Data Converters Dr.Trushit Upadhyaya EC Department, CSPIT, CHARUSAT
Purpose To convert digital values to analog voltages V OUT Digital Value Reference Voltage Digital Value DAC Analog Voltage
Analog Quantity: An analog quantity is one that can take on any value over a continuous range of values. e.g. Temperature, pressure, light, sound, speed etc. Digital Quantity: Digital Quantity is one that takes only discrete values. These values are expressed in digital code. e.g. Binary or BCD Number
Digital to Analog Conversion D/A conversion is the process of converting value represented in digital code into a voltage or current which is proportional to the digital value. In block diagram, A, B, C, D can assume a value 0 or 1, hence there are 2 4 = 16 possible combination of input. Digital Input D C B A MSB LSB DAC V out Analog Output
For each input number (e.g. 0000, 0001, 1111) there would be unique output voltage. The analog output voltage Vout is proportional to the input binary number as: Analog Output = K x Digital Input Where K is proportionality constant, constant for given DAC The output of DAC can not be true analog quantity because it can only take specific values and in strict sense it can be said as pseudo - analog quantity.
By increasing the number of input bits, the number of possible output values can be increased and step size can be reduced (refer to figures) thereby producing the output which is more like analog quantity. Output waveform of DAC fed by A Binary counter
Digital to Analog Converters Continued When the binary counter is continuously relayed through its 16 states by applying the clock signal, the DAC output will be a staircase waveform with a step size of 1 V When the counter is 0000, output of DAC is minimum (0V) and when counter is 1111, the output of DAC is maximum (15 V), known as full-scale output.
Applications of DAC Function Generators/Oscilloscopes Digital Input & Analog Ouput Signal Generators Motor Controllers (General Electronic Controllers) Motor Control Cruise Control Valve Control Digital Audio Systems MP3 Players CD Players Digital Telephone/Answering Machines
DAC Parameters (Performance Parameters) Resolution / Step Size Accuracy / Errors Settling Time Offset Voltage Monotonicity
DAC Performance Parameters Resolution: is the amount of variance in output voltage for every change of the LSB in the digital input. How closely can we approximate the desired output signal (Higher Res. = finer detail = smaller Voltage divisions) A common DAC has a 8-12 bit Resolution Resolution V LSB V Ref N 2 N = Number of bits
2 Volt. Levels 8 Volt. Levels DAC Performance Parameters Poor Resolution(1 bit) Better Resolution(3 bit) Vout Vout Desired Analog signal Desired Analog signal 111 1 101 110 110 101 100 100 011 011 010 010 0 0 Digital Input Approximate output 000 001 Approximate output 001 000 Digital Input
DAC Performance Parameters Accuracy: The accuracy of DAC is usually specified in terms of its full scale error and linearity error, which are normally expressed as a percentage of the converter s full-scale output. Full Scale Error is the maximum deviation of the DAC s output from its expected value. Linear Error is the maximum deviation of the analog output from the ideal output (Shape).
DAC Performance Parameters Settling Time: The time required for the input signal voltage to settle to the expected output voltage(within +/- VLSB). Any change in the input state will not be reflected in the output state immediately. There is a time lag, between the two events.
DAC Performance Parameters Analog Output Voltage Expected Voltage +VLSB -VLSB Settling time Time
Analog Output Voltage DAC Performance Parameters Monotonicity: Monotonic: A increase in output voltage with an increase in digital input is called as monotonic DAC Non-Monotonic: A decrease in output voltage with an increase in the digital input is called as non-monotonic DAC Non-Monotonic Desired Output Monotonic Digital Input
DAC Performance Parameters Offset Voltage: Ideally the DAC output should be zero for zero input, however, there is a small output voltage under this situation referred as offset voltage.
