Ac Measurements using oscilloscope

Atreides

I've writen up this little report on what I did in an electronics pratical, just would like some opinions on it or if I've got something factual completely wrong, any tips would be welcome.


Introduction
One of the most important tools that electrical engineers use is the oscilloscope. An oscilloscope is a laboratory instrument commonly used to display and analyzes the waveform of electronic signals; AC current is measured by utilizing an oscilloscope. Basically, the oscilloscope draws a graph of the signal voltage as a function of time. The waveform is generated using a functional generator. This generates waveforms such as sinusoidal, rectangular and triangular waves so that an oscilloscope can be used in analyzing their characteristics.

Objectives:
1. To display waveforms of electronic signals on an oscilloscope.
2. To understand the concepts of frequency, period and how they relate to each other in a practical setting, by means of the oscilloscope.
3. To identify the characteristics of an AC signal and to learn the methods of calculating them.
4. To observe lissajous wave patterns
5. To measure the phase difference between to waves at different intervals of frequency, using the oscilloscope

Theory
Oscilloscope is defined as an electronic device used to produce visual displays corresponding to electrical signals. The x axis represents time while the y axis represents the voltage level of the electrical input signal. The oscilloscope screen is divided into square boxes each one cm in width and length. The period (the amount of time taken to complete a cycle) Is calculated by counting the number of boxes from any two consecutive points on the wave form that are in phase multiplied by the position of the time base selector, it is measured in seconds. Frequency (the number of cycles per second; measured in Hertz.); is the reciprocal of the period.
The Amplitude of an AC signal is measured in three ways “peak-to-peak” (p-p) “peak” (p) and “root-mean-square” (rms).

1. (p-p): This is the distance from the positive peaks to the negative peak of the wave, measured on the y axis.

2. (p): This is the distance from the maximum displacement of the wave (its peak) to its mean position. It is equal to half the peak-to-peak value.

3. (RMS): For a sine wave, the rms value is 0.707 times the peak voltage value.

Lissajous Patterns: A Lissajous pattern is a graph of one frequency plotted on the y axis combined with a second frequency plotted on the x axis. Y and X are both periodic wave functions. From the shape of the Lissajous pattern, we were able to tell the phase difference between the two signals, as well as their frequency ratio. The frequency ratio is equal to the ratio of the number of points in contact with the vertical axis (Nv) to the number of points in contact with the horizontal axis (Nh), Fh / Fv = Nv / Nh.

Phase difference: If two waveforms have the same frequency and reach their peaks at the same time, they are said to be in phase. If equal frequency waves reach their peaks at different time, there is said to be a phase difference between them, Ô.
Experimental Rig and Instrumentation

1. Voltmeter: Displayed the rms voltage of the AC supplied.
2. Digital meter: Measured the frequency in Kilohertz.
3. Function generator: Used to generate waveforms such as sinusoidal, rectangular and triangular waves at a frequency of 2 Hz – 2 MHz. The rotating frequency control and the range switch are used together to determine the frequency of the output signal.
4. Oscilloscope: Used to display and analyzes the waveform of electronic signals. Lcd display was 10 x 8 cm’s. The x-axis can be adjusted by altering the time per division.
5. Capacitor and Variable resistors: to alter the current flow.

Results


[PHP]Experiment (1)
Voltage(rms) = 5 volts

Frequency / KHz Number of divisions Time/division Period estimate
1 10 .10 ms 1ms 1ms
2 10 .05 ms .5ms .5ms
3 6.6 .50 µs 330 µs 333 µs
4 5 50 µs 250 µs 250 µs
5 10 20 µs 200 µs 200 µs

Experiment (2)
Frequency = 1KHz

Voltage (RMS) Number of divisions voltage per /division V(p-p) V(p) V(p) using formula
1 6.1 0.5 3.05 1.525 1.41
2 6 1 6 3 2.82
3 4.5 2 9 4.5 4.23
4 6 2 12 6 5.68
5 7.5 2 15 7.5 7.07

Experiment (3) lissajous Patterns
Frequency = 100Hz, Amplitude = 5Vrms

Frequency (x) / Hz Nv Nh Frequency (x) / Hz
100 1 1 100
150 3 2 100
200 2 1 100
250 5 2 100
300 1 3 100
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Experiment (4) Phase difference measurement:
This is blank because they are hand drawn sketchs





Discussion
In experiment one Voltage was kept constant and Frequency was varied, the oscilloscope was then used to determine values for the Period corresponding to each value for frequency. The results varied that Frequency is the reciprocal of the period and vice versa.
In experiment two the Frequency was kept constant and the root-man-square voltage was varied, the V(p) was found, this was then compared to the value found using the formula.
In experiment three, two function generators where connected to the oscilloscope One at a fixed frequency, the others frequency was allowed to vary, Using the lissajous patterns displayed on the oscilloscope we where able to verify the formula. These are patterns dependant on what the frequency ratio is, for example a figure eight is formed when one frequency is two times the other.
In experiment four, the higher the frequency of the wave function the lower the Phase difference. At lower frequency it the time for the capacitor to charge and discharge allows it to build up a charge, there is therefore a potential drop across the capacitor, this results in a phase difference between the two wave functions. However at higher frequency the capacitor charges and discharges very rapidly and the capacitor is no longer able to store as much charge, the potential drop across the resistor decreases until eventually all the voltages drops across the resistor and the wave functions as in phase.


Conclusion
• The values for the wave functions period at different frequencies corresponded with predicted results in experiment one.
• However the value of V(p) differed with the predicted value, The difference because more pronounced the higher the Value of V(rms) , this is most likely due to in accuracy in reading the results and the internal resistance of the circuit.
• The results of experiment three coincided exactly with the predicted result of 100Hz thus verifying the formula.
• The two wave functions in experiment four never came exactly into phase, due to internal resistance and the fact that even at very a very high frequency a certain amount of charge is still stored on the capacitor which would cause a phase difference.