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Bucknell ELEC 350 - D/A Converter Based on Summing Amplifier

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IntroductionExperimental ProcedureELEC 350L Electronics I Laboratory Fall 2011Lab #2: D/A Converter Based on Summing AmplifierIntroductionDigital-to-analog (D/A) converters are widely used in many modern communications and instrumentation systems, and they serve as the key element of all MP3, compact disk, and digital video playback units. Although many D/A converters are made using resistor networks with precision manufactured components, a summing amplifier based on an op-amp can also be used for this type of circuit. The voltage gains from the various input ports to the output port are set simply by adjusting resistor ratios. This eases the tasks of controlling the conversion process and of scaling the various binary input voltages to produce an appropriate output voltage. In this lab experiment you will build a D/A converter based on the summing amplifier circuit.Theoretical BackgroundThe basic function of a D/A converter is to translate (convert) a number represented in binary form to an analog voltage value that corresponds to that number. For example, a 3-bit D/A converter might be designed to produce the output voltages shown in Table 1 for the eight possible binary numbers that can be represented by three binary digits.Table 1. Output voltages of a 3-bit D/A converter for all possible inputs.BinaryNumberDecimalNumberOutputVoltage (V)000 0 0.0001 1 1.0010 2 2.0011 3 3.0100 4 4.0101 5 5.0110 6 6.0111 7 7.0Although the output voltages shown in Table 1 range from zero to 7.0 V, a D/A converter can be designed to provide any desired range of output voltages. Most D/A converters are designed to produce equal-sized increments (steps) from one voltage level to the next. In the example shown in Table 1, the step size is 1 V. If smaller step sizes are desired for a given output voltage range (that is, if greater resolution is needed), then a larger number of bits must be used to represent thevoltage values.1 of 4A 3-bit D/A converter can be built easily using a summing amplifier. A typical circuit is shown below in Figure 1. An inverter circuit (constructed around op-amp IC2) has been added to the output of the summer to produce a positive output voltage. (The output of the summer circuit op-amp IC1 is negative if the input voltages v1 through v3 are positive.) It is relatively easy to show that the output voltage of the complete circuit is given by33422411456vRRvRRvRRRRvo.Figure 1. Three-bit D/A converter based on a summing amplifier. The choice of power supply voltages (±15 V in this case) is somewhat arbitrary; however, the desired output voltage range must lie between the two supply voltage values. The small triangles represent connections to ground (the reference node).The input voltages v1 through v3 represent the three bits of a given binary number. A logical 0 is usually represented by 0 V, and a logical 1 is usually represented by a particular positive voltage value. In Figure 1, input voltage v1 represents the most significant bit (MSB), v2 the second bit, and v3 the least significant bit (LSB). The input resistors R1 through R3 must be chosen so that a change in state in the bit applied to a given input causes an appropriate corresponding change in the output voltage. For example, for a converter circuit designed to produce the outputs given in Table 1, if v1 changes from logical 0 to logical 1, the output voltage must rise by 4 V. Likewise, ifv2 changes from 0 to 1, the output voltage must rise by 2 V; and if v3 changes, the output must change by 1 V. Note that the voltage increments are related to each other by powers of 2. The value of R4, along with those of R5 and R5, set the overall output voltage range obtained for the full range of input binary numbers between 000 and 111.+−v3R2R4R1v1−15 V+15 VR3v2+−voR6−15 V+15 VR5IC1IC22 of 4Experimental Procedure- Verify the expression for vo in the “Theoretical Background” section by deriving it yourself in your note taker’s notebook. There are multiple valid approaches for doing this.- Design a 3-bit D/A converter using the summer/inverter circuit shown in Figure 1. Assume that a logical 0 input bit is represented by 0 V and a logical 1 input bit is represented by +5 V.The power supply voltages for the op-amps should be ±15 V. For the input resistors R1 through R3 use standard values roughly in the 10 k- to 100 k- range. Do not use multiple resistors in series or parallel to create nonstandard values; each resistor in Figure 1 should be implemented using one physical component to achieve a very compact design. Choose the value of feedback resistor R4 so that the binary number 111 (represented by v1 = 5 V, v2 = 5 V,and v3 = 5 V) produces a voltage at the output of IC1 of –7 V. The output voltage increment should therefore be 1 V with eight output voltage values ranging from 0 through −7 V, corresponding to the eight binary numbers 000 through 111. (Hint: Use the superposition principle to simplify your design.) Finally, set R5 and R6 to appropriate values so that the output voltage vo of the complete circuit ranges from 0 to +7 V. Your note taker should briefly(but completely) explain how you derived the resistor values.Since you must use standard values for all of the resistors in your circuit, you might not be able to create the exact resistor ratios that you want. Try to get as close as possible to your design values, but don’t spend too much time working out a solution. After all, the resistors available in the lab don’t have very tight tolerances (5% in most cases).- Construct a D/A converter according to your design, and create a truth table like the one shown in Table 1 by measuring the actual output voltages (using the multi-meter) obtained for the various binary input combinations. Use the 0-6 V section of the bench-top power supply to generate the +5 V needed to represent binary 1. Be sure that all power supplies used have a common ground connection. Use SPDT (single-pole, double-throw) switches as shown in Figure 2 to select between logical 0 and 1 for each bit. The truth table should include the desired (target) output voltages as well as the measured voltages for comparison. Include the percentage error between the desired and measured voltage for each input state.Figure 2. Method of applying logical 0 (0 V) or logical 1 (5 V) inputs to the D/A converter. The indicated switches are type SPDT (single-pole double-throw).to v1 in Fig. 1+5 Vto v2 in Fig. 1to


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Bucknell ELEC 350 - D/A Converter Based on Summing Amplifier

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