How does a basic digital-to-analog converter (DAC) perform signal conversion?

A digital-to-analog converter (DAC) transforms digital binary data into an analog signal using weighted contributions from each bit. In this FAQ, we discuss the two most commonly known ways of DAC conversion: weighted resistor DAC and R-2R ladder DAC.

Before getting into the conversion types, let us understand the basic steps involved in a DAC conversion. Figure 1 shows a block schematic representation of the process taking place in a DAC. The system processes an n-bit digital input through several stages:

First, input gates receive the digital signal
Second, an n-bit register stores these values
Third, level amplifiers condition the signals
Fourth, a binary ladder combines these weighted signals to produce the analog output voltage (VA).

Figure 1. Block diagram of a DAC architecture comprising various stages of conversion. (Image: John Wiley & Sons)

N lines connect each stage, maintaining the n-bit resolution throughout the conversion process.

Weighted resistor DAC

A weighted resistor DAC is a type of DAC that uses resistors with values proportional to the weights of the input bits. It converts a digital input signal into an equivalent analog output signal by summing currents or voltages based on the representation of the input.

A simple version of a weighted resistor DAC can be understood starting with Figure 2. The figure illustrates two identical configurations, (a) and (b), of a basic DAC using an operational amplifier in inverting mode.

Figure 2. A simple single-bit DAC using an operational amplifier. (Image: Rakesh Kumar, Ph.D.)

Each setup shows a single-bit input (logic ‘1’ or ‘0’) connected through a switch to either +5 V or ground, feeding a current through a resistor Rin into the inverting terminal of the op-amp. The non-inverting terminal is grounded.

A feedback resistor Rf connects the output Vout back to the inverting input, ensuring negative feedback and linear operation. The current Iin through Rin creates a proportional output voltage Vout via Rf, resulting in an analog voltage representing the digital input state. This configuration is the fundamental building block of a weighted resistor DAC.

Figure 3. A general schematic diagram of a 4-bit weighted resistor DAC. (Image: Rakesh Kumar, Ph.D.)

Figure 3 illustrates a 4-bit weighted resistor DAC using an inverting operational amplifier configuration. Each of the four digital input bits is connected to a switch. The inputs are arranged from the least significant bit (LSB) to the most significant bit (MSB). These inputs pass through individual resistors RA, RB, RC, and RD, which are weighted according to the significance of each bit.

The weighted currents combine at the op-amp’s inverting input, generating a total input current, Iin. The current passes through the feedback resistor, which is converted to a proportional voltage output, Vout. This circuit performs a weighted sum of the digital input bits and provides an analog voltage output corresponding to the digital input value.

Figure 4 illustrates the stepwise operation of the 4-bit weighted resistor DAC, as shown in four subfigures (a) to (d). Each subfigure represents a different input combination applied to a series of switches connected to a reference voltage (+5 V) and ground.

Figure 4. Various modes of operation of the 4-bit weighted resistor DAC starting from 0001 to 1111. (Image: Rakesh Kumar, Ph.D.)

The DAC’s practical application is when the resistors are arranged in a binary manner, as shown in Figure 5. Each switch output is fed through a resistor with binary-weighted resistance values: R, 2R, 4R, and 8R, corresponding to the bit’s significance. This approach’s advantage is that a total of 16 states can be achieved, which improves the DAC’s resolution.

Figure 5. A 4-bit binary weighted resistor DAC that offers better resolution than one with the same resistor values. (Image: Rakesh Kumar, Ph.D.)

R-2R ladder DAC

The problem with a binary-weighted resistor DAC is the requirement of a wide range of resistor values. For example, a 12-bit binary-weighted DAC would need resistors ranging from 1 kΩ (MSB) to 2 MΩ (LSB), making fabrication challenging. Adding to the challenge is the need for a high tolerance value of the resistor for higher accuracy.

These problems can be addressed with an R-2R ladder DAC, as shown in Figure 6. It illustrates a 3-bit R-2R ladder DAC implemented using an inverting operational amplifier configuration. The ladder network comprises repeating resistor segments with values of R and 2R, which form a voltage divider that precisely weighs each digital input bit (from MSB to LSB).

Figure 6. Circuit diagram of a 3-bit R-2R ladder DAC. (Image: Rakesh Kumar, Ph.D.)

Figure 7 shows the operation of the 3-bit R-2R ladder DAC across three different digital input combinations in subfigures (a), (b), and (c). Each configuration includes a resistor network with values R and 2R, connected in a ladder structure. These configurations enable the attainment of eight distinct states, which enhances the resolution.

Figure 7. Three of the eight possible states of the 3-bit R-2R ladder DAC. (Image: Rakesh Kumar, Ph.D.)

The advantage of the R-2R ladder is that it can be extended to more bits without the challenges of resistor values, as found in binary-weighted resistor DAC.

Summary

Weighted resistor DACs are effective with binary combinations of resistors. Due to their simplicity, they are commonly used in applications requiring low-resolution digital-to-analog conversion, such as audio devices, light dimmers, and digital panel meters.

R-2R ladder DACs have a simpler implementation with only two resistor values. This advantage makes them ideal for cost-effective and precise communication systems and instrumentation designs, such as waveform generation and data acquisition systems.