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.

4/09/2015

Today we focused on more operational amplifiers. Although this time we applied cascaded op amp circuits, which is when two or more op amp circuits are connected in a head to tail arrangement.

Circuit Diagram for Wheatstone Bridge

Above is a circuit diagram for a wheatstone bridge. The purpose of the wheatstone bridge is to detect small changes in temperature when implemented with a thermistor and a difference amplifying circuit.

Wheatstone  Bridge Circuit Built and Balanced

The first step of this experiment required us to build a wheatstone  bridge circuit and balance it.

Above is a video of balancing the wheatstone bridge by using a potentiometer. To balance the bridge VG (refer to first picture) should measure a zero potential difference.

Above is a video of our cascaded amplifier in use. As can be seen, when the thermistor is touched the voltage begins to drop, because it detects a change in temperature.

Circuit Built

Above is a picture of our temperature detection circuit. In order to detect changes in temperature we implemented a thermistor in series with the potentiometer. The thermistor is able to detect changes in temperature and as a result the voltage will drop when measuring Vout from the difference amplifier.

Results and Data

Above is the data gathered from the lab.

Summary:

Today, we learned about cascaded amplifiers. A cascade amplifier is a head-to-tail circuit of two or more op amp circuits where the output of one op amp is the input another op amp. For the temperature measurement circuit, a balanced wheatstone bridge is required in order for a fully functioning temperature system. However, a wheatstone bridge requires that the resistors in the circuit to be 100% the same. This is not possible and so this accounts for some error in this lab. We also learned about a digital to analog converter (DAC). A DAC converts digital signals into analog form. This is done by simply using a summing amplifier as discussed in the previous day.

3/31/2015

Circuit Built

The first lab required the implementation of a summing amplifier. For this type of amplifier the output voltage V(out) = - R3/R1 * (Va+Vb). So if R3 and R1 are the same value the input voltages would just add but would be the inverse of the summation of the voltages. We built this summing amplifier by using an operational amplifier. 

Results

 Above is a result of supplying different voltages into the circuit. R3 and R1 are the same values so V(out) should be the inverse of the summation of Va and Vb. For the most part the summing amplifier worked until it reached 3V+ where it began to saturate. 

Graph of Results

Above is the graph of the input voltage vs the output voltage. As can be seen, at 3V+ it begins to saturate which would not be ideal in this case.

Circuit built

 The next circuit built was a difference amplifier. Using an operational amplifier once again, and four identical resistors (10K Ω) allowed us to theoretically state that Vout = -(Va - Vb).

Results

Because we used identical resistors that voltages going in to the op amp would come out to be the difference. In this scenario we used 1V for Vb and when different voltages was supplied for Va the voltage out of the amp would just be -(Va-1). The voltage out would also be the inverse of the difference because we are used an inverting op amp.

Graph of results

As can be seen by the graph, Vout saturates at 4.23V and -3.49V.

Conclusion:

Today, we learned about some new operational amplifier circuits. Theses circuits include an inverting amplifier, summing amplifier, non-inverting amplifier, and a difference amplifier.

Inverting Amplifier:

An inverting amplifier reverses the polarity of the input signal while amplifying it. 

Vout = -(Rf/R1)*Vi

Summing Amplifier:

A summing amplifier simply adds the voltages going into the op-amp but also reverses the polarity.

Vout = -((Rf/R1) *V1 + (Rf/R2) *V2 + (Rf/R3) *V3)

Non-inverting Amplifier:

A non-inverting amplifier provides a positive voltage gain.

Vout =  (1+Rf/R1) * V1

Difference Amplifier:

A difference amplifier amplifies the difference between two inputs but rejects any signals common to the two inputs.

Vout = R2/R1 * (V2-V1) if R1/R2 = R3/R4.