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DIGITAL SYSTEMS TCE1111 1 INTERFACING WITH ANALOG DEVICES (Week 12)

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DIGITAL SYSTEMS TCE1111 2 DIGITAL SIGNAL PROCESSING BASICS Digital signal processing converts signals that naturally occur in analog form, such as sound, video and information form sensors, to digital form and uses digital techniques to enhance and modify analog signal data for various applications. A digital system processing system first translates a smoothly varying analog signal into a series of discrete levels. This series of levels follows the variations of the analog signal and resembles a staircase,as illustrated in Fig 1.This is accomplished by sample and hold circuits.

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DIGITAL SYSTEMS TCE1111 3 An original analog signal (sine wave) and its “stairstep” approximation. DIGITAL SIGNAL PROCESSING BASICS

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DIGITAL SYSTEMS TCE1111 4 Next, the stair step approximation is quantized into binary codes that represent each discrete step on the stair steps by a process called analog-to-digital conversion (ADC). The binary codes are then applied to Digital signal processor (DSP) which performs various operations on the incoming data,such as removing unwanted interference, increasing the amplitude of some signal frequencies etc. After the DSP processes the signal, it can be converted back to a much improved version of the original analog signal by digital to analog converter (DAC). Fig 2 shows a basic block diagram of a typical DSP system. DIGITAL SIGNAL PROCESSING BASICScont..

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DIGITAL SYSTEMS TCE1111 5 Fig 2 Basic block diagram of a digital signal processing system. DIGITAL SIGNAL PROCESSING BASICScont..

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DIGITAL SYSTEMS TCE1111 6 Converting Analog signals to Digital Filtering and sampling Sampling is the process of taking a sufficient number of discrete values at points on a waveform that will define a waveform. Sampling converts an analog signal into a series of impulses, each representing the amplitude of the signal at a given instant in time. Before a signal can be sampled, it must be passed through a low-pass filter to eliminate harmonic frequencies.

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DIGITAL SYSTEMS TCE1111 7 Holding the sampled value After filtering and sampling,the sampled level must be held constant until the next sample occurs. This is necessary for the ADC to have time to process the sampled value. This sample and hold operation results in a stair step waveform that approximates the analog input waveform, as shown in fig 3. Converting Analog signals to Digital

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DIGITAL SYSTEMS TCE1111 8 fig 3 Illustration of a sample-and-hold operation. Converting Analog signals to Digital

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DIGITAL SYSTEMS TCE1111 9 Analog to Digital conversion Analog –to-digital conversion is the process of converting the output of the sample and hold circuit to a series of binary codes that represent the amplitude of the analog input at each of the sample times. The sample and hold process keeps the amplitude of the analog input signal between sample pulses. Fig 4 illustrates the basic function of a ADC converter.

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DIGITAL SYSTEMS TCE1111 10 Figure 4 Basic function of an analog-to-digital (ADC) converter (The binary codes and number of bits are arbitrarily chosen for illustration only). The ADC output waveform that represents the binary codes is also shown. Analog to Digital conversion

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DIGITAL SYSTEMS TCE1111 11 Quantization The process of converting an analog value to a code is called quantization. The ADC converts each sampled value of the analog signal to a binary code. The Quantization operation is illustrated in fig 5.

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DIGITAL SYSTEMS TCE1111 12 Figure 5 Sample-and-hold output waveform with four quantization levels. The original analog waveform is shown in light gray for reference.

