Digital to analog converter (DAC)

A Digital-to-Analog Converter (DAC) converts a digital input (binary, BCD or another digital code) into an analog output — usually a DC voltage — whose value is proportional to the binary number applied. Two common methods are the R-2R ladder network DAC and the binary weighted resistance DAC.

4-bit R-2R ladder network DAC

Figure 5.9.1 shows a 4-input DAC built from a ladder using only two resistor values, $R$ and $2R$ (for example 1 kΩ and 2 kΩ). Each binary input is a switch that connects either to $V_{ref} = 16\ \text{V}$ (logic 1) or to 0 V (logic 0). The ladder output is buffered by an op-amp voltage follower to give $V_{out}$.

When all switches are at 0 V, $V_{out} = 0\ \text{V}$. Taking one switch to 16 V at a time gives:

• input $(1000)_2$: $V_{out} = 8\ \text{V}$
• input $(0100)_2$: $V_{out} = 4\ \text{V}$
• input $(0010)_2$: $V_{out} = 2\ \text{V}$
• input $(0001)_2$: $V_{out} = 1\ \text{V}$

By superposition, several logic-1 inputs simply add their individual contributions, so the analog output is proportional to the binary number. Table 5.9.1 lists $V_{out}$ for all sixteen 4-bit inputs.

Binary weighted resistance DAC

Here weighted resistors $R$, $2R$, $4R$ and $8R$ feed a summing (inverting) amplifier (figure 5.9.2). A logic 0 corresponds to 0 V and a logic 1 to 5 V. The most significant bit (MSB) $B_3$ enters through $R$ and the least significant bit (LSB) $B_0$ through $8R$, with a feedback resistor $R$. For a single LSB input $(0001)_2$, $V_O = -\dfrac{R}{8R}\times 5 = -0.625\ \text{V}$; for the MSB alone $(1000)_2$, $V_O = -\dfrac{R}{R}\times 5 = -5\ \text{V}$. The output is therefore proportional to the digital input. Table 5.9.2 gives the full output chart.

Analog-to-Digital Converter (ADC)

An ADC performs the reverse operation, converting an analog input into a digital output that can be displayed. For example, a temperature difference sensed by a thermocouple appears as an analog voltage, which an ADC turns into digital form.

The counting ADC (figure 5.9.3) uses a comparator, a binary counter, a DAC and an AND gate. A clear pulse first resets the counter to zero. The clock then advances the counter; its binary output drives a DAC whose output is a rising staircase waveform (figure 5.9.4). The comparator continuously compares this staircase $V_O$ with the analog input $V_A$. While $V_A > V_O$, the comparator output is high, keeping the AND gate open so clock pulses reach the counter. Once $V_O$ exceeds $V_A$, the comparator output goes low, the AND gate closes, and the counter stops when $V_A \approx V_O$. The value held in the counter is the digital equivalent of the analog input.

Open-loop applications of the op-amp: comparator and Schmitt trigger

All the circuits above use negative feedback. When the op-amp is used without negative feedback it works in an open-loop configuration, comparing one input against the other.

Working of a comparator. In the basic comparator (figure 5.9.5) the output is $V_O = A(V_2 - V_1)$, the product of the very large open-loop gain $A$ (of the order of $10^5$ or more) and the input difference. Even a few millivolts of difference drives the output into saturation at $+V_{CC}$ or $-V_{EE}$:

• if $V_1 > V_2$, then $V_O = -V_{EE} = -V_{sat}$
• if $V_2 > V_1$, then $V_O = +V_{CC} = +V_{sat}$

With a fixed reference on one terminal and a varying signal on the other, the comparator gives a two-state (digital) output that switches between $+V_{sat}$ and $-V_{sat}$.

Zero crossing detector. A zero crossing detector (figure 5.9.6) applies the varying signal to the non-inverting terminal with the inverting terminal grounded. Then $V_O = +V_{sat}$ when $V_{in} > 0$ and $V_O = -V_{sat}$ when $V_{in} < 0$. The output switches state at every zero crossing of the input, converting a sine wave into a square wave. …