3/26/2015

Today, we focused primarily on operational amplifiers and their use in electrical circuits.

Original

After analyzing circuit with an op-amp we were given the circuit above and asked to find the closed circuit gain and i_0.

Replacement

When given circuit that includes an op-amp we are able to replace the op-amp symbol with the element shown above.

Example Problem

 Circuit analyzed above.

Built Circuit

This lab required the use of an op-amp in order to find saturation. Above is the built circuit.

Results

In order to find the saturation caused by the op-amp, we supplied various voltages ranging from -3-3V. 

Graph of V(in) VS. V(in)

We found that that the voltage began saturating when voltages above 2V or -2V were supplied. Ideally the voltage coming out of the op-amp should be 5V but because the op-amp was inexpensive meant that not so good materials were used which would lead to some voltage loss.

Summary:

Today, we focused primarily on the use of operational amplifiers and the analysis of the instrument in a circuit. Operational amplifiers have a set value for open-loop gain, input resistance and output resistance. However, we can treat operational amplifiers like ideal op-amps and let their open-loop gain and input resistance go to infinity and their output resistance go to zero. We can treat modern op-amps like ideal op-amps because they have large gain and input resistance values. Two very important characteristics of an ideal op-amp is that both input currents into the op-amp are zero (because infinite input resistance) and the voltage across the input terminals are small (V_d refer to 2nd picture).

3/24/2015

Results

The first lab dealt with both ideal and non-ideal power sources. Ideal power sources do not contain a resistor while non-ideal power sources incorporate a resistor. The main focus of this lab was to calculate the internal resistance of our power source which was a Analog Discovery module. We were able to calculate the internal resistance to be about 0.5Ω. However, if we were to change the resistor used in the circuit we will see that the calculated resistance will change as well. This tells us that there is more than an internal resistor being used in the Analog Discovery.

Circuit

We used a 22Ω resistor to calculate the internal resistance. 

We then learned about maximum power transfer and learned that in order to get maximum power output the resistor load must equal the resistance thevenin.

Our next lab dealt with applying the rule for maximum power transfer. For this lab we used two identical resistors that acted as the thevenin and load resistor. Since the internal resistance is so small when compared to the thevenin resistor we were able to neglect the value. We first calculated the theoretical maximum power transfer and then measured our values from the circuit and calculated an experimental maximum power.

Summary:

Today, we learned Norton's theorem and maximum power transform. Norton's theorem states that a linear two circuit terminal can be replaced with an equivalent circuit that consists of a current source in parallel with a resistor. The resistor is equivalent to the thevenin resistor. The current source can be found by dividing the voltage thevenin by the resistor thevenin. We also learned about maximum power transfer. In many situations circuits are designed to provide power to a load. For that reason it is important to transfer maximum power to  the load and in order to do that the load resistance should equal the thevenin resistance. We also learned that power sources contain an internal resistance and a method in which to calculate the resistance.

3/19/2015

Circuit built on everycircuit.com

At the beginning of class we were asked to register for an application that allows us to build various circuit and gives an analysis on them. This app is called "everycircuit". We were then asked to build a specific circuit.

Pre-Lab

 The remainder of the day was spent on a new method of circuit analysis known as Thevenin's Theorem. The lab required the use of various resistance values and in order to make our circuit analysis much simpler we used Thevenin's Theory.

Thevenin Circuit Diagram

We then built a new circuit that resembled the Thevenin circuit diagram. The Thevenin resistance was made by using a potentiometer and the 0.45V was supplied from the Analog Discovery. We varied the resistance by using another potentiometer.

Results  

We measured the voltage difference at the load resistor with the Analog Discovery and the actual resistance resulting from the potentiometer with a multimeter. The goal of the lab was to find the maximum power dissipation by the load. 