R-2R Ladder Type DAC One of the most popular DAC utilizing ladder network containing series parallel combination of two resistor values R & 2R as shown in figure. Operational amplifier is configured as a voltage follower to prevent loading. R 2R Ladder DAC
CASE 1: Input 1000
R-2R Ladder Type DAC continued Case 2: Input 0100 Vout = E/4 Case 3: Input 0010 Vout = E/8 Case 4: Input 0001 Vout = E/16 In general, when the D n input is a 1 and all other inputs are 0, the output is V out = E / (2 N - n )
R-2R Ladder Type DAC continued For example, if E = 5 V then the output voltage when the input is 0100 is 5 / (2 4-2 ) = 1.25 V To find the output voltage corresponding to any input combination, apply the superposition principle and simply add the voltages produced by the inputs where 1s are applied. Typical values R and 2R are 10 k and 20k. Advantage: Resistors of only two values are required hence standard resistors can be used.
Weighted Resistor Type DAC The operational amplifier is used to produce a weighted sum of the digital inputs, where the weights are proportional to the weights of the bit positions of inputs as shown in diagram. Weighted Resistor type DAC
Weighted Resistor Type DACcontinued Since the op-amp is connected as an inverting amplifier, each input is amplified by a factor equal to the ratio of the feedback resistance divided by the input resistance to which it is connected. The MSB D 3 is amplified by R f /R, D 2 is amplified by R f /2R, D 1 is amplified by R f /4R and D 0, the LSB is amplified by R f /8R
Weighted Resistor Type DAC continued The inverting terminal of the op-amp acts as a virtual ground. Since the op-amp adds and inverts output is given as: V out D D D R 2 4 8 R 2 1 0 f D3 Disadvantage: Different valued precision resistor must be used for each bit position of the digital input
Switched Current Source Type DAC Switched current source type DAC
Switched Current Source Type DAC continued Current switching instead of voltage switching used in R-2R Ladder DAC and Weighted Resister DAC. Current can be switched in and out of the circuit faster than voltages. The currents are weighted according to the bit positions they represent and are summed up in an operation amplifier As demonstrated in figure of such type of DAC R-2R ladder is connected to a voltage source E REF. The current in first 2R resistor from supply is given by I 3 = E REF / 2R, because E REF is directly applied across 2R. The current in the second 2R is given by E REF /4R as it is equally divided between 2R and 2R to its right.
Switched Current Source Type DAC I n E R REF 1 2 N n continued In general, the current that flows in each 2R resistor is given by Where n = 0, 1,., N-1 is subscript for the current created by input D n and N is the total number of inputs. The switches that connect the currents either to ground or to the input of the operational amplifier are controlled by the digital input. The op-amp sums up all those currents whose corresponding digital inputs are HIGH. The amplifier is connected in an inverting configuration and its output is V out = - I T R, where I T is the sum of the currents that have been switched to its input.
Demonstration of Switched Current Source Type DAC The switched current DAC has R = 5 k and E REF = 10 V, calculate the total current delivered to the amplifier and the output voltage when the digital input is 1101. Solution: I T = I 3 +I 2 +I 0 EREF EREF EREF 2R 4R 16R 10 10 10 10 20 80 130 80 V out = - I T x R = - (1.625 x 5) = - 8.125 V
Analog To Digital Conversion The analog-to-digital converter (A/D or ADC) produces a digital output, that is proportional to the value of the input analog signal. When an analog signal is processed by a digital system, an ADC is used to convert the analog voltage to a digital form suitable for processing by a digital system. Typical Applications: high-fidelity digital audio processing applications, video and image data acquisition, radar signal processors etc.
Counter Type ADC (Digital ramp ADC) It is simplest type of the A/D converter. It employs a binary counter, a voltage comparator, a control circuit, an AND gate, latches and a D/A converter. The analog signal to be converted is applied to the non-inverting terminal of the opamp comparator. The output of the DAC is applied to the inverting terminal of the opamp. Whenever the analog input signal is greater than the DAC output, the output of op-amp is HIGH and whenever the output of the DAC is greater than analog signal, the output of the comparator is LOW.
