University of Portland EE 271 Electrical Circuits Laboratory Experiment: Digital-to-Analog Converter I. Objective The objective of this experiment is to build and test a circuit that can convert a binary number to an equivalent analog voltage. This circuit is called a digital-to-analog converter (DAC). II. List of Needed Components The following components will be used in this experiment: Eight 1 kω resistors III. Background A digital-to-analog converter (DAC) is a circuit that converts binary numbers to analog voltages. This is a very common circuit that is used in many commercial products. For example, a music player uses a DAC to convert a digital recording to an analog signal that can be amplified and played through speakers. Digital control systems use DACs to generate voltages that are used to control motors or other actuators. The input to the DAC is a binary number (base 2). Binary numbers use a positional number system just like decimal numbers (base 10). In a decimal number, such as 271, the rightmost digit is the ones (or 10 0 = 1) place, the next digit is the tens (or 10 1 = 10) place, and the next digit is the hundreds (or 10 2 = 100) place. So 271 = 2*10 2 + 7*10 1 + 1*10 0 = 2*100 + 7*10 + 1*1 = 271. Binary numbers work the same way, except that the base is 2 instead of 10. In a binary number like 101, the right-most digit is the ones (or 2 0 = 1) place, the next digit is the twos (or 2 1 = 2) place, and the next digit is the fours (or 2 2 = 4) place. So the binary number 101 = 1*2 2 + 0*2 1 + 1*2 0 = 1*4 + 0*2 + 1*1 = 5 in decimal. Table 1 shows the decimal equivalent for all the 2-bit binary numbers. (In this lab we will only consider unsigned binary numbers, which means that they represent positive numbers only.) University of Portland - p. 1 of 9 - Exp - Digital-to-Analog
Table 1: 2-bit binary numbers and the equivalent decimal number 2-bit Binary Number Decimal 00 0*2 1 + 0*2 0 = 0 01 0*2 1 + 1*2 0 = 1 10 1*2 1 + 0*2 0 = 2 11 1*2 1 + 1*2 0 = 3 A simple DAC can be constructed from a resistor network called a R-2R ladder. The name comes from the fact that the R-2R ladder only uses two different values of resistor: R and 2R. The R-2R ladder circuit for a 2-bit DAC is shown in Figure 1. Figure 1: 2-Bit DAC The input to the circuit is a 2-bit binary number, where a 1 bit is represented by the power supply voltage Vs and a 0 bit is represented by 0 Volts. So, for example, to input the binary number 10 into the DAC, we would set Vs2 = Vs and Vs1 = 0V. In order to show how this circuit converts binary numbers to an analog voltage, let s analyze this circuit to find a formula for the output voltage Vout in terms of Vs2 and Vs1. First let s use source transformation to convert the voltage source Vs1 and the series resistance 2R to an equivalent current source in parallel with a resistor as shown in Figure 2. University of Portland - p. 2 of 9 - Exp - Digital-to-Analog
Figure 2: Circuit after source transformation Now the two resistors with value 2R on the right side of Figure 2 are in parallel and can be combined into an equivalent resistance of R (see Figure 3). Figure 3: Circuit after the two parallel resistors were combined Next, we use source transformation to convert the current source in parallel with the resistor to an equivalent voltage source in series with a resistor (see Figure 4). University of Portland - p. 3 of 9 - Exp - Digital-to-Analog
Figure 4: Circuit after source transformation We can combine the two series resistors with value R into a single equivalent resistor with value 2R as shown in Figure 5. Figure 5: Circuit after combining the two series resistors Next, we can again use source transformation to convert the voltage source and series resistor on the right side as shown in Figure 6. Figure 6: Circuit after source transformation University of Portland - p. 4 of 9 - Exp - Digital-to-Analog
Likewise, we can use source transformation to convert the other voltage source and series resistor as shown in Figure 7. Figure 7: Circuit after source transformation Now the two resistors with value 2R are in parallel, so they can be combined into an equivalent resistance of R. The two current sources are also in parallel, so they can be combined into a single current source (see Figure 8). Figure 8: Circuit after combining parallel resistors and current sources University of Portland - p. 5 of 9 - Exp - Digital-to-Analog
