Digital - to - Analog And Analog - to - Digital converters
A/D AND D/A CONVERTERS
Digital - to - Analog converters The input to a D/A converter is an N-bit binary signal. The analog output voltage Vo of an N-bit straight binary D/A converter is related to the digital input by the equation.
where, K = Proportionality factor.
bn = 1 if the nth bit of the digital input is 1. = 0 if the nth of the digital input is 0.
Two Types of Commonly Used D/A Converters.
1. Weighted-resistor D/A converter and
2. R-2 R ladder D/A converter.
Resister for MSB = R Resister for LSB = 2N–1.R
Example : 4 bit D/A, V (1) = 1V, RF = 8R. Obtain analog output for 0101?
D/A Performance Characteristics 1. FSV (full scale voltage): It represents maximum output voltage for the DA converter and is obtained when all bits of digital input are 1.
The output for any bit is e0 = VR/2n
where n = no. of bits.
FSV = VR [1 - (1/2n)]
3. Ccuracy: It is the error between the actual output of DA converter to the expected or theoretical output and expressed as percentage of FSV.
If the converter has an accuracy of ± 0.1% for FSV of 10 V, the minimum error for any output voltage is [(10/100) × 0.1] = 10 mV Ideally the accuracy should be = ± [1/2]1 LSB.
4. Monotonicity: It means that the output increase for an increase of input or decreases for decrease of input. The output should not decrease for increase of input. 5. Settling Time: It is the time taken by DA converter to settle within + [1/2] LSB of its final value.
Major component of the binary weighted resistance DAC:
a) a weighted resistor network, R to 2n-1 R
b) n switches, one for each bit applied bit input.
c) A reference voltage Vref
d) A summing element Defects:
The chief detect of weighted binary DAC is that the resistor values increases in multiples of 2.
If the value of MSB is 2 KW. then for a 10 bit, the value for LSB is 29. 2K = 1.024 MW.
It is difficult to obtain high precision at very high values. It is also difficult to fabricate high value resistance by integrated circuit methods. This is over come by the ladder type DA converter.
R-2R ladder Network In this, only two values of resistors are used.
The number of resistor required for an N-bit ladder D/A converter is 2N in the case of R-2R ladder D/A converter whereas it is only N is the case of weighted-resister D/A converter.
Analog-to-digital converters :Types of ADC
1. Parallel-comparator/flash/simultaneous A/D
2. Successive Approximation A/D converter
3. Count ing A /D conver t er The maximum number of clock pulse required conversion is 2N for an N-bit A/D converter. This conveter is slower than the other two converters discussed earlier.
4. Dual-slope A/D converters Major component of a dual-slope A/D converter.
1. An integrator
2. A comparator
3. A binary counter
4. A switch driver.
Conversion time of ADC
1. Counter of Ramp type ADC
2. Successive approximation ADC
3. Dual slope ADC Slowest conversion time 4. Flash ADC Fastest conversion time tc = (1/f)
Aperture Time Aperture time is called the maximum allowable conversion time tc.
where, w = angular frequency of signal applied
n = number of bit for ADC
ta = aperture time.