# Digital to Analog and Analog to Digital Conversion

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1 Real world (lab) is Computer (binary) is digital Digital to Analog and Analog to Digital Conversion V t V t D/A or DAC and A/D or ADC D/A Conversion Computer DAC A/D Conversion Computer DAC Digital to Analog Conversion (DAC or D/A) 8 bits A/D Computer Digital to Analog conversion involves transforming the computer s binary output in 0 s and 1 s (1 s typically = 5.0 volts) into an representation of the binary data D/A conversion can be as simple as a weighted resistor network 4 - bit DAC Converter Resistor values correspond to binary weights of the number D 3 D 2 D 1 D 0, i.e. 1/8, 1/4, 1/2, and 1 Electronics Workbench Models 4bitDAC.ewb Using EWB we can model this device 1

2 Difficulties: 1. This setup requires a wide range of precision resistors A 10 bit DAC needs resistors ranging from R to R/ The circuit driving the DAC (usually a computer) must supply a wide range of currents for a constant V out As was seen in the Workbench example, the output voltage from a DAC can change by only discrete amounts, corresponding to the level associated with a 1 bit binary change. For a 8-bit DAC Smallest step in output voltage is v/256 8 bits corresponds to 256 different values For a 5.0 volt DAC this step size is ~ 19.5 mv A modification of the weighted resistor DAC is the so called R-2R LADDER DAC, that uses only 2 different resistances An actual R-2R DAC showing input Voltmeter reading is determined by the binary number ABCD and the resistor weights MSB = 1/2 of V ref LSB = 1/4 of V ref = 1/8 of V ref = 1/16 of V ref R-2R Ladder DAC Workbench Model = 1/2 (5) + 1/4 (0) + 1/8 (5) + 1/16 (5) 3.4 volts In actual DACs, the converters will drive amplifier circuits in most cases 2

3 Amplified DAC with bipolar ( ± V out ) output If one wants only positive or negative output, one can use a BASELINE ADJ. for the Op Amp baseline.ewb r2rdac.ewb Analog-to Digital Conversion (ADC or A/D) An ideal A/D converter takes an input voltage and converts it to a perfectly linear digital representation of the signal 8 bits A/D Computer If you are using an 8-bit converter, the binary representation is 8-bit binary number which can take on 2 8 or 256 different values. If your voltage range were 0-5 volts, then 0 VOLTS VOLTS An 8-bit converter can represent a voltage to within one part in 256, or about 0.25 %. This corresponds to an inherent uncertainty of ± ½ LSB (least significant bit). Analog Voltage 1 LSB Decimal 128 = Voltage (Volts) Bit 7 Bit 6 Bit 5 Bit 4 Bit 3 Bit 2 Bit 1 Bit 0 MSB LSB Notice the bits are designated B7 - B0. Bit B7 is the Most Significant Bit while B0 is the Least Significant Bit

4 Number of Bits (N) Resolution (1/2 N ) Increment (mv) for 5 volts Types of Analog to Digital Converters 6 1/ / / / / / Type 2. Integrating or Dual Slope 3. Parallel or Flash 4. Successive Approximation Type As the Clock sends regular pulses to the counter, the counter outputs a digital signal to the Digital-to-Analog converter When is received, control logic initializes the system, (sets counter to 0), and turns on Clock sending regular pulses to the counter. As the counter counts, its output to the generates a staircase ramp to the. As the ramp voltage increases to the, it rises closer and closer to at which point the shifts states 4

5 When the ramp voltage exceeds, the output shifts which signals the control logic to turn off the Once the digital output has been read by the associated circuitry, a new start signal is sent, repeating the cycle. With the off, the counter reading is proportional to Note that the conversion time depends on the size of the input signal V in Conversion time Conv.time With a counter type A/D, if the signal is varying rapidly, the counter must count up and reset before each cycle can begin, making it difficult to follow the signal. Tracking ADC - similar to the counter type except it uses an up/down counter and can track a varying signal more quickly Track & Hold Logic Up/Down Integrating or Dual Slope A/D integrator When conversion is initialized, the switch is connected to which is applied to the op amp integrator. The integrator output (>0) is applied to the integrator -V ref Control logic -V ref Control logic 5