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DIGITAL SYSTEMS TCE1111 13 Analog –to Digital Conversion Methods- FLASH (SIMULTANEOUS ) ADC CONVERTER (1)… The flash method utilizes comparators that compare reference voltage with the analog input voltage. When the input voltage exceeds the reference voltage,a HIGH is generated. A comparator is not needed for all 0’s condition. In general a 2 n -1 comparators are required for converting to an n- bit binary code. The number of bits in an ADC is its resolution. Advantage: Provides a fast conversion times because of a high through put measured in sps (samples per second.) Disadvantage: Large number of comparators necessary for a reasonable –sized binary number

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DIGITAL SYSTEMS TCE1111 14 C1 C2 C3 C4 C5 C6 C7 FLASH (SIMULTANEOUS ) ADC CONVERTER (2)… Figure 6 A 3-bit flash ADC

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DIGITAL SYSTEMS TCE1111 15 FLASH (SIMULTANEOUS ) ADC CONVERTER (3)… Operation of 3- bit flash ADC The flash method utilizes comparators that compare reference voltages with the analog input voltage. When the input voltage exceeds the reference voltage for a given comparator, a HIGH is generated. The reference voltage for each comparator is set by the resistive voltage- divider circuit. The output of each comparator is connected to an input of the 8- input priority encoder. The encoder is enabled by a pulse on the EN input, and a 3-bit code representing the value of the input appears on the encoder’s outputs. The binary code is determined by the highest order input having a HIGH level. Assume the step size of 1 V. The voltage divider sets up reference levels for each comparator so that there are 3 levels corresponding to 1V, 2V, 3V, 4V, 5V, 6V and 7V. The analog input is connected to other input of each comparator. With analog input <1V, all the seven comparator outputs will be LOW. Suppose the analog input is between 2V and 3V, outputs C1 and C2 will be HIGH. The priority encoder will respond to HIGH on C2, and will produce a binary output of 010.

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DIGITAL SYSTEMS TCE1111 16 FLASH (SIMULTANEOUS ) ADC CONVERTER (4)… Example-3-bit Flash ADC Determine the binary code output of the 3-bit Flash ADC for the input signal And the encoder enable pulses as shown below. Assume V REF =+8V

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DIGITAL SYSTEMS TCE1111 17 FLASH (SIMULTANEOUS ) ADC CONVERTER (5) Solution -3-bit Flash ADC The resulting digital output sequence: 100 (4),110(6),111(7),110(6), 100 (4), 010(2), 000(0), 001(1), 011 (3),101 (5),110 (6), 111(7) Waveform of the resulting digital output sequence:

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DIGITAL SYSTEMS TCE1111 18 Dual Slope ADC (1)… A dual slope ADC is common in digital voltmeters and other type of measurement instruments. A block diagram of dual slope ADC is shown in fig 7.

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DIGITAL SYSTEMS TCE1111 19 Dual Slope ADC (2)… Assume that the counter is reset and the integrator output is zero. A positive input voltage is applied to the input through the switch as selected by control logic. Since the inverting input of A 1 is at virtual ground, and assuming that V in is constant for a period of time, there will be constant current through the input resistor R and through the capacitor C. Capacitor will charge linearly because the current is constant and as a result the will be a negative going linear voltage ramp on the output of A 1

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DIGITAL SYSTEMS TCE1111 20 Dual Slope ADC (3)… When the counter reaches a specified count, it will be reset and the control logic will switch the negative reference voltage (-V ref ) to the input of A 1. At this point the capacitor is charged to a negative voltage (-v) proportional to input analog voltage. Now the capacitor discharges linearly because of the constant current from the –V ref.This linear discharge produce a positive going ramp on the A 1 output, starting at –v and having a constant slope that is independent of the charge voltage.

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DIGITAL SYSTEMS TCE1111 21 Dual Slope ADC (4)… As the capacitor discharges, the counter advances from its RESET state. The time it takes the capacitor to discharge to 0 depends on the initial voltage –V. When A 1 reaches 0, A 2 switches to low state and disables the clock to the counter The binary count is latched thus completing one conversion cycle. The binary count is proportional to V in.. This process is illustrated in Fig 8.

