8-bit DAC Using Op-Amps - Example 1

Here is another summing amplifier example with eight inverted inputs, termed 8-bit summing amp DAC. Weighted resistor values enable the circuit to convert a binary input into analogue voltage; hence, this is a DAC application. The output of the first stage goes through a second op-amp, which has a gain of unity, because the input and feedback resistance is the same. It behaves as a buffer, and in addition, inverts the signal.

At first, you see this circuit and think, wow! I am going to be sitting here for the next three hours performing long division like a lab-rat, by using the long summing amplifier formula. However, what if the question was to input binary 10000000_b at its input, where logic 1 is 5 V and logic 0 is 0 V. In that case, it becomes much easier because only one resistor will get 5 V and the rest will have 0 V. The thing to remember here is that the highest resistor value is fed with the least significant bit (LSB), and the lowest resistor value is fed with the most significant bit (MSB). In our binary number the MSB is 1, therefore this is fed to the 10 kΩ resistor, which is the lowest value. Hence, this resistor will have 5 V at its input whilst all the rest of the inputs will have 0 V. Given the output voltage to be 10 V, find the feedback resistor.

Although it looks like a long formula, all the terms with zero volts cancel and only the term with the 10 kΩ resistor remains. As long as you remember that the k is for thousand, you do not have to replace it with a numeral, and I use it to the end in the final answer as well!

With a little transposition and algebra, we get this.

Therefore, the feedback resistor has to be 20 kΩ, and we disregard the negative sign for inverted gain.

8-bit Counter Input

If the op-amp DAC were to receive input from an 8-bit counter, then we would see a stepped response from the op-amp output.

Summing Amplifier Example Questions