# ELG3336: Converters Analog to Digital Converters (ADCs) Digital to Analog Converters (DACs)

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1 ELG3336: Converters Analog to Digital Converters (ADCs) Digital to Analog Converters (DACs) Digital Output Dout ΔV, V LSB V ref 8 V FS 4 V 8 ref 7 V 8 ref Analog Input V in Any analog quantity can be represented by a binary number. Longer binary numbers provide higher resolution, which gives a more accurate representation of the analog quantity. 1

2 Analog to Digital Converters Objective: epresenting an analog varying physical quantity by a sequence of discrete numerical values Analog Digital Sample & Hold f sample Quantization 2

3 Successive Approximation ADC Generate internal analog signal V D/A Compare V D/A with input signal V in Modify V D/A by D 0 D 1 D 2 D N-1 until closest possible value to V in is reached V in S&H Logic V D/A D 0 D 1 D N-1 DAC V ref 3

4 Ladder Comparison The counter, through a digital-to-analog converter, produces a stair-step of increasing voltage. At each step the input signal is compared to the current step level. If the input is higher, then continue to step, if the input is equal or lesser, then stop and read the counter. The count value is read as numeric value of the input. Calculate the maximum conversion time of a 8-bit staircase ramp ADC. The maximum number of count is n c = 28 = 256. The maximum conversion time is: n T 256 c c s 128s 6 f

5 Flash ADC /2 V ref V in Over range V in connected with 2 N comparators in parallel Comparators connected to resistor string (2 N -1) to N encoder D 0 D 1 If Output V IN > V EF High D N-1 V IN < V EF Low /2

6 An ADC is usually in form of an integrated circuit (IC). ADC0808 and ADC0809 are two typical examples of 8-bit ADC with 8- channel multiplexer using successive approximation method for its conversion. ADC0809 National Semiconductor For more information, 6

7 Selection of ADC The parameters used in selecting an ADC are very similar to those considered for a DAC selection: Error/Accuracy: Quantizing error represents the difference between an actual analog value and its digital representation. Ideally, the quantizing error should not be greater than ± ½ LSB. esolution: DV to cause 1 bit change in output Output Voltage ange Input Voltage ange Output Settling Time Conversion Time Output Coding (usually binary) The Nyquist ate: A signal must be sampled at a rate at least twice that of the highest frequency component that must be reproduced. Example: Hi-Fi sound (20-20,000 Hz) is generally sampled at about 44 khz. 7

8 Sample-and-Hold A number of problems exist with the previous sample and hold circuit Load placed on the input of the circuit by charging the capacitor during the sample phase. Current flowing from the capacitor used in the conversion will reduce the voltage stored on the capacitor C sample/hold control line

9 Sample and Hold Circuits Sample and hold circuits hold signal constant for conversion A sample and a hold device (mostly switch and capacitor) Demands: Small C-settling-time (voltage over hold capacitor has to be fast stable at < 1 LSB) Exact switching point Stable voltage over hold capacitor No charge injection by the switch.

10 Accuracy x q (t) Q t T s x q (t) Higher Sampling ate x q (t) Higher esolution Q T s t t

11 esolution Suppose a binary number with N bits is to represent an analog value ranging from 0 to A; There are 2 N possible numbers. esolution = A / 2 N Example 1: Temperature range of 0 K to 300 K to be linearly converted to a voltage signal of 0 to 2.5 V, then digitized with an 8-bit A/D converter. 2.5 / 2 8 = V, or about 10 mv per step 300 K / 2 8 = 1.2 K per step Example 2: Temperature range of 0 K to 300 K to be linearly converted to a voltage signal of 0 to 2.5 V, then digitized with a 10-bit A/D converter 2.5 / 2 10 = V, or about 2.4 mv per step 300 K / 2 10 = 0.29 K per step Is the noise present in the system well below 2.4 mv?

12 Digital to Analog Converters (DACs) Binary Weighted esistor Voltages V 1 through V n are either V ref if corresponding bit is high or ground if corresponding bit is low V 1 is most significant bit V n is least significant bit MSB V ref V1 V 2 V 3 V n n-1 I - + f V out V1 V2 V3 Vn Vout If f n LSB

13 Binary-Weighted Digital-to-Analog Converters Sum of the currents from the input resistors; Consider binary weighting factor. Advantages: Simple Construction/Analysis; Fast Conversion Disadvantages: equires large range of resistors (2000:1 for 12-bit DAC) with necessary high precision for low resistors; equires low switch resistances in transistors 9

14 V V I OUT OUT B3 B2 B1 B0 VEF B2 B1 I f VEF B3 2 4 Bi VEF n 1 2 i V Digital Value esolution EF Binary Weighted esistor B 8 0 Ii f = V o MSB LSB -V EF

15 -2 Ladder The less significant the bit, the more resistors the signal muss pass through before reaching the op-amp The current is divided by a factor of 2 at each node LSB MSB

16 -2 Ladder The current is divided by a factor of 2 at each node; Analysis for current from (001) 2 shown below I 0 2 I 0 4 I V EF B 0 I 0 B 1 B 2 I V 2 2 EF 0 2 V 3 EF Op-Amp input Ground 16

17 -2 Ladder: An Example Find the output voltage of the Op-Amp for the following DAC Given Values Input = (101) 2 V EF = 10 V = 2 Ω f = 2 I V 2 2 VEF 2 3 I I0 8 2 I EF 0 I opamp V OUT 0 opamp f 1.67 ma 1.04 ma 4.17 V I 0 V EF I 0 V EF Op-Amp input Ground B 0 B 2 17

18 2 Volt. Levels esolution 8 Volt. Levels esolution V LSB V 2 ef N Poor esolution(1 bit) Better esolution(3 bit) Vout Vout Desired Analog signal Desired Analog signal Digital Input Approximate output Approximate output Digital Input

19 Digital to Analog Converters Selection Criteria of DAC esolution The number of bits making up the input data word that will ultimately determine the output step voltage as a percentage of full-scale output voltage. Example: Calculate the resolution of an 8-bit DAC. esolution = 8 bits 1 1 Percentage resolution = 100% 100% 0.391% Output Voltage ange This is the difference between the maximum and minimum output voltages expressed in volts. Example: Calculate the output voltage range of a 4-bit DAC if the output voltage is +4.5V for an input of 0000 and +7.5V for an input of Output voltage range = = 3.0V 19

20 Summary Operational amplifiers are important building blocks in analog-to-digital (A/D) and digital-to-analog (D/A) converters. They provide a means for summing currents at the input and converting a current to a voltage at the output of converter circuits. The methods of A/D conversion used are many! In the successive method, bits are tested to see if they contribute an equivalent analog value that is greater than the analog input to be converted. If they do, they are returned to zero. After all bits are tested, the ones that are left ON are used as the final digital equivalent to the analog input. The /2 ladder D/A converter uses only two different resistor values, no matter how many binary input bits are included. This allows for very high resolution and ease of fabrication in integrated-circuit form. The DAC0808 (or MC1408) IC is an 8-bit D/A converter that uses the /2 ladder method of conversion. It accepts 8 binary input bits and outputs an equivalent analog current. Having 8 input bits means that it can resolve up to 256 unique binary values into equivalent analog values. 37

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