Lab: Inverting Differentiator(april 25, 2017)

Date: April 25, 2017

Singularity Functions; Inverting Differentiator;

Activity 1: Singularity Functions

In this activity we were tasked with finding the derivative of sinusoidal graph, square graph, and triangular graph.

The above picture shows our attempt to get the derivatives of each. The triangular wave graph is the only one that is not correct.

Lab 1: Inverting Differentiator

Pre-lab:

In the above picture we determined the Vo as a function of Vin and we graphed what they would look like on the same tie variable.

Next, We were given our R to be 680ohms and C to be 1 micro F. Using these numbers, we determined that the optimal frequency to run this circuit would be at 234Hz.

This is a picture of our circuit.

This is the Vo and Vin if we run our circuit at the optimal frequency of 234Hz.

The table above shows the results of each frequency and gives the theoretical values and the measured values along with the percent error between the two. Any differences between the experimental and theoretical is due to the capacitor values and resistor values used. Theoretically we use whole numbers; the experimental values are not ideal therefore do not give the precision required to achieve theoretical values.

In conclusion:

We were able to see how the voltage in graph is related to the voltage out graph. We noticed that the Vo was the derivative of the Vin; this is further proven by the results of the inverting differentiator lab.

Lab: Source-free RC and RL Circuit( April 18, 2017)

Date: April 18, 2017

The Source-free RC Circuit; Passive RC Circuit Natural Response; Passive RL Circuit Natural Response

Activity 1:

For activity one we determined what time would be if there was one percent discharge voltage left.

In the above picture, first we determine the voltage equation for a source free RC circuit. Then we say that the voltage is at 1 percent and solve for time.

Lab 1: Passive RC Circuit Natural Response

Pre-lab:

In the above picture we estimated the time and voltage across the capacitor. There is also the schematic for our circuit with the resistances being R1=.982k-ohm and R2=2.16k-ohms and the capacitor being 22 microF.

This is a picture of our circuit.

This is the picture of the capacitor voltage response.

This is the calculation for the time constant when being discharged.

This is the capacitor voltage response for the circuit in figure b

Lab 2: Passive RL Circuit Natural Response

First we measured the response for the inductor.

Then we used that time to calculate what the inductors value is.

In conclusion:

In today’s labs, we were able to see the response that the RC Circuit had when being discharged. Also, we were able to see the same thing for the inductor being discharged. With that information we were able to determine that the value of the inductor was about 5.28mH.

Lab:Capacitor/Inductor Voltage-current Relations(April 13, 2017)

Date: April 13, 2017

Capacitor; Capacitor Voltage-current Relations; Inductors; Inductor Voltage-current Relations

Activity 1: Capacitors in a Circuit

            In this activity, we use our understanding of how capacitors work in a DC-circuit to obtain the amount of energy at each capacitor.

            In the picture above, the circuit is in DC-circuit; therefore, we replace all the capacitors with open circuits. Because of this, we can now find the current, I, because the resistors are all in series. Then, we find the voltages parallel to the capacitor because they will be the same. Now that we have the voltage at each capacitor, we use the energy equation for capacitors to solve for W1 and W2.

Lab 1: Capacitor Voltage-current Relations

Pre-lab:

In the above picture, we did the pre-lab where we sketched out the capacitor voltage-current relation. The top graph was for a sinusoidal wave and the bottom graph was for a triangular wave.

We were given that the resistor was 100ohms and the capacitor was 1microF. We also put down the voltage we were applying and the frequency.

For the picture above, the frequency was 1k-Hz and was a sinusoidal wave input.

The picture above was for 2k-Hz and was a sinusoidal wave input.

This picture was for 100Hz and was for a triangular wave input.

When we compare these to the pre-lab sketches we did, we confirm that our prediction was correct.

Activity 2: Capacitor Equivalence

This activity serves to remind us that the equivalent capacitor can be determined just like the equivalent resistor.

