#### What is DAC?

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I electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function.

A Digital to Analog Converter (DAC) consists of a number of binary inputs and a single output. In general, the number of binary inputs of a DAC will be a power of two. There are several main DAC architectures, the most common 2 being Weighted Resistor DAC and R-2R Ladder DAC, the latter will be discussed later in this series.

Weighted Resistor DAC

A weighted resistor DAC produces an analog output, which is almost equal to the digital (binary) input by using binary weighted resistors in the inverting adder circuit. In short, a binary weighted resistor DAC is called as weighted resistor DAC.

The circuit diagram of a 3-bit binary weighted resistor DAC is shown in the following figure:

The bits of a binary number can have only one of the two values. i.e., either 0 or 1. Let the 3-bit binary input is b2b1b0. Here, the bits b2 and b0 denote the Most Significant Bit (MSB) and Least Significant Bit (LSB) respectively.

The digital switches shown in the above figure will be connected to ground, when the corresponding input bits are equal to ‘0’. Similarly, the digital switches shown in the above figure will be connected to the negative reference voltage, −VR when the corresponding input bits are equal to ‘1’.

In the above circuit, the non-inverting input terminal of an op-amp is connected to ground. That means zero volts is applied at the non-inverting input terminal of op-amp.

According to the virtual short concept, the voltage at the inverting input terminal of opamp is same as that of the voltage present at its non-inverting input terminal. So, the voltage at the inverting input terminal’s node will be zero volts.

The nodal equation at the inverting input terminal’s node is:

Substituting, R=2Rf𝑓 in above equation.

The above equation represents the output voltage equation of a 3-bit binary weighted resistor DAC. Since the number of bits are three in the binary (digital) input, we will get seven possible values of output voltage by varying the binary input from 000 to 111 for a fixed reference voltage, VR.

We can write the generalized output voltage equation of an N-bit binary weighted resistor DAC as shown below based on the output voltage equation of a 3-bit binary weighted resistor DAC.

The disadvantages of a typical binary weighted resistor DAC are as follows:

-The difference between the resistance values corresponding to LSB & MSB will increase as the number of bits present in the digital input increases.

-It is difficult to design more accurate resistors as the number of bits present in the digital input increases.

Beyond their application in High-end audio, DACs are present in common devices, namely smartphone, wireless speakers, TVs,... nearly every digital device that can produce sound. Moreover, Digital to analog converters in general play a vital part in video, mechanical and communication systems like military radar systems as well. Very high-speed test equipment, especially sampling oscilloscopes, may also use discrete DACs. The suitability of a DAC for a particular application is determined by figures of merit including: resolution, maximum sampling frequency and others. Digital-to-analog conversion can degrade a signal, so a DAC should be specified that has insignificant errors in terms of the application.

References:

https://www.tutorialspoint.com/linear_integrated_circuits_applications/linear_integrated_circuits_applications_digital_to_analog_converters.htm#:~:text=A%20weighted%20resistor%20DAC%20produces,called%20as%20weighted%20resistor%20DAC.