Summary:

Today, we learned how to build circuits using "everycircuit". The primary use of this tool is to check our results from doing circuit analysis by hand. We also learned a new method for circuit analysis known as Thevenin's Theorem. Using Thevenin's Theorem, we are able to replace a linear two-terminal circuit with an equivalent circuit consisting of a voltage source in series with a resistor. The voltage source and resistor are of equivalent  value of the circuit that was replaced. Using this method allows us to add different loads to the circuit and simplify the calculations rather than using more method analysis techniques. The error in the lab was due to the actual resistance values of the resistors not being equivalent to the values used in the calculations.

3/17/2015

Pre-Lab

We began the day with a lab that required the use of a function generator and oscilloscope. We used the Analog discovery for both. Before we started the lab we predicted what would happen if we were to use a voltage divider on a time varying voltage source. We predicted that the voltage will be cut in half.

Circuit

We built the circuit and connected the Analog Discovery to supply a time varying voltage of different shapes (triangle, sinusoidal, square) tot the circuit. We then used the oscilloscope to record the result.

Square Generator

Triangle Generator

Sinusoidal

As can be seen by the results from the oscilloscope, the amplitude (voltage) was halved with the voltage divider, from 2V to 1V. 

Circuit Diagram

The next lab required the use of the analog discovery as well. To build the circuit above the use of a NPN transistor (2N3904), a 100 Ω, and a 100kΩ resistor. Using the oscilloscope, we graphed the voltage from the 100 Ω resistor and the NPN transistor.  Using Waveforms, we were able to create a step function and send it through the base. We also sent a triangle function through the collector.

Circuit

Above is the circuit built.

Graph using oscilloscope

Saturation with a NPN transistor.

Summary:

Today, we focused primarily on labs. The first lab consisted of getting to know how to use the Analog Discovery and Waveforms to act as both a function generator and oscilloscope. The other lab required the knowledge from the previous lab in order to complete it.Towards the end of the class we learned three new methods of circuit analysis. The three new methods are linearity property, superposition principle, and source transformation. The linearity property can only be applied to linear circuits, which is a circuit whose output is linearly related to its input.The superposition principle applies to circuits where the voltage across an element in a linear circuit is the sum of the voltages across that element due to each independent source. Source transformation allows us to  replace a voltage source in series with a resistor by a current source is in parallel with a resistor. This also applies to current sources.

3/12/2015

Mesh analysis problem

 We began the day with a refresher on how to do mesh analysis.

New circuit analysis method with example problem

We then learned a new circuit analysis method that involved using KCL and KVL to solve the unknown values for the circuit. A new method of circuit analysis is needed because this circuit includes both current and voltage sources.

Results

The lab for the day required the use of mesh analysis in order to solve for i_1 and V_1. Before actually conducting the experiment we used mesh analysis to solve for i_1 and V_1. We calculated the V_1 to be 2.42V and i_1 to be 0.26mA. After building the circuit, we measured V_1 to be 2.45V and i_1 to be 0.26mA with a multimeter. We also calculated the percent error for V_1 to be 1.24% and i_1 to be 0%.

Circuit build

Above is the circuit built in order to measure V_1 and i_1.

Summary:

Today, we learned a new circuit analysis method that we can apply to circuits that include both voltage and current sources. We solved a circuit by "deleting" the current source and making the circuit into two loops that we can apply KVL. The lab was determined to be successful because of the small percent error that arose from our calculated V_1 and measured V_1 value. However, this percent error may be due in part to resistors having a different resistance value than what was originally calculated. We also learned about transistors and how we can use circuit analysis with them implemented in a circuit.  Below is a the circuit symbol for a transistor (a) but this can replaced by (b) in order to perform circuit analysis.

3/10/2015

Work done for circuit analysis

The day began with Professor Mason demonstrating a new method of circuit analysis. This new method involves solving for the voltages in a circuit that contains voltage sources rather than current sources. The method is similar to nodal analysis with current sources.

