Day 4: Nodal Analysis

Nodal Analysis

Started the day off with a quiz. Yay Quizzes. I actually did well though. It was a quiz to show us how annoying KCL and KVL can be. A precursor to what we would be learning in class.

Temperature Measurement System

Here was our given problem. We are given an 8-bit micro-controller and we are to find the temperature resolution such that we have a voltage change of .5V and a range of 23 - 37 degrees Celsius.

Range of 12 degrees in 25 points equals .48˚/bit

According to our analysis, we round that the V_out = (R•V_s)/(R_Th+R). The resistance of the Thermistor at room temperature (T = ~24˚C) was 11kΩ, and when held tightly in hand (T = ~37˚C), the resistance dropped to 7.3KΩ. Through some simple algebra, we found the Resistance necessary to be 6.681kΩ in order to meet the given specifications. Because we were limited to only E12 resistor series, we chose to use a 6.8KΩ resistor. We expected voltage values of 3.1V at 37˚ and 2.6V at 24˚.

Accordingly, we found that our approximated resistor value was very good. At our room temperature value, we measured 2.57V, a -1.1% difference than expected value.

At our warm temperature value, we measured 3.13V, a 0.97% difference than expected value.

In order to optimize our system, we measured actual temperatures. Room temperature = 22˚C.

Warm temperature = 34˚C.

Post lab assignment asked us to meet new specifications of increasing input voltage as temperature increases and .1V/˚C. Through our calculations, we found that this was impossible because it called for a negative resistance. We were able to optimize the theoretical system with an 8961Ω resistor.

Finally, we were introduced to nodal voltage analysis. Since I am doing this blog late, I scoff at my younger self for being so smitten by the idea of nodal analysis, with far superior methods still to be learned. Better than Kirchoff's laws I suppose.