Lab Report Day Ten - Operational Amplifier, Inverting Voltage Amplifier

1. In the beginning of class, we write down five circuit elements we covered so far. We write down resistor, voltage supply, current supply, diode, transistor.

 

2. Today, we talk about the new element: operational amplifier (op amp)

 

We do a pre-lab to see that the relationship between V in and V out. We find that theoretically the relationship would be Vout= -2 Vin (in this problem). 

 

In order to do this experiment, we build a circuit like the graph in the pre-lab.

We use a 1.8k ohm and 3.6k ohm resistor.

We measure their real values to be 1.76k Ohm and 3.6K Ohm.

 

In order to find the saturation region of the op-amp, we supply voltage from -3V to 4V.

 

From the graph, we can see that the saturation region are from -2 V to 2 V. 

 

Discussion:

We find that that the output voltage start to not changing (saturation area) when the input voltage is higher than 2V or lower than-2V. Ideally the output voltage of the op-amp should be 5V (or -5V); since the op amp is cheap, and the internal of op amp is very complex, there are some voltage loss. There could be some ways to improve this op amp, but it will just cost lots of money and becomes way more expansive.

 

Summary:

Today, we talk about operational amplifiers, and explain the internal of it. Most time, we can treat op amp as ideal op amps and let their open-loop gain and input resistance go to infinity and their output resistance go to zero. Once we treat it as ideal op amp, we have an important property that both input currents become zero and thus the input two voltage would be the same.

 

 

 

 

 

 

 

 

 

 

 

 

 

Lab Report Day Nine - Non-Ideal Power Sources, Maximum Power Transfer

1. Non-Ideal Power Sources

At first, we do a pre-lab finding the power of a source when it is ideal and not ideal.

We find that when we assume it is ideal, there is no internal resistance. We find that the current across it is 0.0455 A. And the voltage across it is being set to be 1 V. Thus, the power is just P=VI= 0.0455 W. 

Then, we consider there is an internal resistance. We calculate the current to be 1/(22+Rs). We calculate the output Voltage is 22/(22+Rs). So the Power of it is 22/(22+Rs)^2 W. 

 

 

We measure the 22 ohm resistor to have a real value of 22.4 ohm.

Since this is not an ideal power source, when we want it to have 1 V, it only gives 0.994 V. 

We adjust it to be exactly 1.0 V.

In the circuit, the output voltage we have is 0.980 V. 

This is a very easy set-up.

 Then, we use a 39 ohm resistor, and measure it true value to be 38.8 ohm. 

The output voltage for the 38.8 ohm resistor is 0.993 V. 

 

Summary of Our Results

 

When we measure the 22.4 ohm resistor values, we get a output voltage of 0.980 V. Based on our calculation, we find the internal resistance to be 0.457 ohm.

When we measure the 38.8 ohm resistor values, we get a output voltage of 0.993 V. Based on our calculation, we find the internal resistance to be 0.273 ohm.

It makes sense because the bigger value the resistor has, the smaller influence the internal resistor would act on it. When the resistance is way bigger than the internal resistance, we can just ignore the internal resistor. 

 

 2. Maximum Power Transfer

We first do a pre-lab on Maximum Power Transfer. We use two identical resistors in the circuit with theoretical values of 2.2K ohm. We calculate the theoretical power of it to be 2.84*10^-3 W. 

We take 5 resistors with theoretical values of 2.2K, and take 2 of them that has same true value of 2.16 K ohm.

This is the set up of this experiment. This is also a simple setup. We measure the voltage across it to be 2.48 V. And we calculate the experimental value to be 2.847*10^-3 W. It has a -0.246 % difference. It is very close to our theoretical value.

 

Summary:

Today, we learn Norton's theorem and maximum power transform. Norton’s theorem is just like Thevenin’s Theorem, except that it replace the circuit with a current source in parallel with a resistor. It is important to transfer maximum power to the load. In order to do that, the load resistance should equal the Thevenin resistance. We also learn that power sources contain an internal resistance and how to calculate the resistance.

Lab Report Day Eight - Thevenin's Theorem

At first, we start a lab stimulation with EveryCircuit.

We then do a pre-lab, using EveryCircuit to see if we get the right answer.

The Thevenin resistance is 7.349 k ohm, and the open-circuit voltage is 0.456 V. 

 

This is a sketch our replaced Thevenin’s Theorem.

 

This is the circuit we stimulate form EveryCircuit.

 The purpose of this lab is to use experiment to see how Thevenin’s Circuit works, and compare to the complex circuit. 

At first, we measure the true value of our resistor that we are going to use in the circuit. 

 

 

 This is the set up of this experiment when it is in complex form.

 We measure the voltage across the 4.7 K resistor to be 0.179 V. Our theoretical value is 0.175 V. The precent difference is -2.29%. 

 

 We measure the voltage across the 1 K resistor to be 0.055 V. Our theoretical value is 0.055 V. The precent difference is 0%. 

 This is the circuit replaced by Thevenin’s Theorem. It is much simpler. We use three resistors in series to replace the 7.35 k ohm resistor.

