A series of videos on opamp design and applications will continue with the analysis of the digital-to-analog (DAC) R-2R ladder network. As before, the video will discuss the R-2R DAC circuit and analyze it using the concept of superposition. A four-bit binary input was given as an example. The next video will conclude the analysis of the R-2R ladder network.

As you should have noted the digital-to-analog converter (DAC) R-2R ladder provides an interesting variation of the binary-weighted circuit, generating a voltage output directly. Again, this class of DACs uses a set of resistors of two values only.

The circuit accomplishes the goal to convert a quantity specified by a binary (or multidigit binary-coded-decimal or BCD) number to a voltage or current proportional to the value of the digital input. Going through the analysis using superposition will help show the student that the R-2R digital-to-analog converter is equivalent to the binary-weighted summing circuit.

Hopefully, the analysis provides a good review on using the concept and power of superposition as long as the circuit is linear. Adding up all the individual outputs due resulting from each input to get the overall output is what superposition is all about when analyzing the digital-to-analog converter.

As you can see, the analysis is rather tedious but not difficult after redrawing the circuit to help visualize the analysis. The student should gain increased confidence in using the superposition principle after completing the series of articles and videos on the digital-to-analog converter.

The above analysis is not much different than connecting a set of resistors to an op-amp summing junction of the binary-weighted DAC to get an output proportional to a weighted sum of the input voltages. Like the binary-weighted DAC the R-2R digital-to-analog converter circuit generates an output from zero to the reference voltage (Vref).

We note that the maximum input count is always 2^n -1 when all the bits are set to 1. Thus, the maximum voltage is really Vref*(2^n-1)/(2^n). For example, the set of videos show that for the digital-to-analog converter given as n=4 and Vref=5 then the maximum voltage is 5*(15/16) or 4.6875 volts.

The maximum voltage can be equivalently viewed as one resolution bit below Vref. Here, one resolution bit is equivalent to Vref/2^n or for our example 5/16 or 0.3125 volts.

Below are some references on operational amplifiers and related topics. There are some reference books on the digital-to-analog converter (DAC) as well.

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