A-D and D-A Converters

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1 Chapter 5 A-D and D-A Converters (No mathematical derivations) 04 Hours 08 Marks When digital devices are to be interfaced with analog devices (or vice a versa), Digital to Analog converter and Analog to Digital converter play important role. Give necessity of data converter. [2M] 5.1 Digital to Analog Converters (D-A Converter/ DAC) A digital to analog converter (DAC) takes digital data as its input and converts it into analog voltage or current that is proportional to the weighted sum of digital inputs. Input to a DAC is N-bit binary signal in parallel form. The analog output voltage V0 of an N-bit DAC is generally calculated as, = ( ) Where, K is a proportionality factor and bn is n th bit of digital input (whose value can be either 0 or 1) D to A Converter Specifications Major performance specifications of digital to analog converters are specified below. - Resolution - Accuracy - Conversion speed or Setting (or settling) time - Dynamic range - Linearity - Nonlinearity and Differential nonlinearity - Monotonocity - Temperature Sensitivity Resolution Resolution of a digital to analog converter is number of states (2 n ) into which the full scale range is divided or resolved. Here n is number of bits in the input digital word. Higher the number of bits, better the resolution. 8-bit DAC has 255 (i.e. 2 n 1) resolvable levels. It has 8-bit resolution Accuracy Accuracy of a digital to analog converter is the difference between actual analog output and expected ideal output when a digital input is given. Various sources of errors that may affect accuracy are gain errors, offset errors and nonlinearity errors. 5-1

2 Conversion speed or Setting (or settling) time Conversion speed of a digital to analog converter is expressed in terms of its setting time. Setting time is the time period that has elapsed for analog output to reach its final value after change in digital input has occurred. General purpose digital to analog converters have setting time in the range of microseconds whereas some high-speed DACs have setting time in the range of nanoseconds Dynamic range Dynamic range of a digital to analog converter is ratio of the largest output to the smallest output (excluding zero). It is expressed in db Linearity In DAC, equal increment in digital input should result in equal increment in the analog output voltage. Linearity of DAC is a measure of the precision with which linear input output relationship is satisfied Nonlinearity and Differential nonlinearity Nonlinearity of a digital to analog converter is maximum deviation of analog output voltage from a straight line drawn between end-points in terms of LSBs. Differential nonlinearity is the worst-case deviation of any adjacent analog outputs from the ideal one-lsb step size Monotonocity In ideal digital to analog converter, analog output should increase by identical step size for every one LSB increase in digital input. In such case DAC is said to be having perfect monotonocity Temperature Sensitivity Analog output voltage for any fixed digital input varies with temperature. This is called as temperature sensitivity. This is due to temperature sensitivity of voltage source, resistors, OP-AMPs and other components. 1. State DAC specifications (any four). [4M] 2. State 2 specifications of DAC. [2M] 3. Define specifications of DAC (Any 4). [4M] 4. Define resolution and accuracy with respect to D-A converter. [4M] 5. What are important specifications of DAC (Write any 4). [4M] 6. Define following with respect to DAC. [2M] i) Resolution ii) Setting time Types of Digital to Analog Converters There are various types of digital to analog converts. Two of them are discussed below. They are, - Weighted resistor DAC - R-2R ladder DAC 5-2

3 Weighted resistor DAC For an N-bit digital input, N resistors are used in a resistor network which produces current values according to the bit values. Current is produced for a bit only if its value is 1. For MSB (i.e. N-1 th bit) current I is produced. For N-2 th bit, current I/2 is produced. For N-3 th bit, current I/2 2 is produced and so on. For getting these current values weighted resistors are used. For bit N-1, resistor value R is used. For bit N-2, resistor value 2R is used. For bit N-3, resistor value 2 2 R is used and so on. The sum of all the produced currents is converted to corresponding voltage by using an OP-AMP. As shown in the circuit diagram, digital inputs operate the switches corresponding to bits. 1. Simple to design 2. Less number of resistors are required as compared to R-2R Ladder DAC (almost half). 1. Wider range of resistors is to be used. 2. Such wide range of resistors are difficult fabricate in monolithic ICs. 1. Explain weighted resistor DAC. [4M] 2. Draw circuit diagram of weighted resistor type D-A converter and explain its working. [4M] 3. Draw circuit diagram of weighted register method of D-A converter and explain in brief. [4M] R-2R ladder DAC Instead of using wide range of resistor values, this type of DAC uses only two resistor values. They are R and 2R. Input is applied to resistor network through digitally controlled switches. 1. Only 2 resistor values (i.e. R & 2R) are used. 2. So fabrication becomes easy. 1. More number of resistors (almost double) is required as compared to weighted-resistor DAC. 1. List advantages of R-2R ladder type DAC over binary weighted DAC. [4M] 2. With suitable circuit diagram explain the working of R-2R ladder DAC. Give the output expression. [4M] 5-3

