1. EI205 Lecture 13
Dianguang Ma
Fall 2008

2. Chapter 13
INTERFACING

3. 13-1 DIGITAL AND ANALOG INTERFACING
Analog signals. An analog signal is a continuous function of continuous time. Let’s take the case of a voltage that varies over a range from 0 to r volts. The analog representation of this quantity can take all values between 0 to r volts.
Digital signals. A digital signal is a discrete function of discrete time. The digital representation of the voltage can take only one of 2n possible values (e.g., 16 voltage levels) at the time instants nT (e.g., T = 10-3 sec).
To interface between the analog and digital world, two basic processes are required: analog-to-digital (A/D) conversion and digital-to-analog (D/A) conversion.
The A/D process consists of sampling, quantization, and coding. An A/D converter is characterized by converting an analog quantity into a digital code.
Continuous time is discretized through sampling. The analog signal is periodically measured every T seconds.
Continuous value is discretized through quantization. The sampled value is replaced by the nearest quantization levels.
Using n-bit codes to represent the quantized values is called coding.
A D/A converter converts a digital code into an analog quantity.

4. 13-2 DIGITAL-TO-ANALOG CONVERSION
Consider a n-bit DAC with full-scale range r, as shown below. Given n inputs bits of 0s and 1s, the converter outputs an analog value xQ. That lies on one of the 2n quantization levels within the range r. If the converter is unipolar, the output falls in the range [0, r). If it is bipolar, it falls in [-r/2, r/2).
DAC
(analog output)
(input bits)
(reference)

5. The Unipolar Binary Converter
The manner in which the input bits are associated with the analog output depends on the type of converter and the coding convention used. The three widely used types are:
Unipolar natural binary
Bipolar binary
Bipolar two’s complement
The unipolar natural binary converter is the simplest. Its output is computed in terms of the input bits by:
Where Q is the quantization spacing.

6. The Unipolar Binary Converter
Assume n = 4 and r = 10 volts. The quantization spacing

7. The Operational Amplifier
Before getting into DACs, lets look at an element that is common to most types of DACs. This element is the operational amplifier, or op-amp for short.
An op-amp is a linear amplifier that has two inputs (inverting and noninverting) and one output.
It has a very high voltage gain and a very high input impedance, as well as a very low output impedance.
When used as an inverting amplifier, the op-amp is configured as below:
In the inverting amplifier configuration, the inverting input is approximately at ground potential(0 volts) because feedback and the extremely high open-loop gain make the differential voltage between the two inputs extremely small. Since the noninverting input is grounded, the inverting input is at approximately 0 volts, which is called virtual ground.

8. Binary-Weighted-Input DAC
A DAC of this type uses a resistor network with resistance values that represent the binary weights of the input bits of the digital code.
The values of the input resistors are chosen to be inversely proportional to the binary weights of the corresponding input bits.
One of the disadvantages of this type of DAC is the number of different resistor values. This range of resistors makes this type of DAC very difficult to mass-produce.

9. The I/O Relationship

10. The R/2R Ladder DAC
A DAC of this type uses a resistor network with two resistance values. It overcomes one of the problems in the binary-weighted-input DAC in that it requires only two resistor values.

11. The I/O Relationship

12. DAC0808: 8-Bit DAC
The DAC 0808 is an example of an R/2R ladder-based DAC.
In a typical application, the DAC0808 is connected to an op-amp.
The +VREF input established the analog output voltage.

13. 13-3 ANALOG-TO-DIGITAL CONVERSION
Several types of ADCs are now examined:
Flash (Simultaneous) ADC
Stairstep-Ramp ADC
Tracking ADC
Single-Slope ADC
Dual-Slope ADC
Successive-Approximation ADC
ADC

14. Flash (Simultaneous) ADC
The flash method utilizes comparators that compare reference voltages with the analog input voltage.
The reference voltage for each comparator is set by the resistive voltage-divider.
The output of each comparator is connected to an input of the priority encoder which produces the binary code.
In general, 2n-1 comparators are required for conversion to an n-bit binary code.
The large number of comparators necessary for a reasonable-sized binary number is one of the disadvantages of the flash ADC.
This type of ADC is the fastest.

15. Flash (Simultaneous) ADC
The encoder is sampled by a pulse on the enable input.

16. Flash (Simultaneous) ADC
Analysis. The reference voltage for the ith comparator is

17. Example 13-3
Determine the binary code output of the 3-bit flash ADC for V. The reference voltage is 8 volts.

18. Flash (Simultaneous) ADC
Question:
Why priority encoder?
How to reduce quantization error?

19. Stairstep-Ramp ADC
It is also known as the counter method.

20. A 4-Bit Stairstep-Ramp ADC
For each sample, the counter must count from zero up to the point at which the stairstep reference voltage reaches the analog input voltage.

21. Tracking ADC
The tracking method uses an up/down counter and is faster than the stairstep-ramp method because the counter is not reset after each sample, but rather tends to track the analog input.

22. Tracking ADC
The tracking method uses an up/down counter and is faster than the stairstep-ramp method because the counter is not reset after each sample, but rather tends to track the analog input.

23. Single-Slope ADC
The single-slop method uses a linear ramp generator to produce a constant-slope reference voltage.

24. Dual-Slope ADC
The dual-slop method uses a linear ramp generator to produce a dual-slope characteristic.

25. Dual-Slope ADC
Start by assuming that the counter is reset and the output of the integrator is zero. Now assume a positive input voltage is applied to the input through the switch as selected by the control logic.

26. Dual-Slope ADC
When the counter reaches a specified count, it will be reset, and the control logic will switch the negative reference voltage to the input of the integrator.
At this point the capacitor is charged to a negative voltage proportional to the input analog voltage.

27. Dual-Slope ADC
Now the capacitor discharges with a constant rate. When the integrator output voltage reaches zero, the comparator switches to the LOW state and disables the clock of the counter. The binary count is latched.

28. Successive-Approximation ADC
Perhaps the most widely used method of ADC is successive-approximation. It has a much faster conversion time than the other methods with the exception of the flash method. It also has a fixed conversion time that is the same for any value of the analog input.

29. Successive-Approximation ADC
The basic operation is as follows:
The input bits of the DAC are enabled (made equal to 1) one at a time, starting with the MSB.
As each bit is enabled, the comparator produces an output that indicates whether the analog input voltage is greater or less than the output of the DAC.
If the DAC output is greater than the analog input, the comparator’s output is LOW, causing the bit in the register to reset.
If the output is less than the analog input, the 1 bit is retained in the register.
The system does this with the MSB first, then the next most significant bit, then the next, and so on.
After all bits of the DAC have been tried, the conversion cycle is complete.

30. Successive-Approximation ADC
Assume the analog input voltage is 5.1 volts and the 4-bit DAC has a quantization spacing Q = 1 volt.

31. Homework
Problems ?