Conversion

Introduction

Most digital signal processing systems are interfaced to the analog world through analog-

to-digital converters (A/D) and digital-to-analog converters (D/A). The purpose of this

experiment is to observe how the conversion process modifies the signal. A circuit board having

separate sample-and-hold (S/H), A/D and D/A sections is provided for this experiment. It allows

easy access to the signals at each stage of these conversion processes.

Equipment Needed

Digital Scope with event Function generator Analog/digital conversion averaging capability

circuit board

Pre Lab

Read the appropriate section(s) of your electronics text dealing with A/D and D/A

conversion, as well as S/H circuits.

Procedure

1. Connect the analog/digital conversion circuit board as shown in Fig. 1. Be sure to

observe correct polarity in connecting the +/- 15-V power supplies. The function

generator and oscilloscope ground leads should be connected to either "analog

ground." The power supply common lead is connected to "digital ground." Set the

FG for a dc output1 voltage of 0 V. Connect the scope channel 1 to the analog input

(to the S/H), and channel 2 to the analog output (from the D/A converter).

2. Vary the dc voltage at the analog input slowly from 0 V to 5 V. The eight LEDs

indicate the digital value of the converted analog input voltage. The 8-bit byte

should vary from 00h to FFh . Determine what happens when the analog input

voltage goes below zero, or above 5 V.

3. Using an increment of 1 mV in the analog voltage, carefully determine the voltage

change (to the nearest 1 mV) required to produce a 1-bit change in the digital output.

1 To obtain dc output from the HP 33120A, press and hold the buttons for two waveforms, such

as sine and triangle, simultaneously for several seconds. Remember that the actual output

voltage amplitude will not agree with the programmed value unless the output termination is set

to "High Z."

Analog/Digital Conversion

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Use the dc voltmeter to accurately measure the input voltage. This is the

"quantization step size" of the A/D converter.

4. Use a dc voltmeter connected between "analog ground" and "VREF" to measure the

internal reference voltage of the A/D and D/A converters. The result should be 5 V,

plus or minus 5%. Divide VREF by (2 8 -1) and compare with the quantization step

size measured in the previous step. These two results should be equal.

5. Set the FG for a 100-mVpp 50-Hz triangle wave with a 100-mV dc offset. Connect

channel 1 of the scope to show this analog input waveform, and connect channel 2 to

show the output voltage of the sample-and-hold stage, labeled "S/H OUT." Trigger

from channel 1. You will need to use event averaging to obtain a low-noise display

at 50 mV/div. Record this display which documents the relationship between the

low-frequency input signal and an analog sampled version of it.

6. Keep the same setup as the previous step, except move channel 2 to the "analog

output." This output shows the result of digitizing the sampled signal, and then

converting it back to analog form. Record this display which documents the

relationship between the low-frequency input signal and a sampled and quantized

version of it.

Report

1. Discuss the meaning of "quantization step size." Give its numerical value for this

A/D converter as measured in steps 3 and 4.

2. Determine the quantization step size from the waveform recorded in step 6. Include

this waveform in your report and label it to show how the quantization step size was

determined from it. Note that this is the quantization step size for the D/A converter,

not the A/D converter.

3. Compute the signal-to-noise ratio (SNR) of the signal leaving the D/A converter in

this experiment. Assume that the signal is (a) a sine wave, adjusted to have a peak-

to-peak voltage exactly equal to the full-scale voltage of the D/A converter, and (b) a

sine wave having a peak-to-peak voltage of 100 mV. For comparison, the SNR of a

vinyl record in new condition playing a loud passage of music is about 60 dB,

dropping to 40 dB as it wears out, and a CD player can achieve better than 90 dB

SNR.

4. Describe in a qualitative manner what the S/H section is doing. (You may need to

do some library research to answer this.)

Analog/Digital Conversion

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Reference - Signal-to-Noise Ratio

As you have observed in this experiment, the output signal from the D/A converter is

actually a "stair-step" approximation to the original continuous input signal. The difference

between the output and input signals can be considered to be noise. Approximate calculations

(which assume that the signal is not correlated with the conversion clock) give the rms noise

voltage as follows:

Vn,rms =

V 12REF2b (1)

where b is the number of bits used (8 in this case) and VREF is the D/A reference voltage. The

rms value of the processed signal should be computed based only on its ac content. SNR is

defined as follows:

V sig,rms

2

SNR =

Vn,rms (2)

SNR is most commonly stated in decibel notation as:

Vsig,rms 2 Vsig,rms

SNRdB =10log10 Vn,rms = 20log10 VREF + 10.8 + 6b (3)

Analog/Digital Conversion

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Fig. 1 Top view of analog/digital conversion experiment circuit board. Observe polarity when

connecting the +/- 15-V power supplies.

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Fig. 2 Schematic diagram of analog/digital conversion experiment circuit board.