# EECS 373 Lab 7: Data Converters

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

11/07/2011

## 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.

## Overview

### Pre-Lab Assignment

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

### In-Lab Assignment

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.

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"

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

Using the signal generator as a signal source, provide a sine wave that centers a sine wave over the input range of the ADC (0 - 2.56 volts). A DC offset of 1.25 volts should be fine with a Vpp (peak to peak) voltage of 2.5 volts. Be sure the signal generator output is set to High Z to insure accurate signal levels. Verify with the scope before attaching to the kit to avoid damage to the ACE.

#### Aliasing Measurements

Slowly increase the frequency of the signal generator while observing and measuring the frequency of DAC. Determine the frequencies or frequency ranges for the following questions. You will need this information to answer questions in the post lab.
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

Quantizing in the DAC output can produce high frequency components that in the audible range sound like common radio static. To remove these components a low frequency pass filter can be used to reject the high frequency components. We will use a simple passive filter consisting of 2 components.

To remove the high frequency components, consider a half power point near the max frequency that you wish to pass. The half power point or 3db down point (.707 volts below input voltage) is give for a low pass filter to be 2pi f = 1/RC. Let's consider the case for smoothing a 1 KHz signal. Choosing 2 KHz for the 3 db down point gives 6.28 × 2000Hz × RC = 1. We must choose common RC values. Starting with 1K ohm resistor gives a C of 0.08 UF (micro farads or 10^-6 farads). The closest value in the lab is .068 uf. This will produce a 3db frequency of ~2.34KHz. Close enough!

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

In order to observe the ADC result correctly, we output the data through screen instead of using the scope. Adding the following line in the while(1) loop. Follow lab 5 instructions to setup UART_0 for printf output.
`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.

TAKE CARE TO MATCH THE GROUND TAB ON THE BANANA PLUG TO BNC ADAPTER TO THE GND PLUG OF THE POWER SUPPLY OR YOU WILL SMOKE THE SMARTFUSION KIT!

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.

 Voltage Range (mv) Conversion Value 0     <---> 0 <---> 0<-->1 unstable <---> 1 <---> 1<-->2 unstable <---> 2 <---> 2<-->3 unstable <---> 3 <---> 3<-->4 unstable

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.

When testing or characterizing devices, it is convenient to use a prototype board (protoboard) or breadboard. The board we will use is the Sparkfun Breadboard.  For more information about protoboards see Wikipedia : BreadBoard. In this case, we will provide power, control and output signal connections between the protoboard and SmartFusion expansion card.

From the specification you will see the accelerometer is a surface mount device. To make connections to this device, you will have to solder little wires onto the pads or better yet use what is known as a breakout pcb to facilitate the connections. You may have to do something like this if you use such a component in your project.

Fortunately, Spark fun provides this component mounted to a PCB board with convenient solder points connected  to the device pins. Here is the link  Sparkfun MMA7361L Kit .  We have even soldered on a set of pins (a header) so you can plug it into the protoboard.

The first order of business when breadboarding a device is to determine the power connections and requirements. You will find in the specification that the accelerometer requires 3.3 volts. It is important not to exceed the maximum rating or apply the voltage in reverse (negative voltage) or you will smoke the device.

Place the accelerometer in the protoboard as shown below.  You may have to rock the pins a bit to get it to go in the protoboard.  The power pins are labeled GND and VCC on the accelerometer board. Rather then hook the power directly to these pins, jumper them over to the power rails on the protoboard. Supply 3.3 volts to the power rail from the expansion board or you can use a power supply. If you use a power supply, use the banana plug terminals on the protoboard to make the connection. You will also need to provide a GND connection from the expansion board or power supply.

Notice that a decoupling  capacitor is added across the power rail. This is generally good practice when using a protoboard. Notice also that a header pins are used to make some of the connections. These are very handy when working with protoboards. They are available in the lab in 40 pin lengths and can simply be broken to shorter lengths as shown in the protoboard.

Next it is necessary to provide inputs to a few of the control signals on the accelerometer. There is a self test control input labeled ST and a gain select labeled GSEL that will need to be set to GND.  There is also a sleep mode that must be disabled by applying VCC to the input. This pin is labeled SPL. The 0GD pin is an output that will signal when 0 G is detected. In addition you should add some header pins to the X, Y and Z outputs so you can easily attach a probe or jumper. Additionally, put a jumper in the GND rail to conveniently attach your scope probes.

