Computers don't exist in a vacuum. They have to interface with the
world in many ways. You can sit at a keyboard and type and you're
using a computer interface. You click a mouse button and that's another
interface. Measurement devices often need to communicate with computers
A motor needs a voltage
to run at a certain speed. A computer has to generate than voltage
and it will have to be applied to the motor. If the computer calculates
the voltage, then A D/A converter can take a digital signal from the computer
and generate the required voltage.
are numerous other situations where you need to have a computer produce
a specific voltage for some purpose.
Here's what you should be able to do after this lesson.
Given a D/A converter
with a given range and number of bits,
To be able to calculate
the resolution of the converter.
A Simple Digital
To Analog Converter
We are going to start by examining a simple circuit. This circuit
is an operational amplifier circuit with three input voltages.
Each input voltage is
either zero volts or five volts and represents a logical 0 or 1.
The input resistors are
chosen so that they are not all equal.
The resistors are related
by: Rc = 2Rb = 4Ra.
understand how this circuit works we will need to obtain a symbolic expression
for the output voltage - one in which we express the output voltage in
terms of the binary number that the input represents. We already
have an expression for the output voltage.
= (RfVa /Ra) + (RfVb
/Rb) + (RfVc /Rc)
We need to interpret this output voltage
expression when the inputs represent a binary number.
Let's examine the expression for the output voltage using the relation
we required for the resistors.
Each input voltage is either zero (0) or five (5) volts, representing either
a zero or a one. Although we shouldn't mix Boolean algebra variables
and ordinary algebraic variables, we are going to. We're going to
And, the question we are left with is "What
is (4A2 + 2A1 + Ao
The expression - (4A2 + 2A1 + Ao
) - can be regarded as the binary number represented by A2,
A1 and Ao. This table shows
In other words, A2
is the 4 bit, A1 is the 2 bit and Ao
is the 1 bit.
After all this, we reach these conclusions for this circuit.
The inputs can be thought
of as a binary number, one that can run from zero (0) to seven (7).
The output is a voltage
that is proportional to the binary number input.
The circuit itself converts
a digital representation of a number to an analog version of the same number.
The circuit is a digital-to-analog converter also known as a D/A converter.
What if we wanted to convert a digital signal with more bits? The
answer to this question should be fairly obvious.
More input resistances
The resistances should
be chosen in ratios of 2.
The LSB has the largest
More significant bits
have resistances that decrease by a factor of 2.
Next, we're going to look at some circuits that use the D/A converter.
One application of a D/A
converter is to convert signals generated within a computer to voltages
outside the computer. Examples where this is useful include control
systems, where a control signal could be calculated by a computer (implementing
some known control algorithm) and then converted to a voltage using a D/A
converter. That voltage could end up driving a motor for a pump -
among many other things that might occur.
D/A converters also occur
within larger systems. Shown below is an example.
A pulse generator generates
a pulse train - a sequence of zeros and ones.
The pulse train is counted
by a counter.
The counter output is
the input to the D/A.
The D/A output is compared
to the voltage input, and when the D/A output exceeds the voltage input,
the comparator output changes state and stops the counter.
The second example is really an A/D converter. It's interesting that
many A/D converters contain D/A converters within them. D/A converters
are often emedded in places where you might not expect to find them.
You use them all the time.
You may not think that you have ever used a D/A, but we will convince you
that you have. We'll do that by having you use one you have used
First, we need a source of digital signals that we can convert to analog
signals. The most common source like that is a music CD. Consider
what happens when you play a music CD. (Note, we're deliberately
emphasizing the phrase music CD because we want to emphasize it is not
a CD with program files on it that we want to use.)
Your CD has tiny little
pits on the surface. You can't really see them, but they are there.
A low power laser is flashed
on the CD, and the reflectivity is different where there is a pit.
That means that the reflected laser signal can be used to read the zeroes
and ones on the CD.
So, as the CD spins in
the holder, a sequences of zeroes and ones is generated and sent on.
That sequence of zeroes
and ones is converted to an analog voltage that is amplified and fed to
an earphone or a speaker.
So, you see that you have
used an A/D before - if you have ever used a CD player.