5/28/2015

Circuit Built

The lab for today consisted of applying different signals with multiple frequency components. This circuit consisted of a resistor (1kΩ) in series with a capacitor (100nF) and resistor (1kΩ) in parallel.

Theoretical Results

Before beginning the lab we were asked to determine the magnitude response of the circuit. We then created different wave functions to supply to the circuit. We created a custom waveform, 20(sin(1000πt)+sin(2000πt)+sin(20,000πt)) and sinusoidal sweep function. Using the Analog Discovery we were also able to measure Vin and Vout from the circuit.

20(sin(1000πt)+sin(2000πt)+sin(20,000πt))

Looking at the graph, the high frequency part is more suppressed than the low frequency part. 

Sinusoidal Sweep

As can be seen by the graph, the frequency is being suppressed as time passes and jumps back up again while the process is repeated.

Summary:

Today, we learned about frequency response. The frequency response of a circuit is determined by the variation in its behavior with change in signal frequency. We can use the transfer function H(w) to find the frequency response of a circuit.The transfer function of a circuit is the frequency dependent ratio of a phasor output Y(ω) (voltage or current) to a phasor input X(ω) (source voltage or current). We can use these equations to analyze the transfer function.

5/26/2015

Circuit built

For our lab today we supplied an AC supply to a resistor in series with a load that consisted of an inductor and a resistor. This lab was done to show the use of apparent power and power factor to quantify the AC power delivered to the load.

Results

Above are results and calculations. The resistance is series with the load was changed each time. we measured the voltage coming out of the load as well as the voltage across the resistor in series with the load.

With 10 Ω

With 47Ω

With 100 Ω

Modified Circuit

The next part of the lab required us to include a capacitor in parallel with the load. The main reason for this is to get the voltages being measured to be more in phase.

10Ω

47Ω

100Ω

Summary:

Today we learned about apparent power and power factor. We found that the apparent power is the product of the rms values of voltage and current and is in units of voltage amperes. We also found that the power factor is the cosine of the phase difference between voltage and current. It may also be found by the cosine of the angle of the load impedance. The purpose of this lab was to be able to calculate the AC power delivered to a load and the power dissipated from transmitting this power. Our initial circuit only contains an inductor but a capacitor is then implemented later on. By adding a capacitor, it increases the power factor of the load which will lead to a more efficient power delivery to the load. It is shown in the graphs that the phase difference becomes less apparent when a capacitor is added.

5/14/2015

Results

The first lab of the lab required us to build an inverting voltage amplifier using an op-amp. However, this time we are supplying an AC source through the circuit. We were first asked to calculate the theoretical voltage gain and the phase shift.

Circuit Built

Using the Analog Discovery, we were able to supply different frequencies of sinusoidal AC through the circuit. We also used the on board oscilloscope to measure the voltage going in and coming out from the amplifier. We calculated the experimental voltage gain by using Vin/Vout. We calculated the phase shift using deltaT/T *360.

100 Hz

We calculated the voltage gain to be 0.87 and the phase shift to be 21.8°.

1 KHz

We calculated the voltage gain to be 0.189 and the phase shift to be 86.4°.

5 KHz

We calculated the voltage gain to be 0.043 and the phase shift to be 83.02°.

Op-Amp Relaxation Oscillator

Our next lab required us to build an op-amp relaxation oscillator and manipulate the resistance to obtain a frequency of 475 Hz. (The last 3 digits of one of our members SSN).

Measured Vout

Above is a graph of Vout from the op-amp relaxation oscillator. The graph was supposed to look a little more square than the above image. This may be caused by some interference in the circuit.

Summary:

Today we implemented AC into op-amp circuits and analyzed them in a similar fashion as if it were to be a DC circuit. We built an inverting op-amp circuit as well as a op-amp relaxation oscillator. Our op-amp relaxation oscillator did not produce the results that were expected but this may be due to some interference in the circuit.

5/12/2015

Circuit Built

The circuit built for this lab included a 1Ω resistor and a 1uH inductor.

Results

For our pre-lab we calculated the phase shift and the amplitude gain of Vout and Vin. Vin is the voltage that was supplied to the circuit (1.5V) and Vout was the voltage from the inductor.

