Digital to Analogue Conversion

• Convert digital values to analogue voltage levels
  Digital to Analogue Conversion (DAC)
  
  

The I2C bus

I2C Master and slave

• mcp4275 DAC
  
  
• bmp180 barometric pressure sensor
  
  
• pcf8581 8 bit ADC
  
  
• ads115 16 bit ADC
  
  
• at24c32 eeprom
  
  
• ds1307 real time clock
  
  
• mma845x accelerometer
  
  

I2C addressing

I2C buses and I2C addresses on the Raspberry Pi

Initiating an I2C transfer

I2C clock frequency

I2C bus supports different transfer speeds:

• Standard: 100 kbps
  
  
• Fast: 400 kbps
  
  
• High speed: 3.4 Mbps

while the Raspberry Pi can run I2C transfers of up tp 1.66 Mbps

However: you need more low level libraries or direct register

access to accomplish these high speeds

MCP4725

Specs of the MCP4275

MCP4275 registers

MCP4275 I2C fast write

How does the I2C write cycle look like in the MCP4275?

The MCP4275 fast write cycle write only the DAC register and not the EEPROM.

This is enough for what we want to do.

MCP4275 normal write cycle

Read back the DAC data

pigpio: i2c_open

I2C access initialization with pigpio

In addition to opening the library with pigpio_start we now also must

make a connection to the I2C driver:

Accessing I2C with pigpio

Coming back to fast write mode, we must write 3 bytes:

• Address + R/W
• Register
• Data

The first byte is created and written within the library extracting the I2C address

for the I2C initialization call

i2c_write_byte_data

The pigpio library provides a function

This means we have to split our 12 bit DAC data into 2 parts:

The highest 4 bits go into i2c_reg, the lower 8 bits into bVal

Writing the DAC value, an example

dacValue is a short, while reg and value are unsigned char

DAC performance

There are a number of criteria which characterize the performance of a DAC

• Its resolution or its least significant bit (lsb)
  
  
• Its settling time (maximum speed you can go)
• Its integral non-linearity or relative accuracy
• Its differential non-linearity
• Its offset error
• Its gain error ...

Relative accuracy

Differential non-linearity

Offset error

Gain error

Settling Time

Digital to Analogue Conversion:

the mcp4275

Lecture 10

Uli Raich

UCC semester 2017/2018

The I2C bus

The I2C bus is an industrial standard 2 wire bus using a data (SDA) and a clock (SCL) line.

Adding Vcc and Gnd we need a mere 4 wires to connect

a I2C device to the Raspberry Pi cobbler

The I2C bus was invented by Philips

Typical I2C connections

Open drain signals

Open drain signals mean that you can pull a line down

but you cannot set it to a high level.

If nobody pulls the line down, then it is at Vcc level,

pulled up by a pull-up register.

Like this the contention problem is solved where one device tries

to set a line to a high level, while another sets it to low,

thus creating a short circuit.

I2C Master and slave

The I2C bus has at least one master (in our case the interface in the

Raspberry Pi’s ARM processor) and several slaves

We have the following I2C slave devices:

• mcp4275 DAC
• bmp180 barometric pressure sensor
• pcf8581 8 bit ADC
• ads115 16 bit ADC
• at24c32 eeprom
• ds1307 real time clock
• mma845x accelerometer
• pcf8574 I/O expander used on the 2-line LCD display

I2C addressing

Since there can be several slaves on the bus there must

be a means of distinguishing them through addressing:

Every I2C slave has a 7 bit address associated with it

Usually this address is determined by the manufacturer but

often there are address pins on the devices allowing the

user to have several devices of the same type on the bus

I2C buses and I2C addresses on the Raspberry Pi

The Raspberry Pi has 2 I2C buses with bus 1 being put onto the cobbler

You can find out the addresses of the I2C slaves are currently

connected with the i2cdetect command

Initiating a I2C transfer

Start stop conditions

The master starts a transfer by creating a

start condition:

• high to low transition on SDA while SCL is high

• stop condition: low to high transition on SDA while SCL is high4

Data transmission

Data are transmitted with the SDA line stable with SCL is high

A write cycle

A write cycle:
After the start condition the device address. The eighth bit, the R/W bit is kept low.

The second data byte is considered the register byte and the last one the data byte
The slave acknowledges each byte transfer.

The read cycle

The read cycle is a bit more complex:

First the master sends the slave address with R/W set to write

Then it sends the register information.

After that another address byte is sent, this time with RW set to read

And finally the slave sends the data. The master still sends the clock but

releases the SDA line allowing the slave to control it

How does a DAC work?

If you want to know more about DAC technology (and you should!)

have a look at this excellent tutorial, from which I have copied the above illustration.

Can we smooth the output signal?

Yes, it is possible to smooth out these steps.

We need a low-pass filter, which filters out high frequencies

(the abrupt steps we have in the output signal) and lets pass only slower transitions.

When looking carefully at the output of our sine generator you will

also see these steps. In this case however they come from the

limited number of sine values (100) we calculate. To improve the resolution

we would have to increase the number of samples and the frequency

with which we send these values to the DAC.

The MCP4725 12 bit DAC

As a demo device we bought the MCP4725 DAC
This is a 12 bit DAC which can be accesses by the I2C bus
Here is its data sheet

and here a photo of the device

Slide 1: Digital to Analogue Conversion: the mcp4275

Lecture 10

Uli Raich

UCC semester 2017/2018

Slide 2: Analogue versus digital

Up to now we only treated digital signals:

• on/off for the LEDs
• on/off to read the LED state
• Powering or not powering coils to generate magnetic fields in a stepping motor

• Temperatures are changing continuously and not in steps
• Pressure is an analogue value
• Distance, time, current, resistance … are all analogue values

Slide 3: Converting from digital to analogue

Since our computer is a digital device we must

• Convert digital values to analogue voltage levels
  Digital to Analogue Conversion (DAC)
• … and we must convert external analogue values to digital
  Analogue to Digital Conversion (ADC)

Slide 4: Digital to analogue conversion

A digital to analogue converter does not really convert into a continuous waveform
Since we have digital values as a base, there will be steps in the output waveform
The size of these steps depends on the resolution of the DAC
What is the smallest step a 12 bit DAC can produce on a 0..5V scale?

-- Uli Raich - 2017-10-31

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