EECS 373 Lab 7: Data Converters

Copyright © 2010-2011 Ye-Sheng Kuo, Thomas Schmid, Matt Smith, Lohit Yerva, and Prabal Dutta.

11/07/2011

Schedule

EECS 373 Fall 2011 Home Page

EECS 373 Labs Google Calendar

Introduction

As you might guess, with all the other goodies included in the SmartFusion MSS the folks at Actel did not forget ADC and DAC resources. The MSS ACE (Analog Computing Engine) is relatively complex component providing DAC/ADC functionality, sampling control, analog threshold detection, filtering and DMA access just to mention a few. Despite this apparent complexity, the ACE can be relatively easy to use. The ACE like the other MSS components is automatically interfaced to the peripheral bus and a user friendly GUI is provided for configuration. Of course, a library of drivers is also generated.

Objectives

The purpose of this lab is to...

1. Learn how to configure the ACE for basic DAC and ADC operations.
2. Learn to measure ADC quantization and typical transfer function characteristics.
3. Learn the basics of sampling by observing aliasing of sampled sine wave.
4. Learn how to build a simple audio amplifier.
5. Sample and record an audio signal for playback using the ACE and your audio amplifier.

Background

ADC Quantization and Transfer Function Characteristics

Quantizing error is inherent in most measurements and limits the certainty of measurement. The quantizing error for an ADC is defined to be 1 LSB. It can also be expressed in volts or LSBv for an n-bit ADC .

Quantizing error in volts = voltage range of conversion/2^n

For our converter, the voltage range is 2.56 volts.  If we program the ACE to be an 8 bit ADC, the quantizing error in milli-volts will be

LSBv = 2.56 volts/2^8 = 10 mv

So, you can only know the value to 10 mv. The ideal quantum size of 1 LSB can actually vary to be larger or smaller from fabrication issues and other sources. These effects are characterized as integral non-linearity (INL) and differential non-linearity (DNL).  Under normal conditions in the lab you will NOT observe this.

Plotting the conversion value against the analog value defines the ADC transfer characteristic or input to output relationship.

The first graph shows the ideal transfer function excluding quantizing effects. The second case illustrates the affect of quantizing resulting in a stair case like transfer function. In this case the quantization error is from 0 LSB to 1 LSB. The last graph illustrates an ADC model that shifts the transfer function to center the quantizing error over the conversion intervals. In this case, the quantization error is +/-  ½  LSB. In both cases the quantizing error is 1 LSB, but the relationship of the conversion value to the input voltage is shifted by ½ LSB.

Sampling Basics

When converting relatively stable voltages to digital values a few samples are sufficient to represent the voltage. However, when sampling time varying signals the question arises, just how many samples are required to represent the signal. The Nyquist-Shannon sampling theorem predicts that periodic signals can be reproduced when the original signal is sampled at >= 2 times its period. If the signal is sampled at a rate that is less than the 2 times its period, the reconstructed signal will have a different frequency and shape. A simple predictor is given by the following equation: 

alias frequency = sampled signal frequency - sampling frequency

The reconstructed signal is commonly referred to as an alias and is a common problem in applied signal processing. There are many topics forming the foundation of signal processing, but these basics should cover our needs for the present.

Additional Material

• Programmable Analog UG
• MSS ACE configuration UG
• MSS ACE Driver UG
• Wikipedia : Sampling theorem
• Wikipedia : BreadBoard
• Wikipedia: Low-pass filter
• Resistor Color Code
• Datasheet : LM741
• Datasheet : LM386

Overview

Pre-Lab Assignment

1. Read through the lab 7 notes.
2. Read through the data converter lecture.

In-Lab Assignment

1. ADC/DAC Basics
2. Aliasing, Quantization error, Smoothing filter
3. Simple Audio system

In-Lab Assignment

Aliasing, Quantization error

Configuring the SmartFusion ACE 

For this part of the lab we will configure the ACE component in the MSS, synthesize, Place and Route and flash the FPGA.  Disable everything but the ACE and UART_0.

Each SmartFusion Eval Kit has 10 direct analog input channel and 2 Sigma-delta DACs. We want to use just one of each. Open the Libero, SmartDesign. Double click ACE

In left column, add a ADC Direct Input service. Put ADCDirectInput_0 in Signal Name and click OK. On the top of configurator, set the resolution to 8 bits.

Add another Sigma Delta DAC service, select ACE Accumulator as DAC input and select the DAC resolution to 8 bits. Click OK.

Set your ADC Direct Input Package Pin to V12 ( ADC5 ), and Sigma Delta DAC Package Pin to V7 ( SDD0 )

Go to Controller tab, select only ADC1_MAIN. Add all Available signals to sampling rate requirement. Click Calculate Sequence and Actual Rate

Notice that the Total sampling rate should be 87.000 ksps. We want to slow it down to 8 ksps.
Set the Operating sequence entry to Manual and insert a WAIT TIME operating sequence slot, using , and configure it to 115us. Move the Wait for 115.00us above Restarts the execution sequence for this timeslot. Click Calculate Actual Rate. The Actual Rate for ADC / DAC should be 8.000 ksps.

Click OK and go to Firmware tab. Check the UART, GPIO, and ACE drivers.

Click Save and Generate. Put the IP core to canvas and run the synthesis, place & route and flash your SmartFusion.

