Temperature Measurement System Lab

Objective: 
Solving for unknowns needed the use of KVL or through element voltages which becomes longer work of problem solving based on the number of equations created. Instead, we are introduced with a new method called the Node Voltage Method where we find nodal voltages and ignore voltage sources. However, we are introduced with ground in a circuit which is also known as a reference node that has zero potential. We apply the equation (i = (V high-V low)/R) depending on the current we are looking for across a resistor. However we must also apply KCL to generate the needed equations. Overall, the Nodal Voltage Methods simplifies things by reducing the number of equations. We are also introduced to Super nodes which is created by having a voltage source whether dependent or independent and connected between two non reference nodes. We can then apply KVL on the super node. With this in mind if there are, for example 3 unknown, then we will need 3 equations which can be solved in MATLAB. We will use this program for the Temperature Measurement System Lab and for future use in other lab.
voltage divider
cheapest temperature

Group Practice Problems:

1. The problem in Figure 1 was a quiz question that had to be completed in 10 minutes. Unfortunately, we did not finish it on time. We figured it would take a long time. However, we were introduced to the Nodal Voltage Method which simplifies the number equations and make this problem easier to solve. 

Figure 1. The image shows a quiz question where our team had to find the voltage at R1.

2. The problem in Figure 2 shows how use the Node Voltage Method where we pick 3 node voltages and reference point where the ground connects. From this we apply the equation: i = (V high-V low)/R at each node voltage. We then apply KCL. The rest of the problem is just plugging the current to the KCL equations. Our first attempt did not go so well as seen below in figure 2 since we forgot to include one of the current when using KCL. Yet, we found the mistake and fixed it.

Figure 2. The image above shows a new method of find currents when there is ground called Node Voltage Method.

Temperature Measurement System Pre Lab and Actual Lab Procedures:

1.  Before we begin with the experiment, we start a pre lab where we are asked to find the V out and the resistance, given a input voltage of 5V as seen in figure 3. . However, the value R has to chosen carefully so that Vout increases by a minimum of .5V over the temperature range of 25C-37C. In order to find the Rth between

2. We begin our calculations by first find the resistance of the thermistor given the temperature by looking at the temperature resistance curve as seen in figure 4. We see that there is a voltage division in the circuit in figure 3. Therefore, we acquire an equation for output where V = I R where I = 5/(R+Rth). So, our equation will be Vout=R*5/(R+Rth). Since we want a voltage difference output of .5, then we create an equations where Vout(Final)-Vout(initial) = .5. Out results can be seen in Figure 5 where we acquire a quadratic equation. Finally we entered our quadratic equation  into MATLAB as seen in Figure 6. in which we acquire a theoretical resistance of 4338<R<17633. 

Figure 3. The image above shows a circuit where Rth represents the thermistor. 

Figure 4. The graph shows a temperature-resistance curve where the thermistor is used in the circuit. We see that the resistance changes as a function of temperature. 

Figure 5.  The image shows the calculated results for find the Theoretical resistance. 

Figure 6. Calculating the Resistance needed in order to acquire a voltage difference of .5V in MATLAB

3. We acquired a theoretical resistance of 4338<R<17633. However in order to create or set up our circuit we need to find a reasonable resistance provided with what we have in class. We chose a resistance of 10k since it ranges between our theoretical resistance values. The actual resistance of fixed resistor is R= 9.84+/-.05k 

4. We also measure the resistance of the thermistor at room and body temperature. The thermistor resistance at room temperature of 25C is Rth= 10.5k+/-1 and thermistor resistance at 37C is Rth= 7k+/-1 when covered with our fingers representing bod temperature of 37C.

5. The circuit can be seen in figure 7 and voltage output measurement were taken when applying the thermistor at room temperature and body temperature. We acquire a measurement of Voltage output at low temp V= 2.40V and voltage output at body temperature of V = 2.93V. A video is provided that demonstrates the operation of our circuit, link: https://youtu.be/6BJOS9yp6gs

6.  We see that the difference between the voltages are Vdiff = 2.93- 2.4 = .53 which is close to what we expect to get for output voltage difference of .5 V. The percent error for voltage output difference is 6% based on the formula of percent error= |(experimental - theoretical)/ theoretical|*100.

Figure 7. Circuit setup for Temperature Measurement System.

Summary of the Lab and Overall Learning Outcome:

Our pre lab calculations tells us to find the theoretical resistance needed so that the voltage difference output is .5V. We acquire a theoretical resistance of 4338<R<17633 with the help of MATLAB. We picked a resistance of 9.84k provided by what we have available in class. We measure resistance of thermistor at room temperature 25C, R= 10.5k+/-1 and at body temperature 37C , R =7k+/-1. We can see that as temperature increases for thermistor, then resistance deceases which is what we expect based on the the graph provided in figure 4. As the thermistor increases in the temperature then we expect a high output voltage. Our results show our expectations since voltage output at body temperature was 2.93V+/-.05 compared to 2.40V+/-.05 when temperature at the thermistor was at room temperature. We acquire a 6% error which shows that our circuit performance compared well with our expected results.