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DIGITAL SYSTEMS TCE1111 22 Dual Slope ADC (5)

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DIGITAL SYSTEMS TCE1111 23 Successive - approximation ADC (1)… Fig 9 shows the basic block diagram of a 4 bit Successive - approximation ADC. It consists of a DAC, Successive-Approximation Register (SAR), and a comparator

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DIGITAL SYSTEMS TCE1111 24 Successive - approximation ADC (2)… Basic operation The input bits of the DAC are enabled one at a time starting with the MSB As each bit is enabled the comparator produces an output that indicate whether the input signal voltage is greater or lesser than the output of DAC. If the DAC output is greater than the input signal,the comparator’s output is LOW, causing the bit in the register to reset. If the DAC output is less than the input signal, the bit 1 is retained in the register. The system does this with the MSB first, then the next right bit of MSB, then the next and so on. After all the bits in the DAC are tried, the conversion cycle is complete.

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DIGITAL SYSTEMS TCE1111 25 Successive - approximation ADC (3)… Illustration of Basic operation with an example Assume that the DAC has the following output characteristics: V out =8V for the 2 3 bit (MSB), V out =4V for the 2 2 bit, V out =2V for the 2 1 bit, and V out =1V for the 2 0 bit (LSB).

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DIGITAL SYSTEMS TCE1111 26 Successive - approximation ADC (4)… Illustration of Basic operation with an example

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DIGITAL SYSTEMS TCE1111 27 Successive - approximation ADC (5)… Illustration of Basic operation with an example Step 1: 2 3 bit (MSB) = 1 The output of the DAC is 8 V. Since this is greater than the input of 5.1 V, the output of the comparator is LOW, causing the MSB in the Successive Approximation Register (SAR) to be reset to a 0 Step 2: 2 2 bit =1 The output of the DAC is 4 V. Since this is less than the input of 5.1 V, the output of the comparator switches to HIGH, causing this bit retained in SAR.

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DIGITAL SYSTEMS TCE1111 28 Successive - approximation ADC (6) Illustration of Basic operation with an example Step 3: 2 1 bit = 1 The output of the DAC is 6 V. Since this is greater than the input of 5.1 V, the output of the comparator switches to LOW, causing this bit to be reset to 0. Step 4: 2 0 bit =1 The output of the DAC is 5 V. Since this is less than the input of 5.1 V, the output of the comparator switches to HIGH, causing this bit retained in SAR. After 4 steps, conversion cycle is completed. Binary code in the register is 0101, which is approximately the binary value of the input of 5.1 V. V out =8V for the 2 3 bit (MSB), V out =4V for the 2 2 bit, V out =2V for the 2 1 bit, and V out =1V for the 2 0 bit (LSB).

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DIGITAL SYSTEMS TCE1111 29 SIGMA - DELTA ADC (1)… This method is based on delta modulation where the difference between two successive samples is quantized. The output of a delta modulator is a single bit data stream where the relative number of 1’s and 0’s indicates the level of amplitude of the input signal. The number of 1’s over a given number of clock cycles establishes the signal amplitude during that interval. A maximum number of 1’s correspond to maximum positive input voltage. A number of 1’s equal to one - half the maximum corresponds to an input voltage of 0. No 1’s correspond to the maximum negative input voltage. This is illustrated in a simplified way in fig 10.

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DIGITAL SYSTEMS TCE1111 30 SIGMA - DELTA ADC (2)… Figure 10 A simplified illustration of sigma-delta analog-to-digital conversion.

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DIGITAL SYSTEMS TCE1111 31 SIGMA - DELTA ADC (3)… Figure 11 Functional block diagram of a sigma-delta ADC.

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DIGITAL SYSTEMS TCE1111 32 SIGMA - DELTA ADC (4)… The basic block diagram in Fig 11 accomplishes the conversion. The analog input signal and the analog signal form the converted quantized bit stream form the DAC in the feedback loop are applied to the summation point. The difference signal output of the sum is integrated and the 1-bit ADC increases or decreases the number of 1’s depending on the difference signal. This action attempts to keep the quantization signal that is fedback equal to the incoming analog signal. The 1 bit quantizer is essentially a comparator followed by a latch.

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DIGITAL SYSTEMS TCE1111 33 SIGMA - DELTA ADC (5) The single bit data stream is converted to as series of binary codes.The counter counts 1’s in the quantized data stream for successive intervals.The code in the counter then represents the amplitude of the analog input signal for each interval.