6 As conversion is initiated, the control logic enables the which then sends pulses to the counter until the counter fills (9999) integrator As the counter resets ( ), an overflow signal is sent to the control logic integrator this activates the input switch from to -V ref, applying a negative reference voltage to the integrator -V ref Control logic -V ref Control logic overflow The negative reference voltage removes the charge stored in the integrator until the charge becomes zero. The operation of this A/D requires 2 voltage slopes, hence the common name DUAL-SLOPE. At this point, the switches states producing a signal that disables the and freezes the counter reading. The total number of counts on the counter (determined by the time it took the fixed voltage V ref to cancel ) is proportional to the input voltage, and thus is a measure of the unknown input voltage. Integrator Output Voltage charging up the capacitor full scale conversion discharging the capacitor half scale conversion quarter scale conversion fixed time measured time Since this A/D integrates the input as part of the measuring process, any random noise present in the signal will tend to integrate to zero, resulting in a reduction in noise. Flash Converters These type of A/D s are used in almost all digital meters. Such meters usually are not used to read rapidly changing values in the lab. Consequently the major disadvantage of such converters (very low speeds) is not a problem when the readout update rate is only a few times per second. If very high speed conversions are needed, e.g. video conversions, the most commonly used converter is a Flash Converter. While such converters are extremely fast, they are also very costly compared to other types. 6

7 Parallel or Flash Converters The resistor network is a precision voltage divider, dividing V ref (8 volts in the sample) into equal voltage increments (1.0 volts here) to one input of the. The other input is the input voltage Each switches immediately when exceeds V ref. s whose input does not exceed V ref do not switch. A decoder circuit (a to-3 priority decoder here) converts the outputs to a useful output (here binary) The speed of the converter is limited only by the speeds of the s and the logic network. Speeds in excess of 20 to 30 MHz are common, and speeds > 100 MHz are available (\$\$\$\$\$). While integrating or dual-slope A/Ds are widely used in digital instruments such as DVMs, the most common A/D used in the laboratory environment is the successive approximation. The cost stems from the circuit complexity since the number of s and resistors required increases rapidly. The 3-bit example required 7 converters, 6-bits would require 63, while an 8-bits converter would need 256 s and equivalent precision resistors. Successive approximation converters are reasonably priced for large bit values, i.e. 10, 12 and even 16 bit converters can be obtained for well under \$100. Their conversion times, typically ~ µs, are adequate for most laboratory functions. Successive-Approximation A/D Successive-Approximation A/D input D/A Converter V ref input D/A Converter V ref Digital Output Data Digital Output Data STRT Successive Approximation Register STRT Successive Approximation Register At initialization, all bits from the SAR are set to zero, and conversion begins by taking STRT line low. First the logic in the SAR sets the MSB bit equal to 1 (+5 V). Remember that a 1 in bit 7 will be half of full scale. 7

8 Successive-Approximation A/D Successive-Approximation A/D input D/A Converter V ref input D/A Converter V ref Digital Output Data Digital Output Data STRT Successive Approximation Register STRT Successive Approximation Register The output of the SAR feeds the D/A converter producing an output compared to the input voltage. If the D/A output is < Vin then the MSB is left at 1 and the next bit is then tested. If the D/A output is > Vin then the MSB is set to 0 and the next bit is set equal to 1. input voltage ¾FS Successive bits are set and tested by comparing the DAC output to the input in an 8 step process (for an 8-bit converter) that results in a valid 8-bit binary output that represents the input voltage. ½FS ¼FS D/A output for 8-bit conversion with output code CLOCK PERIOD Successive approximation search tree D/A output compared with to see if larger or smaller for a 4-bit A/D Note that the successive approximation process takes a fixed time - 8 cycles for the 8-bit example. For greater accuracy, one must use a higher bit converter, i.e. 10-bit, 12-bit, etc. However, the depth of the search and the time required increases with the bit count. 8

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