4 3. Sketch R-2R ladder DAC and describe its working. [4M] Applications Digital to Analog Converters There are various applications of digital to analog converters. Some of them are, - As a multiplier - As a divider - Programmable Integrator - Low frequency function generator ICs available as Digital to Analog Converters - DAC 80 series 5.2 Analog to Digital Converters (A-D Converter/ ADC) A analog to digital converter (ADC) takes analog voltage as its input and converts it into N-bit digital output. In DAC input range is fixed (e.g. for 4-bit DAC only 16 different values of input are possible). But in ADC, input analog voltage can have any value. Whereas, for N-bit ADC the digital output can have only 2 N discrete values. Therefore, the whole range of input analog voltage is required to be represented 2 N intervals. This process of dividing input voltage range in specific number of intervals (2 N here) is called quantization. For each such interval, unique N-bit binary code is assigned. This process of assigning unique N-bit binary code to each interval is called encoding A to D Converter Specifications Major performance specifications of analog to digital converters are specified below. - Resolution - Accuracy - Gain and offset errors - Sampling frequency - Quantization error - Nonlinearity and Differential nonlinearity - Conversion time Resolution Resolution of analog to digital converter is amount of input analog voltage that needs to be increased for getting increment of digital output to the next higher binary code. 8-bit ADC can be said to have 8-bit resolution Accuracy Accuracy specification of analog to digital converter describes sum of all errors. Various errors include gain error, offset error and quantization error. 5-4

5 Gain and offset errors Gain error is difference between actual full-scale transition voltage and ideal full-scale transition voltage. Offset error is error at analog zero for A/D converter operating in bipolar mode Sampling frequency As per Shannon-Nyquist sampling theorem rate at which the input analog signal is sampled should be at least twice of the highest frequency of input analog signal. This rate is called sampling frequency Quantization error Quantization error is natural in digitization process. It can be reduced by increasing number of bits in the output digital signal. For 8-bit ADC, quantization error is 0.4% Nonlinearity and Differential nonlinearity Nonlinearity of analog to digital converter is its deviation from linear transfer curve. Differential nonlinearity is the worst-case difference between actual analog voltage change and ideal one-lsb voltage change Conversion time Conversion time is the time difference between start of conversion to the completion of conversion of analog input voltage to output digital value. 1. Define conversion time with respect to A to D converter. [2M] 2. Define following terms with reference to A/D converters and list any four applications of A/D converters. [4M] i) Resolution ii) Quantization error Types of Analog to Digital Converters There are various types of analog to digital converts. Three of them are discussed below. They are, - Ramp ADC - Dual-slope ADC - Successive approximation ADC 1. Give classification of ADCs. [2M] Ramp ADC It is also called as single slope analog to digital converter. Circuit diagram for ramp ADC is shown below. Analog input voltage (V A) works as positive input of the comparator. The negative input of comparator is taken form ramp generator, which is ramp of fixed slope. Counter and ramp generator are initially reset to zero. Counter starts counting from first clock cycle. Ramp generator is also synchronized with the same clock pulse. Counter stops when 5-5

6 ramp input equals to the analog input (V A) voltage. Here count of the counter is directly proportional to the analog input voltage. 1. Cost is less. 2. Reasonably good accuracy. 1. Accuracy depends on characteristics of ramp generator. 1. With suitable diagram explain the working of ramp type ADC. [4M] Dual slope ADC Dual-slope ADC contains four major blocks as Integrator, Comparator, Binary counter and Switch driver. The process begins with switch position S 1=0. So integrator gets input voltage as V a. This results in HIGH value of V c, which enables AND gate and clock pulse reaches to clock input of counter. Counter counts from to 111 Then switch driver changes the switch position to S 1=1 giving voltage V R as input to integrator. This makes integrator to move in positive direction and thus resulting LOW value of Vc, which disables AND gate and resulting in stopping of counting of counter. 1. Low sensitivity to noise 2. Low cost 1. There are limitations on maximum resolution of dual slope ADC. 1. Explain dual slope ADC. [4M] 2. Explain dual slope A/D converter. [4M] 3. State advantages and disadvantages of dual slope ADC. [4M] Successive approximation ADC The concept of successive approximation is similar to weighing an object of unknown weight with the help of traditional balance scale and predefined weights of ½Kg, ¼Kg and so on. Different variations are tried on trial and error basis. i.e. Successive approximation is done for finalizing the actual value. Circuit diagram of Successive approximation ADC is shown below. The comparator works as a balance scale. Output of this comparator is used setting or resetting the bits at the output of programmer. This output is converted into equivalent analog voltage from which offset voltage is subtracted and then applied to inverting input terminal of comparator. 5-6

7 1. Higher speed of operation. 2. Good ratio of speed to power. 1. Cost is high. 1. Draw successive approximation ADC. [2M] 2. Draw a block diagram of successive approximation method of A-D converter. [4M] 3. Draw block diagram of successive approximation method of A-D conversion and describe it. [4M] 4. Give advantages and disadvantages of successive approximation. [4M] 5. Compare successive approximation and dual slope type ADC (any four points). [4M] Applications Analog to Digital Converters There are various applications of analog to digital converters. Some of them are, - Music Recording - Scientific Instruments - Rotary Encoder - Digital Signal Processing 1. List any four applications of A to D converter. [4M] ICs available as Analog to Digital Converters - ADC 80 Some more 1. Give any two applications of ADC and DAC. [2M] 2. Give two applications each of DAC and ADC. [4M] 3. Explain the need for DAC and ADC and write one IC number for DAC and ADC. [4M] 5-7

Advantages of Analog Representation. Varies continuously, like the property being measured. Represents continuous values. See Figure 12.

Advantages of Analog Representation. Varies continuously, like the property being measured. Represents continuous values. See Figure 12. Analog Signals Signals that vary continuously throughout a defined range. Representative of many physical quantities, such as temperature and velocity. Usually a voltage or current level. Digital Signals