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DIGITAL SYSTEMS TCE1111 34 Digital to Analog Conversion Methods- Binary – weighted - input DAC (1)… Fig 12 shows a 4-bit DAC with binary weighted inputs..

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DIGITAL SYSTEMS TCE1111 35 Binary – weighted - input DAC (2)… Each of the input resistors will either have current or no current depending on the input voltage level. If the input voltage is zero, the current is also zero. If input voltage is high,the amount of current depends on the input resistor value and is different for each input resistor. Since there is practically no current into the op-amp inverting (-) input, all of the input currents sum together and go through R f. Since the inverting input is at 0v,the drop across R f is equal to the output voltage,so V out = I f R f.

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DIGITAL SYSTEMS TCE1111 36 Binary – weighted - input DAC (3) The values of the input resistors are chosen to be inversely proportional to the binary weights of the corresponding input bits. The lowest value resistor (R) corresponds to the highest binary weighted input (2 3 ). The other resistors are multiples of R (R, 2R, 4R and 8R) and correspond to the binary weights of 2 2, 2 1, 2 0. Thus the output voltage is proportional to the sum of binary weights because the sum of the input currents is through R f.

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DIGITAL SYSTEMS TCE1111 37 The R/2R Ladder DAC (1)… R/2R Ladder DAC is shown in fig 13.

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DIGITAL SYSTEMS TCE1111 38 The R/2R Ladder DAC (2)… Assume that D 3 input is high (+5 v) and the others are low(0 V).This condition represents the binary number 1000. Essentially no current goes through the 2R equivalent resistors because the inverting input is at virtual ground. Thus all the current (I= 5V/2R) through R 7 also goes through R f and the output voltage is -5V.The op-amp keeps the inverting input near 0V because of negative feedback. Thus all current goes through R f rather than into the inverting input.

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DIGITAL SYSTEMS TCE1111 39 The R/2R Ladder DAC (3)… Fig 14

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DIGITAL SYSTEMS TCE1111 40 The R/2R Ladder DAC (4) Fig 14 (b) shows the equivalent circuit when the D 2 input at +5V and the others are grounded. This condition represents 0100, i.e.2.5V in series with R. This results in a current through R f of I = 2.5V/2R, which gives an output voltage of -2.5V.

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DIGITAL SYSTEMS TCE1111 41 Performance characteristics of DAC (1)… 1.Resolution : The resolution of a DAC is the reciprocal of the number of discrete steps in the output. For example a 4-bit DAC has a resolution of one part in 2 4 -1 = 1/15*100 = 6.67%. 2.Accuracy: Accuracy is derived from a comparison of the actual output of a DAC with the expected output. It is expressed as a percentage of a full-scale or maximum output voltage. If a converter has a full- scale output of 10v and the accuracy is +/- 0.1%,then the maximum error for any output voltage is (10V)(0.001) = 10 mV

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DIGITAL SYSTEMS TCE1111 42 Performance characteristics of DAC (2)… 3. Linearity: A linear error is a deviation from the ideal straight-line output of a DAC.A special case is an offset error. which is the amount of output voltage when the input bits are all 0’s. 4. Monotonicity: A DAC is monotonic if it doesn’t take any reverse steps when it is sequenced over its entire range of input bits. 5. Settling Time: Normally defined as the time it takes a DAC to settle within +/- ½ LSB of its final value when a change occurs in the input code.

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DIGITAL SYSTEMS TCE1111 43 Performance characteristics of DAC (3) Example: Determine the resolution, expressed as a percentage, of the following: a. an 8-bit DAC b. a 12-bit DAC Solution: a. For the 8-bit DAC, 1/2 8 -1 *100 = 1/255*100=0.392% b. For the 12-bit DAC, 1/2 12 -1 *100 = 1/4095*100=0.0244 %

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DIGITAL SYSTEMS TCE1111 44 Real World Example A modem (converts digital signals into analog signals for transmissions over phone lines and the back to digital signals again at the destination computer)

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