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PHYSICS 176 UNIVERSITY PHYSICS LAB II Experiment 4 Alternating Current Measurement Equipment: PHYSICS 176

UNIVERSITY PHYSICS LAB II

Experiment 4

Alternating Current Measurement


Equipment:
Oscilloscope, Function Generator.

Supplies: Filament
Transformer.


A sine wave A.C. signal has three basic properties: amplitude, frequency, and phase. The measurement of
amplitude and frequency with an oscilloscope is illustrated below. The vertical and horizontal axes can be set to
various voltage/div and time/div scales respectively.



The peak-to-peak amplitude of the sine wave is the voltage V
pp
between the top of the wave and the bottom. Its
value is found from the trace on the oscilloscope screen as follows:


V
pp
= (peak-to-peak amplitude in div) x (volts/div)

The period of the sine wave is time T between successive peaks of the wave. Its value is found from the trace on
the oscilloscope screen as follows:


T = (distance between peaks in div) x (time/div)

The frequency of the sine wave signal is the inverse of the period:


f = 1/T Hertz

(1 Hertz = 1 second
-1
)

The mathematical expression for the sine wave signal is usually in terms of the peak amplitude V
p
= V
pp
/2 and the
angular frequency = 2f.


Signal voltage = V
p
sin (t + )

The phase angle is given in radians (2 radians = 360
E). The phase angle describes how one sine wave signal is
shifted relative to another. The dual trace oscilloscope allows two signals to be displayed on the screen
simultaneously and this permits a measurement of their relative phases. The measurement of phase will be
considered in more detail in Experiment 5.
1 A. Oscilloscope
Operation

The front panel of TDS 1002 oscilloscope is given below. It is divided into easy-to-use functional areas.


Vertical controls:
Cursor 1 and Cursor 2: Position the waveform vertically.
Ch1 Menu , Ch2 Menu: Display the vertical menu selections and toggles the display of the channel
waveform on/off.
Math Menu: Displays the waveform math operations menu.
Volts/Div: Selects calibrated scale factors.
Horizontal controls:
Position: Adjusts the horizontal position of the waveform.
Horiz. menu: Displays the Horizontal menu.
Set to zero: Sets the horizontal position to zero.
Sec/Div: Selects the horizontal time/div (scale factor) for the window time base.
Trigger controls: Used to set up the trigger level.
Menu and Control buttons:
Save/Recall: Displays the Save/Recall menu
Measure: Displays the automated measurements menu
Acquire: Displays the acquire menu
Cursor: Displays the cursor menu
Utility: Displays the utility menu
Auto Set: Automatically sets the oscilloscope controls to produce a usable display of the input signal.
This is your panic button. Punch it in anytime something goes wrong and you do not know why
Default set up: Recalls the factory set up.
Single Seq: Acquires a single waveform and then stops.
Run/Stop: Continuously acquires waveforms.
Print: Starts print operations.

The BNC connectors labeled Ch1 and Ch2 are two inputs. Each input is an amplifier which takes the input
signal and uses it to drive the electron beam up and down. To use channel 1 only, punch in the button Ch
1; similarly for channel 2. Because there are two input channels, the TDS 1002 is called a dual trace
oscilloscope. However, there is only one electron beam, which is shared by the two channels.


2 The electron beam appears on the screen left to the controls . It sweeps across the screen with a speed
selected with the Sec/Div control.

Each channel input has AC-GND-DC coupling selected by pushing the Ch1/Ch2 menu buttons:


AC: A blocking capacitor is in series (internally) with the input so that the trace on the screen shows only
the A.C. signal part of the input.


GND: The scope trace is a horizontal line which represents the level of zero volts D.C. (ground level).


DC: The trace on the screen is shifted relative to the GND level by an amount equal to any D.C. voltage
input. There may be an A.C. voltage (signal) superimposed on the D.C. voltage.


