Lecture 6: Digital/Analog Techniques

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Bennett Banks
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1 Lecture 6: Digital/Analog Techniques The electronics signals that we ve looked at so far have been analog that means the information is continuous. A voltage of 5.3V represents different information that a voltage of 5.4V For most of the remainder of the semester, we ll investigate the processing of digital information In digital electronics, we define a range of voltages called low and another range called high For example, 0-2V may be low, and 5-10V may be high The information carried is either a 0 (voltage in low range) or 1 (voltage in high range) circuits are built so that voltages in the middle are not possible if such a voltage is observed, it means something is broken!

2 Advantages to Digital It seems that we lose a lot of information in going from analog to digital processing But more and more real signal processing is digital, because: noise is much less of a concern. A small noise voltage on top of the signal can distort analog information, but has no effect digitally digital information is easier to store. One could design a system of capacitors to retain a fixed analog charge, but even small leakage would result in the information being lost over time digital information can easily be processed in logical operations like AND and OR. These operations are at the heart of all computers

3 Analog to digital conversion To bridge the digital/analog gap, we ll explore how one might convert between analog and digital signals We start with digital signals (bits) carried on a set of wires one bit per wire The set of bits represent a number in binary number system with base 2, instead of the base 10 we re used to for example, the number 5 in binary is = 1* * *2 0 the more bits we have, the more numbers we can represent We want to convert this information to an analog voltage (carried on a single wire)

4 One way to make a digital-to-analog converter (DAC) is the following: Least significant bit (LSB) Most signifi cant bit (MSB) The digital input determines which of the four switches is closed low bit means switch is open with all four switches open, V out is 0

5 Let s see what happens as we close other switches: If we close the LSB switch, we find (using ideal op-amp rules): R V = 0 = V 8IR = V out I 2 V R V Vout = = 8R2 16 this is the smallest voltage increment possible for this DAC Closing the MSB switch gives: V = 0 = V IR = V out I V out V R V = = R2 2 R 2 8 times bigger than LSB value

6 Now we ll close all four switches: The resistance between +V and V - is: = = R R R R R R T R RT = 15 Which means the output voltage is: R R V = 0 = V I 15 = V out I 2 15V R 15V Vout = = R 2 2 which is 15 times the LSB value

7 While that circuit will work in principle, it s not really practical to keep current draw low, R can t be too small let s say we make it 10kΩ if we want a 10-bit DAC, the biggest resistor would then be 2 9 x 10kΩ, which is 5MΩ hard to put that kind of resistance on an IC There s also a problem due to stray capacitance that means that adjacent wires can act as small capacitors for this circuit, the total stray capacitance might be ~100pF that means that the time it takes for the output to reach its desired value after the switches are closed is t = RC = Ω = 4 5M 100pF 5 10 s that might seem pretty quick to you and me, but to a computer it would be painfully slow

8 A better DAC Let s try this design instead: D C B MSB A I 0 I 4 I 3 I 2 I 1 LSB I R Note that V - is a virtual ground that is, its voltage is nearly 0 Hence moving the switches does not change the total current flowing from V CC but it does change the current flowing through the feedback resistor

9 The output voltage is: V = 0 = v out I RR v = I R Looking at the ladder from point A, the equivalent resistance to ground is: = + R 2R 2R Meaning we could redraw the ladder as: out R T T R = R

10 Looking at this equivalent ladder from point B, we see the same resistance to ground as the original ladder had from point A. So we could draw a new equivalent ladder as: At this point, we see the pattern will keep repeating thus the total resistance of the ladder is R this is true no matter how long the ladder is The total current flowing from V CC is V CC /R

11 What about the individual currents I 1 through I 4? Look at the ladder from point D there are two paths through ground: 1. Through a single resistor 2R (this is where I 1 flows) 2. Through a resistor R, and then the ladder at point C but we already know that all ladders have resistance R so the total resistance for this path is also 2R this means the current splits up evenly at point D, so: I 4 1 VCC = IT = 2 2R Similarly, even current splits occur at points C, B, and A, so: VCC VCC VCC I3 = ; I2 = ; I1 = 4R 8R 16R

12 Now let s switch the LSB so it s connected to V - the total current flowing toward V - is then I 1 = V CC /16R which means v out is V CC /16 If instead the MSB switch is connected to V -, we have VCC vout = I4R = 2 So we see this circuit does in fact act as a DAC Advantages: only two resistor values needed resistance can be modest (no matter how many bits are to be converted) settling time is therefore much faster

13 Analog-to-Digital Converters (ADCs) We sometimes also want to go in the other direction, and convert an analog voltage to a set of bits used all the time in physics experiments for example, to convert analog information about the ionization from a charged particle into digital form for storage and processing on a computer We ve already seen one such circuit the comparator this converts an analog voltage into one bit of information But what if we want more bits?

14 That s easy! We ll just use a lot of comparators: Each op-amp compares V in to V +

15 The V + values at each op-amp input are the result of the voltage divider from V CC i.e., the op-amp on bottom sees a voltage of V CC /8, while the one on top sees 7V CC /8 Note that there are only 8 possible outputs from the comparators this is a 3-bit ADC Additional processing is required to convert the eight output lines from the comparators to a binary number that s what the chip on the right side of the schematic does it s called a priority encoder

16 The main advantage of this design is that it s fast result of voltage comparisons can propagate through opamps and priority encoder in a few ns The drawbacks are: you need a lot of comparators (256 for an 8-bit DAC, 65,536 for a 16-bit DAC!) accuracy is limited by tolerance of resistors

17 Ramp DAC Parts of this are familiar the comparator and active integrator Other parts are digital devices we haven t seen before the AND gate s output is 1 if both inputs are 1, and 0 otherwise we ll talk about this more next week AND gate

18 The clock is just a square wave generator output periodically switches between 0 and 1 The counter s output is a binary number equal to the number of times the input has been 1 since the last time the counter was reset The circuit works as follows signal is sent to discharge capacitor and reset clock (capacitor discharged though FET switch) input to comparator (v c ) is integral of V ref in other words, a linearly increasing voltage as long a v in > v c, comparator output is 1 thus, output of AND gate is 1 whenever the clock is 1 once v in < v c, the comparator outputs 0 counter stops incrementing! The couter output is v in in binary

19 This ADC is more precise and simpler than the one using many comparators However, it s slower (have to wait for voltage to integrate) An even better solution is the dual slope ramp ADC The only difference is that the inputs are rearranged:

20 In this case, when one starts the conversion the switch is set to the unknown v in This is then integrated for a fixed number of clock cycles usually a multiple of the AC power period Then the switch is set to v ref, and the counter is told to start counting capacitor then starts discharging when voltage across capacitor falls to 0, comparator output goes to 0, and counter stops As before, the value stored in the counter is now proportional to v in

21 This ADC is more precise than the single-ramp one because: same clock is used for both charging and discharging the capacitor so if the frequency drifts slowly over time, we don t care similarly, if the capacitor degrades slowly, that won t affect the output noise coming from the power line is averaged out in the initial integration

Data Converters. Dr.Trushit Upadhyaya EC Department, CSPIT, CHARUSAT

Data Converters. Dr.Trushit Upadhyaya EC Department, CSPIT, CHARUSAT 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: