Dependent Sources and MOSFETs and Voltage-Current Characteristics Lab

Objective: 

The goal is to review and define resistance in which R = resistivity* Length/Area. We can see that resistance is proportional to length (R~L)  and resistivity (R~resistivity) and inversely proportional to area (R~1/A). Defining the equation can be seen in Figure 1 as well as using the equation so solve an in class problem where we were given the power, voltage of a source, and the resistivity of a material. From this, we were told to find the cold and hot resistance and an approximation for length and area. Finding the hot resistance was plugging in and manipulating the equation. However, finding the cold resistance was a bitt different since a lot of engineering results in estimating. As a result, we concluded a cold resistance of R cold<R hot. We also covered how to find the nodes, branches, and loops in a circuit. Most importantly, the fundamental theorem of network topology (b = L+N-1) would help us find the loops since, some times, may be difficult to find for complicated circuits. We would then apply our learning outcome of the lecture to our labs based on Voltage and Current Characteristics, and Dependent Sources and MOSFETs. Furthermore, we also have the opportunity to use MATLAB in our labs since it requires linear regression

Group Circuit Practice Problem and Learning Outcome:

1. Resistance:
We covered the idea that resistance depends on the resistivity of the material, length, and cross sectional area as seen in Figure 1. In addition, the problem below asks to find the resistance. In this case, we use ohms law where V=IR but we take in mind that when current flows from a high potential to a low potential, then V= IR and when current flows from low to high potential, then
V = -IR. This idea can be seen in Figure 2 where an unknown current and voltage across a and b is found. 

Figure 1. Above shows the equation for resistance based on the length, cross sectional area, and resistivity of the wire.

2. Branches, nodes, and loops:
The way in which we can represent branches is by looking whether there is a two terminal element or in other words, is connected to voltage source or a resistor. The nodes are found by seeing whether there is a point that has two or more branches. A loop is any closed path in a circuit but the equation
b = L+N-1 may be needed since loops may be hard to visualize with more complicated circuits. 

Figure 2. The image shows a circuit for which the number of branches, nodes, and loops were found using the equation
b = L+N-1 

Figure 3. The image shows a circuit where the unknown current in amps was found and the voltage across a and b (Vab).

Voltage- Current Characteristics Lab Summary with Procedures:

1. The first portion of the lab explores Ohms law (V=IR) where we are a given a voltage source and a resistor of 100 ohms according to the manufacturer. Yet, we measured a resistance of R = # which is lower than specified. We connected the resistor in series and collected 6 measurements of voltage and current. we expect to calculate the overall resistance by looking at the slope of a current vs voltage plot.  Our data measurements may be seen in Figure 5 and plotted the points as well as include a linear fit. We figured that R = V/I and concluded that the resistance would be the same as we increased the voltage in increments of approximately 5 volts. 

Figure 4. The image above shows how a circuit was connected with a resistor in series. From this, we acquired various measurements of voltage and current.

2. MATLAB table and Plotting:

We placed our measurements in a table as seen in Figure 5 as well as finding the linear curve fit with a degree of one, and the correlation coefficient. We acquired a linear fit equation of R = 0.0106V-0.0027. The linear curve fit may be seen in Figure 6. 

Figure 5. The image shows a table of our measurements, the curve fit linear constants and the correlation coefficients. 

Figure 6. A Linear curve fit using the MATLAB Program. 

Summary of Dependent Sources and MOSFETs Lab with Procedures:

1. A MOSFET is used in a circuit which serves to control the power supply's current as seen in Figure 7 and 8. In other words, the increase in voltage, should increase the current out of the power supply which can seen from our measurements in Figure 9. We also measure the resistance of the resistor of R = 98.1 ohms. Our table of measurements in Figure 9 shows that there is a Threshold Voltage from .72<V<.74 since it is where the drain current beings to increase significantly.

Figure 7. The image shows a representation on how the circuit is built with the use of a MOSFET

Figure 8. The actual circuit set up with the a use of a MOSFET 

Figure 9. Table of measurements of current as voltage gradually increases until no current passes through the MOSFET

2. We plot the gate to source voltage vs drain current as seen in Figure 10. We can see on the graph that as the voltage increases, the current increases as well until current stabilizes. This is known as a Voltage controlled current source or VCCS.

Figure 10. Current vs Voltage plot 

3. We are also able to find the value of g for the circuit which is the slope of our data points as seen in figure 11. Our g for the circuit is g=0.433 as seen in figure 11.

Figure 11. We used the points that are more linear and found a linear fit equation. 

Summary of the Labs and Overall Learning Outcome:

The voltage-current characteristics lab explores the idea of ohms law where V=IR or R=V/I. If we plot our measurements of voltage and current while voltage was increased with increments of 5V, then we would see a linear representation of plotted points. Therefore, we can curve fit the line as a polynomial of degree of one. In other words, a linear equation. We can see that the y intercept is not at 0 but -0.0027 which is close to 0. We can assume that there is a linear resistor that obeys ohms law where the slope of .0106 ohms is the resistance. 

The dependent sources and MOSFETs Lab explores the use of a voltage controlled current sources where the gate voltage control the current in the circuit. As we increase the gate voltage, the more current flow was shown based on our results. We then found the threshold voltage by determining the voltage in which the current increased significantly.