June 2019 StudentZone Quiz Solution

Question 1:

Using Ohm's law and the formula for resistors in parallel, what is the output voltage of the R-2R DAC when inputs D7 and D6 are connected to each combination of ground and 3.3 volts? Please present the results as a table.

Answer 1:

Considering the digital inputs D0-D5 to be grounded and applying the formulas for parallel and series resistance computations we can reduce the R-2R ladder to the following circuit:

Starting from right side of the circuit and applying the Thevenin equivalent circuit we obtain the series resistor of value 10K (parallel combination of two 20K resistors) and the open circuit voltage from the resistor divider. This process continues methodically, step by step for each stage of the R-2R ladder.

The resulted analog output voltage as a function of the two digital inputs D6, D7 is the following:


The results for each combination of ground and 3.3V for the two digital inputs (D6, D7) are presented in the table below:


Question 2:

How much current will flow through this resistor network when input D6 is connected to 3.3 volts and D7 to ground?

Answer 2:

By applying the Thevenin equivalent analysis, the contribution of D6 at the output of the R-2R ladder is VD6/4. The equivalent output resistance of the R-2R network is equal to R=10K.

Therefore, the current flowing through the resistor network when D6 is connected to 3.3V can be obtained by applying the Ohm’s law.