Experiment 12: Frequency Response and Filters

Introduction:

     In electrical engineering, signal modification is a crucial component to many solutions to real world problems. In this experiment, we will be working with high pass and pow pass analog filters to form a deeper understanding on how frequencies are amplified or reduced. There will also be data and error analysis.

List of Materials

Capacitor box set to 0.1 micro Farad, 1000 Ω resistor, Frequency generator, DMM, leads.

First, we calculated the theoretical gain of the low pass filter frequency response for variable values of frequency. We then set up the circuit accordingly to this diagram.

Low Pass Filter Frequency Response Set up

Finally the circuit.

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Here's our result

We move onto the next step in the experiment: High pass filter frequency response: simply measure across the resistor instead.

Actual results of the high pass frequency filter circuit

Finally, we use excel to graph our function., the input RMS voltage from the function generator was 5V. In order to calculate gain, we took the voltage obtained through the measurements and divided by 5V rms. The Y axis is the experiment's gain and the X axis is the frequency.

As we can see, the high pass frequency filter tops off at around 2000-3000 Hz, which is probably the natural frequency of the circuit.








For the low pass frequency filter, it is obviously shown in this graph that low frequencies around 10-100 hz aren't affected while the higher frequencies drop off.

NOTE: one observation we noted during the lab is that as the frequency increased, the Vin had to be slightly increased in order to maintain a steady Vrms. 

Conclusion

This lab demonstrated how certain frequencies with certain circuit elements can allow voltage through specific frequencies, and block all others. This is particularly useful if you are trying to broadcast/receive a signal at a specific frequency. Our largest margin of error was around 2.5%, which is indeed supah hawt and secksy.

Experiment 11: AC Circuit Capacitor

Introduction: For this lab, Professor Mason hooked up a circuit into a digital oscilloscope to give a visualization of how AC voltage behaves within a capacitor.

The sinusoidal wave heading into the capacitor

It is observed that the sine wave changes when the frequency changes.

For this section, a AC voltage supply was hooked onto a capacitor. The capacitor was found to be 3.3 microfarads. It is still unknown how we obtained that value.

Freemat Assignement: Complex Numbers

Introduction:
 This assignment on the computer got us familiar with complex number operations in Freemat.

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Tutorial on Second Order Systems

Intro/Conclusion

In this lab we became familiar with second order systems using this tutorial. Below are questions and answers,

Experiment 10: Capacitor Charging/Discharging

Introduction: Capacitors are electrical components that store energy in the form of an electric field. This lab demonstrates the charging and discharging pattern of a capacitor.

- Calculate necessary circuit component values that will satisfy the objectives of the lab circuit.
- Create the circuit and run tests.
- Conclusion

Procedure:

First, we calculated expressions for a non-ideal charging/discharging capacitor circuit.

We then calculated for the component values of an ideal capacitor circuit such that the lab's parameters were met.

2.5 mJ of  Energy into the capacitor.

The variable resistance box has a max power output of 1W, which is more than enough for how we are using it.

Because the oscilloscope was set on continuous recording, we couldn't acquire the charging graph, so instead we used a stopwatch and a voltmeter to measure the voltage of the charging capacitor within 20 seconds.

Materials 1 Voltmeter and 1 stopwatch (optional), 1 oscilloscope, 2 variable resistors, 1 33 microfarad capacitor, cables.

The circuit setup, we found that the voltage of the charging time at around 20 seconds to be 11 volts.
The time taken for the capacitor to discharge took about two seconds which was expected.



Leakage Resistance:

Error calculation:

The charging and discharging graphs, how it should appear if the oscilloscope read once and not continuous.

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Conclusion: The experiment sucessfully proved the validity of the equations used for the charging and discharging of a capacitor. The leakage resistance was found to be roughly 10 times greater than the charging resistor, which is expected due to the leakage resistor being parallel to the capacitor.

Experiment 9 Integrating and Differentiating OP Amps

Introduction: We processed signals through a series of circuits with capacitors, resistors, and OP amps.

 

Integrating OP amp, Yellow = output Red = input voltage. Note the decrease in amplitude and similar frequencies.  

Saturation. The voltage applied to the OP amp wasn't enough to apply the necessary change, so the output became a square wave with a capacitor-like exponential decay.

Differentiating OP amp, not the increase in amplitude and similar frequency. The phase is noticeably shifted.

Experiment 8: Practical Signal Conditioning

Introduction:
     This experiment requires us to perform level-shifting and scaling processes of an operational amplifier to convert the temperature-proportional voltage in centigrade exiting out of the LM35 into voltage that is proportional to fahrenheit.

Procedure:
   We first start by testing the LM35, applying 9 volts into it relative to ground and seeing what voltage we get as output. Sure enough, we obtained 220 mA, or room temperature.

Now that the LM35 was shown to work, we solved for the output voltage of the op amp circuit according to this diagram.:

We also knew the formula for temperature conversion from celcius to fahrenheit, and we solved for the equation to be in terms of voltage.

Calculation:
Solving for the circuit diagram, we figured the output voltage to be related to the input voltage and the reference voltage by this relation below. Then we solved to find the reference voltage. We also took out resisters from the box that had the correct proportions to our calculated value.

Add caption

Pictures of the experiment:
Materials: 3 variable power supplies (9V, 9V, .4V) , lots of wires, breadboard, LM35 temperature sensor, OP amp, potentiometers...

The complete circuit.

power supplies

Output Voltage:

Error calculation. the .716 mA came from calculation from the value obtained through converting the output of the LM35 voltage into fahrenheit voltage using the celcius-temperature equation.

Conclusion

     The experiment successfully demonstrated the practical uses of an operational amplifier's ability to multiply and add. The conversion had an error of 9.2, which was probably due to the disproportion of the resistors to the actual ratio (18/22 isn't exactly .8) and the uncertainty of the resistors.