Counter Type ADC continued The resolution of ADC is equal to the resolution of the DAC it contains. The resolution can also be thought of as the built-in error and is often referred to as the quantization error. Output Waveform of 4- bit Counter type ADC
Counter Type ADC continued The resolution can be given as Resolution = FSR / 2 N Disadvantage: Conversion time depends on the magnitude of the analog input. The larger the input, the more will be the number of clock pulses that must pass to reach the proper count and hence larger conversion time. For each conversion, the counter has to start from reset only and count up to the staircase reference voltage reaches the analog input voltage. Hence, extremely slow conversion rate.
Tracking Type ADC Improvised version of counter type ADC Can any one guess / describe operation of Tracking type ADC?
Tracking Type ADC continued Output waveform of Tracking Type ADC
Tracking Type ADC continued Conversion time of this ADC is the time interval between the starting of the conversion and the time the comparator outputs a LOW (stop of count) is given as: Tc (max) = (2 N-1 ) clock cycles = (2 N-1 ) x time for 1 cycle The average conversion time = Tc (max)/2 Disadvantage: I want at least 5 students in class who can guess disadvantage of this type of ADC based on previous explanations.
Flash Type ADC One of the fasted type of ADC converter. It utilizes Parallel Differential comparators, that compare reference voltages with analog input voltage. 3 bit Flash Type ADC
Operation of Flash Type ADC As the analog input voltage exceeds the reference voltage at each comparator, the comparator outputs will sequentially saturate to a high state. The priority encoder generates a binary number based on the highest-order active input, ignoring all other active inputs (refer to next slide for Encoder Truth Table)
8-to-3 bit priority encoder Truth Table
Flash Type ADC continued The main disadvantage is n-bit converter needs2 n 1 comparators, 2 n resistors and a priority encoder. A reference voltage E REF is connected to a voltage divider that divides it into seven equal increment levels. Each level is compared to the analog input by a voltage comparator. For any given analog input, one comparator and below it will have HIGH output. All comparator outputs are connected to a priority encoder, which produces a digital output corresponding to the input having the highest priority, which in this case is largest input.
Flash Type ADC continued The voltage applied to the inverting terminal of the uppermost comparator is (by voltage divider action) [7R / (7R+R)] x E REF = (7/8) x E REF Similarly voltage applied to second comparator is [6R / (7R+R)] x E REF = (6/8) x E REF and so forth. The increment between voltage is (1/8) x E REF The flash converter uses no clock signal, because there is no limiting or sequencing period.
Modified Flash Type ADC Improved version, needs lesser hardware. e.g. 8-bit conversion can be done using 30 [(2 x 2 4-1)] comparators instead of 255 (2 8 1) comparators 4 MSBs and 4 LSBs are converted separately. Modified Flash ADC
Successive Approximation Type ADC One of the most widely utilized ADC. Much shorter conversion time than the other types, with exception of flash type. It has a fixed conversion time which is not dependent on the value of the analog input
Successive Approximation Type ADC continued Block diagram of Successive Approximation type ADC
Successive Approximation Type ADC continued It consists a DAC, output register, a comparator, control circuit / logic. Operation: The bits of the DAC are enabled one at a time, starting with MSB. As each bit is enabled, the comparator produces an output of the DAC V AX. If the D/A output is greater than the analog input, the comparator ouput is LOW, casuing the bit in the control register to rest. If the D/A output is lesser than the analog input, the comparator output is HIGH, and the bit is retained in the control register.
Successive Approximation Type ADC continued The system enables MSB first, then the next significant bit and so on. After all the bits of the DAC have been tried, the conversion cycle is complete. Example: V A = 10.3 V for 4-bit ADC, conversion starting with MSB 1000 first.
Successive Approximation Type ADC continued Analog to Digital Conversion Conversion Process Sets MSB Converts MSB to analog using DAC Compares guess (output) to Analog input Set bit Test next bit