If the input signal is periodic (which is the usual case), you want the horizontal sweep of the electron beam to start
at the same point of the signal pattern each time; otherwise the trace of the signal on the screen will not appear
stationary. This is accomplished by triggering the sweep of the electron beam with a chosen level of the input
signal (Trigger controls).

In order to find the trace initially (when the scope is first turned on), push the AutoSet button . The sweep is then
triggered by the power companys 60 Hz line voltage. In order to trigger on a displayed signal use the Trigger
controls.


B. The Filament Transformer

In the days when vacuum tube circuits were common, the tube filament was heated (to boil off electrons form the
tube cathode) by passing an A.C. current through it. The A.C. voltage across the filament was derived from the
secondary winding of a filament transformer. The A.C. voltage across the primary winding of the transformer was
the power company's line voltage.

When an A.C. voltage


v(t) = V
p
sint

is applied to a resistor R, an A.C. current


i(t) = (V
p
/R)sint

flows through the resistor. The instantaneous heating effect of this current in terms of heat dissipated/second
(joules/second) is the instantaneous power


p(t) = i
2
(t) R = (V
p2
/R) sin
2
t

The time average power is

P
av
= ½ (V
p2
/R)

since the time average of sin
2
t is ½.

A.C. voltages are often referred to by their root-mean-square values

V
rms
= .707 V
p


3 Then the time average power, in terms of the root-mean-square voltage is


P
av
= V
2rms
/R

which has the same form as the power formula for D.C. (P = I
2
R = V
2
/R).

The root-mean-square value of the power company's line voltage is about 110 volts. The root-mean-quare value of
the filament transformer output is typically 6.3 volts (or sometimes 12.6 volts).


C. The Function Generator

The function generator produces square waves, triangle waves, and sine waves shown below:




















In this Lab you will be using TENMA 72-6644 10 MHz function generator. The front panel of the generator is
given in the next page.

To operate the generator:

Turn on the power switch.
Select the waveform of the generated signal by pushing the corresponding Function switch.
Push Frequency Selector switch to select the frequency range at your desire. Fine adjust the frequency of the signal
by turning the Frequency Control Dial.
The amplitude of the output signal is controlled continuously with operating the Amplitude Control Knob. If the
Amplitude Control knob is pulled out, the output amplitude is set to 20dB fixed.
The OFFSET control knob may be used to offset the waveform above or below ground (0 volts) by a D.C. voltage
in the range ±10 volts. To adjust the DC level pull out the OFFSET control knob then turn slowly CW(positive
volts) or CCW (negative volts). If the OFFSET knob is pushed in, there is no DC level, but only AC voltage exists
in the output signal.
The shape/symmetry of the output signal may be varied with the Symmetry Control knob. To adjust the symmetry
of the waveform, pull out the Symmetry Control knob and turn slowly in the CCW direction.



4












5
D. The Circuit Ground

When you measure signals it is a good practice to have the function generator, the oscilloscope and your circuit
at a common ground. It is essential that you identify the ground connections on the oscilloscope and on the
function generator output cable.

On one end of the function generator cable there is a silver BNC connector which plugs into the output of the
function generator box. The other end of this cable may again be terminated with a BNC connector or have
two leads: one with a red collar and one with a black collar. The lead with the red collar carries the signal
produced by the function generator, while the lead with the black collar is the ground. When an end with two
leads is used connect the ground lead to the ground of the circuit you are building

The oscilloscope probes also have two leads: one carries the signal and the other (black collar with an
alligatortype clip) is the ground. Always connect this end to the ground of the circuit you are building.


The grounds must always be connected to the same point of any circuit. When building circuits it is useful to
use a ground bar so that ground is easily identified. The ground bar is a silver metal rod about ten inches long
with two brass connectors to fasten it to the pegboard.

The filament transformer also plugs into a wall socket, but the primary winding has no D.C. connection with
the secondary winding. Therefore the transformer secondary winding is D.C. isolated from the ground in the