Oscilloscope

We measured Vin and Vout using the oscilloscope from the Analog Discovery and used the math channel to plot Iin(t) ((Vin-Vout)/R). It is shown that Vin and Vout have different amplitudes and are out of phase.

Summary:

The purpose for the lab today was to analyze the steady-state response of electrical circuits from sinusoidal inputs. We were able to find the amplitude gain by comparing the phasors representing Vin and Vout. We also learned how to analyze AC circuits using different methods of analysis. These methods include, nodal analysis, mesh analysis, superposition, thevenin and norton analysis. We can use theses methods the same way we would for a DC circuit except this time we will be using jimaginary numbers.

5/07/2015

Circuit With Resistors, Circuit With Resistor & Inductor, and Circuit With Resistor and Capacitor

Today we did a lab that involved analyzing different circuit elements when AC is supplied. These circuits include a circuit with resistors, circuit with resistor & inductor, and a circuit with resistor and capacitor.

Results 

Above are our results and calculations. We used a 47 Ω (R1) in each circuit. For the resistor circuit we used a 100 Ω resistor in series with the R1. For the inductor circuit we used a 1uH inductor in series with R1. Lastly, we used a 0.1uF capacitor in series with R1. In the resistor circuit we showed that both the current and voltage are in phase when an AC is supplied. In the inductor circuit the voltage leads the current by 90°. In the capacitor circuit the current leads voltage by 90°. each circuit was supplied an AC of 2V with different frequencies of 1kHz, 5kHz, and 10 kHz frequencies.

Resistor Circuit at 1kHz Freqeuncy 

Resistor Circuit at 5kHz Freqeuncy

Resistor Circuit at 10kHz Freqeuncy 

Summary;

Today, we analyzed circuits supplied with AC. We found that a resistor circuit supplied with AC has no phase change between the voltage and current. The voltage leads the current by 90° in a circuit with an inductor and the current leads the voltage by 90° in a circuit with a capacitor. We also learned that circuit elements also produce impedance. To calculate the impedance for a resistor, inductor or a capacitor, we use the formulas below. We can find the total impedance of a circuit by first calculating the impedance of each circuit element and treating them as resistors, where the add inversely in parallel and add directly in series.

5/05/2015

Oscilloscope

Today, we looked at how an oscilloscope works. An oscilloscope can essentially measure anything such as brain waves or a simple sound by the use of a transducer.

Inside an Oscilloscope

Inside the analog oscilloscope, there is something like this. The oscilloscope produces a graph on the screen by shooting electrons on the screen after passing it through different plates positioned vertically and horizontally. The graphs the electrons produce depend on what is the oscilloscope is measuring. In the case above, the oscilloscope is measuring sinusoidal alternating current. The amplitude of the graph depends on the max voltage of the AC.

Summary

Today we focused mainly on AC circuit analysis. AC circuit analysis is different from the circuits we have been analyzing before, because they contain time varying voltages. We learned how to convert Cartesian coordinates to Polar coordinates and back again in order to make our calculations simpler. This must be done because we are dealing with alternating current. We also learned about how oscilloscopes work.

4/30/2015

The lab for today required the use of an RLC circuit.

RLC Circuit Built

We built the circuit using a 1.1Ω resistor(R1), a 47 Ω resistor (R2), a 10uF capacitor and a 1uH inductor.  This circuit was built so that R2 and the inductor were in series while together being in parallel with the other components in the circuit.

Graph of Step Function Through RLC Circuit

After building the circuit we then sent a step function voltage through the RLC circuit using an Analog Discovery and measured it with the on board oscilloscope.

Pre-Lab & Results

Above is our results and calculations.

Summary:

Today we learned how to analyze circuits containing a resistor, capacitor and an inductor in parallel. There are three possible cases that may occur in a RLC circuit which may result in the circuit being over damped, under damped, or  critically damped. The over damped case occurs when (α > ω_o ), critically damped case (α = ω_o ) and under damped case (α < ω_o ). Using these three cases we are able to determine an equation for the voltage or current as a function of time.

4/28/2015

RLC Circuit in Series

For this lab we built a RLC circuit in series. Using the Analaog discovery we supplied a step function into the RLC circuit. This is a second-order circuit and after a few calculations we found the circuit to be under damped due to  α < ω 0 .

