8.1 Fundamentals of Data Conversion

Real-world quantities are inherently analog, meaning they vary continuously over time. In contrast, digital signals are discrete, having only a finite number of defined levels. To interface between analog circuits and digital systems (like microprocessors), data converters are essential. An Analog-to-Digital Converter (ADC) translates an analog signal into a digital code, while a Digital-to-Analog Converter (DAC) performs the reverse operation.

The performance of these converters is defined by two key specifications:

• Resolution: This specifies the smallest change in analog voltage that can be discerned by the converter. It is determined by the number of bits (N) in the digital representation. It can be defined in two ways: Resolution=\frac{1}{2^{N}} or as the step size: Resolution=\frac{V_{FS}}{2^{N}-1} where V_{FS} is the full-scale (maximum) analog voltage. Resolution is inversely related to the number of bits; more bits lead to a finer (smaller) resolution.
• Conversion Time: This is the time required for a converter to complete a conversion process. For an ADC, it is the time taken to convert an analog input into a valid digital output. For a DAC, it is the time taken to convert a digital input into a stable analog output.

We will first examine the Digital to Analog Converter in more detail.

8.2 Digital to Analog Converters (DACs)

A Digital to Analog Converter (DAC) is an electronic circuit that converts a digital binary code into a proportional analog signal, typically a voltage or current.

Weighted Resistor DAC

The weighted resistor DAC uses an inverting summing amplifier with a set of binary-weighted resistors. Each input bit of the digital word controls a switch that connects its corresponding resistor to either ground (for a ‘0’ bit) or a reference voltage (for a ‘1’ bit). The resistor values are weighted in powers of two (R, 2R, 4R, etc.). The generalized output voltage equation for an N-bit DAC is:

V_{0}=\frac{V_{R}}{2}\left \{ \frac{b_{N-1}}{2^{0}}+ \frac{b_{N-2}}{2^{1}}+….+\frac{b_{0}}{2^{N-1}} \right \}

The main disadvantages of this design are the wide range of resistor values required and the difficulty in fabricating highly accurate resistors, especially for a large number of bits.

R-2R Ladder DAC

The R-2R Ladder DAC overcomes the disadvantages of the weighted resistor type by using a network constructed from only two resistor values: R and 2R. This ladder network produces the correct binary weighting of currents that are summed by the Op-Amp. The primary advantages of this topology include:

• Ease of design: Only two resistor values are needed, which is much easier to fabricate accurately and match on an integrated circuit.
• Scalability: The design can be easily extended to a higher number of bits by simply adding more R-2R sections to the ladder.

Due to these benefits, the R-2R ladder is the preferred architecture for most modern DACs. Now we will examine the inverse process.

8.3 Analog to Digital Converters (ADCs)

An Analog to Digital Converter (ADC) performs the crucial task of converting a continuous analog signal into a discrete digital representation. ADCs are broadly categorized into two main types: Direct and Indirect.

Direct Type ADCs

Direct type ADCs perform the conversion by directly comparing the analog input against internally generated voltage levels.

• Counter type ADC: This ADC uses a counter that increments from zero. The counter’s digital output is fed into a DAC, which generates a corresponding analog voltage. A comparator stops the counter when the DAC’s output voltage exceeds the analog input voltage. The final count is the digital representation.
• Successive Approximation ADC: This is a more efficient method. It uses a Successive Approximation Register (SAR) to perform a binary search for the correct digital code. It tests one bit at a time, from MSB to LSB, converging on the final digital value much faster than the linear search of the counter type.
• Flash type ADC: This is the fastest type of ADC. It uses a parallel architecture consisting of a resistive voltage divider and a bank of comparators. For an N-bit converter, 2^N-1 comparators are used. The analog input is simultaneously compared to all the reference voltage levels, and a priority encoder instantly generates the corresponding binary output.

Indirect Type ADC

Indirect type ADCs first convert the analog voltage into an intermediate domain, such as time or frequency, before converting it to a digital value.

• Dual Slope ADC: This type is known for its high accuracy. The conversion process has two stages. First, the analog input voltage is integrated for a fixed period of time. Second, the integrator’s input is switched to a known negative reference voltage, and the integrator discharges back toward zero. The time it takes to discharge is measured by a counter. This discharge time is directly proportional to the input analog voltage. This method is used in applications like digital multimeters where accuracy is paramount.