Digital to analog converter in a nutshell

First of all, what is digital to analog converter or DAC? Trivially, the DAC is the circuit that transfer digital value to analog value. For example, you have 1101 in binary, you will get 2.4 volt after getting through DAC. If you imagine that the DAC is the black box, you will have parallel digital input and just only one analog output. For declaration, let we want to build the 4 bit DAC. We have D[3:0] as digital input and Va is the output. It means that we separate the output voltage in 16 values because we have 4 bit DAC. The output voltage here is depend on how the circuit build and it can write in terms of mathematical model as it describe in the figure.

Moreover, the resolution is the different between one digital value: voltage at 0001 and voltage at 0000. It tell us the performance of the DAC. If you want to decrease the resolution, the easiest way is to increase the bit of DAC.

To build the DAC circuit, the weight summing amplification circuit is introduce. This circuit can be analyze using the superposition theorem. The maximum voltage and the resolution is shown in the figure below.

However, this circuit have a little problem when we cannot get the precise resistor. In practical we cannot get the precise resistor for sure. For example here, we have 1 percent tolerance for each resistor and we calculate for the maximum and minimum voltage at the highest digital value which is 9.56 V and 9.18 V respectively. So, the different is 0.38 which is more than the resolution. It means that you can get the exact the analog value.

Let’s imagine that if we have 8 bit DAC, what the resolution will be and is it less than the difference between maximum and minimum value here.

Therefore, the result here show that the value here is more than the resolution which mean it cannot show the exact value of the digital input. To solve this we need another circuit. The R-2R ladder is introduce here as the figure below. To analyze the R-2R ladder circuit, the Thevenin equivalent circuit is applied. You can put the inverting amplifier to the end of circuit for amplify the value.

Now we are going to do the experiment based on the R-2R ladder circuit. We will use the Arduino to generate the digital value and use the oscilloscope to capture the analog value. The circuit is look like this figure.

In Arduino, we generate the counter begin with 0 to 15. As aforementioned above, we separate the maximum voltage to 16 each. Now the maximum voltage from Arduino is around 5 V. So the result from this circuit is shown.

Thanks for reading.