 We measure the voltage across the 4.7 K (actual value 4.57 k) resistor to be  0.175 V. Our theoretical value is 0.175 V. The precent difference is 0%. We can see that when we use less elements with Thevenin’s Theorem, we can get a more accurate value.

The summary of our data table. 

Then, we use a potentiometer to replace the load resistor. It can provide various resistance . We measured the resistance of the potentiometer, and record the voltage across it. 

This is the set up of the circuit.

 

 Here is a summary table of our results. 

 We put the data in EXCEL. We get our maximum power to be 7.1225*10^-6 W, when the load resistance is 6490 ohm. 

Here is a graph of the Power vs. Resistance graph. We can see it is approximately a straight line. So we can say that the power of the load resistor can be considered constant. And we calculate the average value of the power, which is about 6.8442*10^-6 W. 

 

Summary:

In today’s lab, we practice more on Thevenin’s Theorem, have better understanding of Thevenin’s Theorem, and build circuits using Thevenin’s Theorem. We can see that since the Thevenin’s Circuit is much simpler. Thus, it will be more accurate on the results. Also, based on our experiment, we can see that the power of a load resistance is about constant. It will only change a little bit when the resistance changes. 

Lab Report Day Seven - Time-varying Signals, A BJT Curve Tracer

 

1. Time-varying Signals

In this lab, we first make some predictions about the output wave for the circuit below if R1 and R2 are identical. 

We guess that they would have the same shape, with different amplitude. The top three are the input wave, and the bottom three are the output waves. The amplitude of the output would be half of the input. 

 

First, we are going to measure the resistance of two resistors with same value. We get both of them have the same theoretical value, 1K ohm, and same true value, 978 ohm.

 

 

This is the set up of the experiment. 

 

This is the graph for the sine wave.  The frequency and period are its original value. The amplitude becomes half. 

 

 

This is the graph for the triangular wave. The frequency and period are its original value. The amplitude becomes half. 

 

This is the graph for the square wave.  The frequency and period are its original value. The amplitude becomes half. 

 

 

2. A BJT Curve Tracer

 

In this lab, we are going to investigate the collector current, IC vs. collector voltage, VCE characteristics of the BJT. We are going to use a breadboard, a 100K Ω Resistors, a 100 Ω Resistor, and a small signal NPN transistor.

 

The true value of the 100 ohm resistor is 99.5 ohm. % difference is (100-99.5)/100*100% = 0.5%

 

The true value of the 100K ohm resistor is 99.4 K ohm. % difference is (100K-99.4K)/100K*100% = 0.6%

 Here is the set up of our circuit.

 

Here are our first input wave (Channel 1) and second input wave (Channel 2).

  

Here is the oscilloscope of the wave it detected.

We can see that Ic vs Vce have 5 curves.

 Summary:

Today we learn some new methods of circuit analysis. We talk about linear circuit. Source transformation is a useful procedure replacing voltage source or current source. We do a Time-Varying signal lab to see how a voltage divider actually works, and we introduce BJT, and figure out how BJT works.

 

Lab Report Day Six - Mesh Analysis III

The purpose of this lab is to use our knowledge of mesh analysis to calculate the theoretical value of the voltage across the 22k ohm resistor and the current i1 (See the following graph)

 

Here is the pre-lab of this experiment. 

 

 

We first measure the real resistance of the resistors, since they have uncertainties.

The 22k ohm resistor has a real resistance of 22k ohm, which has 0% difference. (This must be a very good resistor, the first time seeing a resistor with 0% difference)

The 1.8k ohm resistor has a real resistance of 1.7k ohm, which has 5.88% difference.

 

The 4.7k ohm resistor has a real resistance of 4.6k ohm, which has 2.13% difference.

 

The 6.8k ohm resistor has a real resistance of 6.8k ohm, which has 0% difference. (Another good resistor)

 

The summary table of the real value of the resistors.

 

Here is the set up of our breadboard.

 

This is the value we get for V1. V1=2.44V (Theoretical value: 2.464 V)

 

This is the value we get for i1. i1=-0.24 mA (Theoretical value: -0.26 mA)

 

 

 

The summary table of the real value of the resistors and the theoretical value and the experimental value of the voltage and current. We get 7.69 % difference in our i1 value, and 0.97% difference on our V1 value. 

 

Discussion: 

 

Our measured voltage is very close to our theoretical value (0.97% difference), and we have smaller but still close value for our measured current (7.69% difference.) This uncertainty could be caused by the resistor (since they do not have exact the theoretical value, as shown above). Also, the resistance of the wire could also be a cause, but in this case, even if it has resistance, it would be small compared to the resistors. Overall, we do fine on this lab. 

 

 

Summary:

In the beginning of today's class, we take a group quiz, and later on, we finish a mesh analysis lab. We successfully prove that we do fine on our prediction and calculation. We also talked about the Transistors (NPN and PNP), which we have learned some properties of in Physics 4B. Now, we can use a lot of ways to solving circuit problems.