User:Brian P. Josey/Notebook/Junior Lab/2010/08/30

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Oscilloscope Lab
In this lab, we worked with a digital oscilloscope to become familiar with its operation and use. To do this, my partner and I generated various different signals from a function generator, and measured both their amplitude and period. After becoming comfortable with it, we used the AC coupling feature on the oscilloscope to measure the fall time in the oscilloscope’s internal R-C circuit on a low frequency square AC wave. For this lab, we used a Tektronix TDS 1002 Oscilloscope, and a BK Precision 4017A Function Generator. These two were connected with a BNC cable between the function generator’s output to the channel 1 input on the oscilloscope.

Basic Use of Oscilloscope
Before actually using the oscilloscope, I had to learn more about the controls on both the oscilloscope, and the function generator. On the function generator, there are several different groupings of controls, they relevant ones we used are:


 * Range - the range buttons are located in the first row immediately to the right of the power button. The ranges run from 1 to 10m (10 million) and give the scale of the frequency of the signal, in Hz, that the function generator sends to the output signal.
 * Wave Type- These three buttons on the upper right of the function generator are labeled with one complete wave of either a sine, triangle or rectangular wave, and change the output type of the signal.
 * Frequency- These are the knobs at the lower left, and change the frequency, displayed on the digital, in a large number of units, Coarse, or just a few, Fine
 * Output- This knob on the far right changes the amplitude, in V, of the output signal.
 * DC Offset- This knob changes the amount of additional directed current is added to the signal. Increasing it will raise the graph on the oscilloscope, but not change its amplitude. To activate the dc offset, the DC Offset button under the range buttons has to be pressed in.

On the oscilloscope, there are a couple of important controls.


 * Position and units/div:- These knobs take up most of the space on the control panel. The position knob will move the displayed signal up or down for channel one and two, or side to side for horizontal. The units/div knobs will change the scale at which the signal is displayed, and is measured in volts/grid division, or sec/ grid division.
 * Measure- This button in the upper middle portion will bring up the measure feature and can be altered depending on the menu selected with the buttons just to the right of the display.
 * Cursor- The cursor button will pull up a pair of cursors than can measure the distance between two lines on the display in either the horizontal or vertical direction. They are adjusted with the position knobs.
 * Trigger- These controls on the far right will pull up the triggering feature. This is discussed more thoroughly below.

Characteristics of Signals
Prompted by the lab manual, we generated several different waves, and measured two quantities for each, the amplitude and period. For each wave we generated, we measured these quantities three times. The first was by counting the number of divisions on the grid between the end points. We then used the cursors to close in on the signal and measured the difference between their distances. Finally, we used the measure feature. Each of these waves had a frequency of 120 Hz, but varied in their potential, dc offset and type.

Triggering
Triggering is the process by which the oscilloscope determines how it will display the input signal on the display. It does this by finding a specified voltage and finding its location on the wave. This can be on either the rising part of the wave, or the falling part of the wave. The oscilloscope then isolates this points and places it on the far left of the screen, and draws the signal going across to the right like it would a normal signal. The advantage to doing this is that it allows the user to clearly define the signal, and work with it in whatever way they need it.

AC Coupling
AC Coupling is the process in which the oscilloscope removes the DC portion of the signal with the use of a capacitor. This contrasts with DC Coupling, which does not remove the additional DC signal in the source signal. Mathematically, AC coupling for a simple sine wave could be represented by:

$$ V(x) = V_1 \sin {x} \, $$

Where V is the voltage at a point x, and V1 is the maximum voltage. DC coupling then adds an additional voltage, V2:

$$ V(x) = V_1 \sin {x} + V_2 \, $$

To get at it on the oscilloscope, you use the menu for the channel you are working with, and select AC from the coupling menu. This will remove the DC component completely form the signal. However, at very low frequencies, ~10 Hz, the signal becomes distorted due to the internal resistance and capacitance of the oscilloscope. This distortion, image on the right, is from the characteristic oscillation in an RC circuit, and can be used to determine the fall time, τ, of the circuit, which is also know as the RC constant. With the initial conditions of a square wave at 8.56 V and oscillating at 11 Hz, we measured using the measure function, a fall time of 37.1 ms. We then measured the voltage and time of the peak on one of the square waves, V1 = 7.20 V and t1 = -35.20 ms respectively, and at a second point down the graph, V2 = 4.00 V and t2 = -21.20 ms. Then using these points of data, we could calculate the fall time with this formula:

$$ V_2 = V_1 e^ { \frac {-\Delta t} {\tau}} \, $$

where Δt is simply the difference in t2 minus t1. This gave us a value for the fall time of 23.82 ms. This value is different from the measured value, being only 64% of the oscilloscope value. Physically, the fall time represents the amount of time it takes for the voltage to fall by 10%, and our calculated value could be off from the fact that we picked a point that wasn't near the 10% mark, which is difficult to discern on the screen.

Acknowledgments and References
I want to just give a quick shout out to the people the helped me with this experiment. I was helped by both Katie and Koch, and worked with Derrick (no link) the first week and Kirstin the second week. I also resorted to using Thomas', Paul's and Alexandra's notebooks as references and guides in doing my own experiments. For the triggering portions, I used Wikipedia's page on oscilloscopes, and a page from National Instruments for AC and DC coupling.


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