Results

Above are our calculations. Although not shown on the board, for under damped i(t) = e^(-at)(B1coswt+B2sinwt) 

Graph of Response

The circuit was supplied a 2V step function at a frequency of 100Hz.

Summary:

Today we analyzed second order circuits. Second order circuits contain two circuit elements which in this case are capacitors and inductors. They are know as second order circuits because their response is described by differential equations involving second derivatives. The response of a second order circuit also includes a dampening where; if α > ω 0 the circuit is over damped, if α = ω 0  the circuit is critically damped, and if α < ω 0 the circuit is under damped. Each case has a unique equation that can be used to describe i(t). Our lab emphasized the testing of an RLC circuit where the measured and expected results are compared. For our circuit, we predicted that it would be under damped and our graph of the results supported our expectation, which was the gradual loss of the initial stored energy. α determines the rate at which the response is damped.

4/21/2015

Differentiating Op-Amp Circuit

Today the lab required us to build a differentiating op-amp circuit. We built this circuit using a 470 nF capacitor and a 470 Ω resistor.

Results

The pre-lab required us to calculate the theoretical Vout from the op-amp when it is supplied a sinusoidal function of different frequency. The sinusoidal function supplied from the analog discovery had an amplitude of 1V offset of 0 and varying frequencies of 1kHz, 2kHz, and 500 Hz. Using the analog discovery we also used the oscilloscope to measure the voltage coming out of the op-amp. The output voltages are shown above

1kHz Sinusoidal Function

Using the oscilloscope we found the output voltage to be 1.22 V

2kHz Sinusoidal Function

Using the oscilloscope we found the output voltage to be 2.48 V

500 Hz Sinusoidal Function

Using the oscilloscope we found the output voltage to be 0.646 V

Summary:

Today we learned more about 1st order linear circuits. We also learned about new op-amp circuits. The op-amp circuits we learned about are integrating and differentiating op-amp circuits.  The lab we did required us to build a differentiating op-amp circuit. We found that for the 1st trial the voltage output had a percent error of 13.7%, the 2nd trial had a percent error of 11.9% and the last trial had an error of 7.4%. I believe the error is due to the capacitance of the capacitor not being 470nF and calculating the output voltage with that value. It may also be due to the instruments being used not being perfect.

4/16/2015

Circuit Schematic

For this lab we  examined the response of a RC circuit. We measured the difference in circuit response in a switching on and off of a DC input. For this circuit we used a 22 uF capacitor, a 1KΩ resistor (R1) and a 2.2KΩ resistor (R2).

Graph of Results

Above is a graph of the response from the circuit. A trigger is needed in order to grab the results after removing the power source.

Summary:

Today, we analyzed first order circuits which are circuits that involve a circuit element such as an inductor (RL) or capacitor (RC). These circuits are characterized by a differential equation. For the experiment it was found that the way in which we reduce the applied voltage effects the circuit's natural response. By turning off the power supply, it does not disconnect the power supply from the circuit but simply acts as a short which as a result left R1 to be included in the circuit and reduced the amount the time needed for the capacitor to discharge.

4/14/2015

Circuit Built

The day began by learning about capacitors. Our lab consisted of measuring the voltage across a resistor (100 Ω) and 1 µfarad capacitor in a circuit. The resistor is in series with the capacitor.

Pre-Lab & Measured Instruments

We sent three different time varying signals across the circuit using an Analog Discovery device. Before we actually did the lab we were asked to predict what would happen to the current when a capacitor is used.

Oscilloscope Screenshot

The first time varying signal sent into the circuit was a sine function with an amplitude of 2V and a frequency of 1kHz.

Oscilloscope Screenshot

The second time varying signal sent into the circuit was another since function but the time with a frequency of 2kHz.

Oscilloscope Screenshot

The last time varying signal sent into the circuit was a triangular function with an amplitude of 4V and frequency of 500Hz.

Summary:

Today we learned about capacitors and inductors. Capacitor's capacitance that are in series in a circuit are added inversely while capacitors in parallel are added directly. Capacitors are not ideal and so the capacitor symbols are usually accompanied by a resistor in parallel. Inductors are essentially just coils of wire. Like capacitors, inductors are not ideal and are usually accompanied by a resistor in series. Inductors can also act like capacitors at high frequencies. Capacitors and inductors are not commonly used with direct current.