One last source transformation results in the circuit in Figure 9. Figure 9: Circuit after source transformation In Figure 9, we can see that if output terminals are connected to an open circuit, no current will flow through the resistor, so the voltage across the resistor will be zero (by Ohm s Law). Then Kirchhoff s Voltage Law (KVL) implies that the output voltage Vout will equal the source voltage: VVVVVVVV = VV SS1 + VV SS2. Since the circuit in Figure 9 is equivalent to 2 4 the circuit in Figure 1, this equation for Vout also holds for the circuit in Figure 1. Suppose that we use Vs = 4V as the power supply voltage so that a 1 bit is represented by 4V and a 0 bit by 0V. The output voltage for all four possible 2-bit binary numbers are shown in Table 2. Table 2: All possible inputs and outputs for 2-bit DAC 2-Bit Binary Number Decimal Vs2 Vs1 Vout 00 0 0 0 VVVVVVVV = 0 2 + 0 4 = 0VV 01 1 0 4 10 2 4 0 11 3 4 4 VVVVVVVV = 0 2 + 4 4 = 1VV VVVVVVVV = 4 2 + 0 4 = 2VV VVVVVVVV = 4 2 + 4 4 = 3VV As shown in Table 2, the output of the R-2R ladder circuit in Figure 1 is an analog voltage that has the same value as the decimal equivalent to the input binary number. Thus the circuit in Figure 1 converts a 2-bit binary number into an equivalent analog voltage. (In this circuit the output voltage equals the decimal value of the input, but in practical DAC circuits it is much more common for the output voltage to be proportional to the decimal value, but not actually equal to it.) University of Portland - p. 6 of 9 - Exp - Digital-to-Analog
A 3-bit DAC can be constructed as shown in Figure 10, and it can be shown that the output voltage is given by VVVVVVVV = VV SS3 + VV SS2 + VV SS1. 2 4 8 Figure 10: 3-bit DAC IV. Prelab Assignment Assume that the power supply for the 3-bit DAC in Figure 10 is set to 8V, so that the value of Vs1, Vs2, and Vs3 will either be 8V for a 1 bit, or 0V for a 0 bit. Compute the output Vout for all of the possible input binary numbers (see Table 3). Table 3: All possible inputs and outputs for 3-bit DAC 3-Bit Decimal Vs3 Vs2 Vs1 Vout Binary Number 000 0 001 1 010 2 011 3 100 4 101 5 110 6 111 7 University of Portland - p. 7 of 9 - Exp - Digital-to-Analog
V. Procedure Part 1: Measure the resistor values Measure and record the resistor values. Are they all within the 5% tolerance? Part 2: Construct a 2-bit DAC circuit In this part of the experiment, we will construct the 2-bit DAC circuit in Figure 1. Part 2a: Set the positive variable power supply on the Proto-board Adjust the internal positive variable supply on the Proto-board to Vs = 4V. See the Protoboard tutorial on the course website for details of how to adjust the voltage and how to connect to the positive variable supply and to ground. Part 2b: Use the Logic Switches to represent the input bits For the input binary number, we need to generate the power supply voltage Vs = 4V to represent a 1 bit and 0V to represent a zero bit. A convenient way to do that is to use the Logic Switches in the lower left-hand part of the Proto-board. See the Proto-board tutorial on the course website for details of how these switches work. Set the switches so that a 1 bit is represented by the internal positive variable supply which is set to Vs = 4V. For Logic Switch S1, verify that the output is the power supply voltage Vs when the switch is set to produce a 1 bit, and the output is 0 V when the switch is set to produce a 0 bit. Repeat for Logic Switch S2. Part 2c: Build the 2-bit DAC circuit Build the 2-bit DAC circuit shown in Figure 1 using R = 500 Ω, 2R = 1 kω, and using the Logic Switches to generate Vs1 and Vs2. Part 2d: Measure the output voltage Vout Measure the output voltage Vout for each of the four possible input values and put the results in a table similar to Table 2. Add a column in the table for % error for each output voltage. University of Portland - p. 8 of 9 - Exp - Digital-to-Analog
Part 3: 3-bit R-2R ladder Build the 3-bit DAC circuit in Figure 10. Set the positive variable supply in the Protoboard to Vs = 8V. Measure the output Vout for all the input values and record the results in a table similar to Table 3. Add a column in the table for % error for each output voltage. VI. Conclusion Write a paragraph that summarizes what you have learned in this lab. What does the R-2R DAC circuit do? Which circuit analysis techniques were important to analyzing the R-2R circuit? University of Portland - p. 9 of 9 - Exp - Digital-to-Analog