Results & Calculations

This lab required us to use the new method of nodal analysis with voltage sources in order to calculate V_1 and V_2 in the circuit diagram shown above. Using the new nodal analysis method, we calculated V_1 to be -4.424V and V_2 to be -2.424V. After building the circuit we used a multimeter to measure the voltage at thos points. The measured value for V_1 was -4.34V and for V_2 it was -2.38V. We calculated the percent error from our calculated value and measured value from V_1 to be 1.9% and for V_2 to be 1.8%. I believe this error arose from the resistors not being the exact values that were expected. We calculated V_1 and V_2 by using  6.8kΩ, 10kΩ, and 22kΩ resistance values. However, when we measured the actual resistance of the resistors implemented in our circuit the values were 6.63kΩ, 9.97kΩ, and 21.8kΩ which differed from the values used in our calculations and resulted in different voltage values for V_1 and V_2.

Circuit

Above is the circuit we built in order to measure the V_1 and V_2. We used Curtis' Analog Discovery device to supply the 5V, -5V and -3V needed in the circuit. The multimeter was used to measure the resistance values of the resistors and the voltage at V_1 and V_2.

Summary:

Today, we learned a new circuit analysis method that will simplify the number of equations needed in order to solve for the unknown voltages at different nodes. This method is different from the previous nodal analysis method because it deals with voltage sources. We also learned mesh analysis, This circuit analysis requires the circuit to be planar. It works by assigning mesh currents to the loops and using Kirchhoff's loop law. However, the loops cannot intersect other loops. For our lab, I believe in order to reduce the error for our values we should first measure the resistance values of our resistors and then use those values in our calculations.

3/5/2015

Taken from MH Education

Using nodal analysis on this circuit would be far easier that using the loop rule to find the unknown voltage. Nodal analysis reduces the amount of equations needed in order to find the current and/or voltages. 

Results

Today, we did a lab that involved a thermistor. The focus of the lab was to use voltage division in order to increase the voltage by 0.5V by heating the thermistor from 25°C to about 37°C using the heat from our hand. We accomplished this task by adding a 12k resistor in series with the thermistor. The 12k resistor was actually measured to be 11.85k Ω. We were able to find the range of resistance that would work by using voltage division and setting it equal to 0.5 because we wanted the voltage to at least increase by 0.5V when measuring the voltage with a multimeter. We also found that the closer the resistor value is to the resistance values we got from our calculations, the better the voltage would increase by 0.5V.

Above a video of the voltage increasing by applying heat to the resistor. (NOTE: this is not the resistor used to increase the voltage by 0.5)

Summary:

Most of the day consisted of working on the lab and discussing nodal analysis. The lab involved using voltage division in order to increase the voltage at a specific amount using a thermistor that would decrease in resistance when heated. Nodal analysis is the method of determining the potential difference between nodes on a circuit. The main purpose of nodal analysis is to simplify the amount of equations needed in order to find current or voltage in a given electrical circuit that would otherwise be tedious using Kirchhoff's loop rule. 

FreeMat

3/3/2015

The day began with an experiment that involved a hot dog. We were asked what would happen if a hot dog was to be connect to a 120 volt power supply. We predicted that the hot dog would explode when connected to the 120 volt power supply, but it turned out to just cook slowly. Above is a video of the hot dog.

Prediction

We then were asked what would happen when LEDs were placed in the hot dog at different positions both parallel and perpendicular to the hot dog. It was found that the LEDs placed parallel to the hot dog only lit up. The LEDs with the leads far apart were brighter that the LED with the leads close together, 

Above is a video of what happened when the LEDs were stuck in the hot dog.

Demonstration

This lab consisted of building a "night light". Using a bipolar junction transistor (BJT) and a light detecting resistor, we were able to make the LED light when it became darker.

Circuit

Above is how we assembled the circuit for the night light.

Results

Summary:

Today we did more with Kirchhoff's Law by working on problems that involved soling for current and voltage using the loop rule. We also learned that we can cook a hot dog by running electricity through it and make a desk lamp by sticking some LEDs in the hot dog. We also learned how to make a night light by using two new electronic pieces, which was a light detecting resistor and a BJT. A light detecting resistor changes resisitivity based on the amount of light it detects. A BJT is a transistor that requires contact from two different types of conductors.