### Observing the Accelerometer Output with the Oscilloscope

When using devices for the first time, it is helpful to get a sense for their performance by observing the behavior with standard lab equipment. Lets try this with accelerometer by observing its behavior with the oscilloscope. The accelerometers gain is set such that the accelerometer will detect +/- 1.5 g maximum. You can use gravity as your yardstick. Connect a scope probe ( a real scope probe, not grabber clips) to the Y axis output. Make the following measurements. Save your values for your post lab report.

When the protoboard is oriented flat on the desk, what value do you read?

When you tilt the board to the right, what smallest value do you read?

When you tilt the board to the left , what largest value do you read?

### Voltage Scaling and Buffering

Scaling

The accelerometer will potentially produce a full scale voltage near its supply voltage or 3.3 volts. You can observe this on the Oscope by shaking the sensor exceeding +/- 1G. This can be a problem if you want to observe sensor extremes on the ADC. The ADC can not measure voltages exceeding its reference voltage of 2.56 volts. Voltages exceeding 2.56 volts will be capped.  If you want to measure forces at this extreme you will have to scale the accelerometers voltage range of 0 - 3.3 volts to the ADC range of 0 - 2.56 volts.

In this case we need to reduce the signal by the scaler 2.56 volts / 3.3 volts = 0.7758. Since we are reducing the signal, it is possible to reduce the voltage with a simple voltage divider.

Where Vout is equal to Vin (R2 + (R1 + R2)).  See this link for more details.  Using standard resistor values it is possible to achieve the correct scaling with R1 = 2.7K and R2 = 10K. This will result in a scaling multiplier of  0.7874. Close enough!!

You will find that if you connect this circuit to the accelerometer it will not scale as expected. This is because the accelerometer output does not act like an ideal voltage source (no source resistance). There is an output resistance that is in series with the voltage source that will combine with R1 to change the voltage divider ratio. The circuit is modeled like this.

Determine R accel.
Hint: Vaccel is can be determined by measuring the open circuit voltage at V1 (R1 and R2 disconnected). Then measure V1 under the load of R1 and R2. Be sure to keep the accelerometer stable during these measurements.

Provide your calculations and findings for the answer sheet in the Post Lab.

You can isolate the accelerometer from  the divider with a impedance buffer or more commonly known as a voltage follower.  The voltage follower has a very large input resistance and a very small output resistance. As a consequence, it does not load the source voltage and does not load the voltage divider. The voltage follower can be implemented with an op amp as follows.

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.

On your protoboard, wire the scaling circuits for all 3 accelerometer axis using the op amp buffer.  You can supply the op amp chip with 3.3 volts from the expansion board. You can check the output of the divider for correct scaling by using the Oscope. Do not connect to the ADC yet.

The input resistance of  the ADC can also act to load R2 of the voltage divider. It manifests as a resistor in parallel with R2.  Therefore, if the load resistor is large, the effective parallel combination of R2 and the load resistor will be R2 or it will not effect the voltage divider. Fortunately, this is the case with our ADC and there is not need to buffer or compensate the divider for loading effects.

Note, before you can attach the divider to the ADC input channels, you will have to program the ACE to enable these channels (below) or you may observe loading effects.

Configure the  ACE ADC for 3 inputs or services.

Remember to Generate in the MSS. This will add the additional hardware and update the ADC drivers. You will have to copy the updated drivers to your softconsole project.

The ADC channels are referenced in the ADC drivers with the Signal names choosen in the ACE, ADC setup. For example, to add ADC channels 2 and 3 consider the following code.

`#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

Write an application program so that the LEDs mirror the accelerometer status. That is, when the board is sitting flat the middle LEDs should be illuminated, as the board is tilted, the LEDs should reflect the current board position:
```
LEDs:   00011000      10000000      0000001

/          \
BOARD:  --------          /            \
/              \
/                \
```
Selection through the 3 accelerometer axes with the push buttons. You can choose the switch combinations and it is OK if you have to hold the switch to maintain the selection. Consider using the builtin MSS GPIO module to provide your LED and switch hardware interface (this will involved opening the MSS configurator, configuring the GPIO block to route GPIOs through the "Fabric" (FPGA), and then mapping the GPIOs to the LEDs and switches).

## Post-Lab Questions

The post lab questions can be found on this answer sheet. Use this form to submit your answers or copy into to a word processing program.