The above picture shows step by step how each equivalent capacitor is calculated. In series, they add together; in parallel, they follow Req=(R1+R2)/(R1*R2).

Activity 3: Inductors

This activity serves as practice for using the inductors to find current.

This is the picture of the question.

This is the step by step of solving for the current when an inductor is in the circuit. First, we note that the voltage across an inductor is a time dependent event. Then we write down the relationship between voltage, inductors, and current. We solve for di then integrate to get current. We plug in all the values to get the current at the specific time, i(t). Then we realized that they gave us the initial current; therefore, we add them together to get the final current.

Lab 2: Inductor Voltage-current Relation

In this lab, our aim was to analyze the relation between the voltage difference across an inductor and the current passing through it.

In the picture above, we applied a sinusoidal input voltage at 1k-Hz, amplitude of 2V, and was offset to 0V.

In the picture above, we applied a sinusoidal input voltage at 2k-Hz, amplitude 0f 2V, and was offset to 0V.

In Conclusion:

            Today, we learned about capacitor, inductors, and their relation of the voltage and current running through them. In the first lab, we see that regardless of the type of voltage wave we insert to the capacitor, the current wave will be the derivative of that voltage wave. The second lab showed us that changing the frequency results in a change in amplitude for the current.

Lab: Measurement System Design(April 11,2017): Activities: Cascading op amp: wheatstone Bridge

Date: April 11, 2017

Cascading op Amp Circuit; Wheatstone Bridge Circuit; Temperature Measurement System Design

Activity 1: Cascading op Amp

             In the first activity, we looked at a cascading op amp that essentially is two non-inverting op amps together.

The picture above shows the circuit that we had to analyze.

The picture above shows how we can solve each non-inverting op amp individually and uses the results at Va as the input voltage for the following non-inverting op amp. We still follow ideal op amp rules which mean that since the voltage Va and Vb both connect via the terminal they are equal to each other. Furthermore, in order to find the current we simply use current analysis and since the current moves from high voltage to low voltage the Vo is subtracted by the Vb and as we stated before Vb is equal to Va which we already calculated.

Lab 1: Temperature Measurement system Design

Pre-lab: the pre-lab asks us to understand the wheatstone bridge circuit so that we can implement it into our temperature measurement system.

In the above picture, we work out the relationship between Vab and all the resistors implemented in the design. Note: the R+deltaR will be a nob that will help us change the resistance value of the wheatstone bridge. Initially we want to balance the bridge with the nominal resistance as the source of balance because we want all the resistors to be identical but realistically they are not, we want all our R values to be 10k-ohms. The nominal resistor takes care of this issue. Furthermore, one of the resistors will be a thermistor, which will change depending on its heat. We determined that the thermistor range will be from 10k-ohm at room temperature and 7k-ohm at hot temperature.

In the above picture, we start backwards with the design. Since we want a specific output voltage we work around that idea. The left side of the board shows the difference amplifier. In order to simplify the work of determining the voltages we use the relationship learned for difference op amps, Vo=R2/R1(deltaV). We know Vo and deltaV therefore we can pick R1 to be any resistor from the box and solve for R2; doing this gives us R1=1k-ohmand R2= 5.33k-ohm. Both of these resistors exist in our box, so we use them. Since we already analyzed the wheatstone bridge we know the relationship between Va and Vs, Vb and Vs; therefore, we can determine that Vs should be 5V to get an output, Vo, of 2V.

The picture above shows our entire temperature measurement system design.

The video showing the results of our circuit. We did not get the proper Vo; however, we did make the Vo raise when we added heat to the thermistor.

In Conclusion:

            We were able to make the systems output voltage increase as the temperature increases. Furthermore, we also did not get the proper output voltage. We wanted to get Vo=2V; instead, we got a value of 0.2V. When heat was applied to the thermistor, Vo reached a max of about 0.275V.  We learned how a cascading op amplifier works. We learned that in designing a cascading op amp one of the major advantages is that even thought they result into one circuit, each part can be calculated separately, then the information of one part can help solve for information of the next part.