A Simple ADC/DAC Application

Create a C project in Softconsole as you did before, set the linker script, import the drivers. The following code reads the ADC
and  write the DAC with the ADC conversion value

#include <stdio.h>

#include <inttypes.h>

#include "drivers/mss_ace/mss_ace.h"

#include "drivers/mss_uart/mss_uart.h"


ace_channel_handle_t adc_handler;

int main(){
    ACE_init();

    /* DAC initialization */
    ACE_configure_sdd(
    	SDD1_OUT,
    	SDD_8_BITS,
    	SDD_VOLTAGE_MODE | SDD_RETURN_TO_ZERO,
    	INDIVIDUAL_UPDATE
    );
    ACE_enable_sdd(SDD1_OUT);

    /* handler for ADC channel */
    adc_handler = ACE_get_channel_handle((const uint8_t *)"ADCDirectInput_0");

    while(1){
    	uint16_t adc_data = ACE_get_ppe_sample(adc_handler);
    	ACE_set_sdd_value(SDD1_OUT, (uint32_t)(adc_data>>4));
    }
    return 0;
}

Put the code in a main.c file. Compile the source code and launch the debugger session.

Connecting to the DAC and ADC

Hook the signal generator to the extension board  header pin 5 ( paper label)  in the bottom right corner to provide input to the ADC. If you don't have a paper label this is labeled ADC1. Observe the DAC output on the 2nd BNC connector from the header pin.

Test ADC and DAC setup

Aliasing Measurements

1. Over what frequency range is the reproduced signal frequency (DAC output) and signal shape visually reproduced well?
2. Over what frequency range is the reproduced signal frequency intact, but the signal shape noticeably quantized?
3. At what frequency is the reproduced signal frequency nearly zero?
4. At what frequency is the reproduced signal frequency nearly half the source?

Implementing a Smoothing Filter

Set the source signal to 1 KHz sine wave. Observe the DAC output. Notice the quantizing steps in the output wave form. With the input and output waveforms displayed on the scope, it should look something like this.

For the post lab, record the number of quantizing steps there are per cycle.

Construct a low pass filter with a 1K ohm resistor and 0.068uf capacitor on a protoboard. Wire the DAC to the input of the filter and observe the output.

You should notice a signal that is pretty close to a continuous sine wave. The signal will be attenuated because of the filter.

The filter output amplitude should be about 0.707 the value of the input voltage value at the 3db down frequency (2.34KHz) . Notice that it is considerably lower. Adjust the frequency until the filter output value is 0.707 the value of the source frequency and record the frequency for the post lab.

Measuring Quantization Error

printf("adc_result: %u\r\n", (adc_data>>4));

You will measure the transition or boundary voltages for the first 4 ADC conversion values 0, 1, 2 and 3. The lab power supply 0-6 volts output can be adjusted to ~ 1mv, so you can use this as a voltage source. The voltage meter on the power supply is not accurate enough for 1 mv measurements, so you should use the DMM. Be sure to use the cable configurations shown in the following configuration or you will introduce interference that will make it difficult to resolve the transition voltages.

The procedure for measuring the transitions voltages is to simply start at 0 volts then gradually increase the voltage until you see the conversion value change. The voltage at which the ADC conversion value changes Is the transition voltage. You will find that the transition voltage does not occur neatly on distinct boundaries. In fact, it will toggle between adjacent conversion values for several millivolts. It will look something like this

Input Voltage (mv)      0-------4-------8--------------14-------18--------------24-------28--------------etc

Conversion Value     0,0,0,0-1,0-1,-1,1,1,1,1,1,1-2,1-2,1-2,2,2,2,2,2,2-3,2-3,2-3,3,3,3,3,3,

The conversion uncertainty over the transition boundary is from signal variation in the source voltage. In other words, it is an error source from the measurement procedure. It is NOT from ADC quantizing.  You can assume the first voltage reading that is associated with an unstable conversion value is the transistion volage for that interval. For example, in the above example 0 to 4mv is the conversion interval for 0, 4mv to 14mv is the conversion interval for a value of 1, etc.

Mearsure the conversion value as a function of the input voltage as shown above for conversion values 0 through 3. Save these values for your post lab report.

Reading Accelerometer Signals with ADC

For this part of the lab we will use the ACE, ADC to acquire the signals of a typical device:  the Freescale MMA7361L  triple axis accelerometer. This sensor is commonly used in EECS 373 projects and represents a typical analog device interfacing application. 

Breadboard the Accel

Observing the Accelerometer Output with the Oscilloscope

Voltage Scaling and Buffering

A very handy op amp for this purpose is the Microchip MCP6024 .  It has 4 op amps in the same package and works well for our voltage ranges. The following showes how to connect the buffer and divider.

Providing more ADC channels

#include <stdio.h>
#include <inttypes.h>
#include "drivers/mss_ace/mss_ace.h"
#include "drivers/mss_uart/mss_uart.h"

ace_channel_handle_t adc_handler2;
ace_channel_handle_t adc_handler3;

int main(){
    ACE_init();
    /* DAC initialization removed */

    adc_handler2 = ACE_get_channel_handle((const uint8_t *)"ADCDirectInput_2");
    adc_handler3 = ACE_get_channel_handle((const uint8_t *)"ADCDirectInput_3");


    while(1){
    	uint16_t adc_data2 = ACE_get_ppe_sample(adc_handler2);
	uint16_t adc_data3 = ACE_get_ppe_sample(adc_handler2);
    }
    return 0;
}

Post-Lab Assignment

LEDs:   00011000      10000000      0000001

                           /          \
BOARD:  --------          /            \
                         /              \
                        /                \

Post-Lab Questions