D/A Converters
Why Interface Circuits?
A Simple Digital To Analog Converter
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Why Interface Circuits?

        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 also.

        There are numerous other situations where you need to have a computer produce a specific voltage for some purpose.
Goals

        Here's what you should be able to do after this lesson.



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.

        To 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.

Vout = (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.

Rc = 2Rb = 4Ra

Then, the output voltage expression becomes:

Vout = (RfVa /Ra) + (RfVb /Rb) + (RfVc /Rc)
Vout = (RfVa /Ra) + (RfVb /2Ra) + (RfVc /4Ra)

        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 say

Va = 5A2
Vb = 5A1
Vc = 5Ao

So
Vout = (Rf/4Ra)(4Va + 2Vb + Vc )
Vout = (5Rf/4Ra)(4A2 + 2A1 + Ao )

        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 the equivalence.
 
 

A2
A1
Ao
Binary #
4A2+2A1+Ao
0
0
0
0
0
0
0
1
1
1
0
1
0
2
2
0
1
1
3
3
1
0
0
4
4
1
0
1
5
5
1
1
0
6
6
1
1
1
7
7

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.

        What if we wanted to convert a digital signal with more bits?  The answer to this question should be fairly obvious.         Next, we're going to look at some circuits that use the D/A converter.
        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 before.

        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.)


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