Re: Phase in AC Circuits

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Mon, 16 Mar 1998, kifer/belk wrote:

> I hope some of you can help me.  I read somewhere, but immediately
> buried it in my "important" reprints pile, about how to put the voltage
> of both the inductor and capacitor on the same dual-trace oscilloscope
> in such a way as to show their phase difference.  If any of you can
> describe how to do this or perhaps refer me to a site that explains how
> to do this I would be grateful.
>
> Greg Kifer
> Olathe North High School
> gsanda@tfs.net

Well, you can just connect channel A across the capacitor and channel B
across the inductor. If the A and B inputs have a common ground, that
ground should be at the point between the capacitor and inductor (assuming
the two components are connected in series. However, if the circuit is
being driven by a signal generator, which probably has a chassis ground
connected to the power line's safety ground, and if the scope has similar
connection to the safety ground, then you'll be shorting out one
component. In this case you'll need to "lift" one of the instrument
grounds, preferably that of the signal generator. This can be done with a
grounding adapter for the power plug with a green wire pigtail, and the
green wire left unattached. 

Does the oscilloscope have an X-Y mode in which the X deflection can be
driven by an external signal (instead of the internal ramp generator?) If
so, you can display the two voltages on the X and Y axis. The phase shift
can then be determined from measurements on the displayed ellipse, by the
standard method described in many electronics books. The same cautions
apply for the grounding. Look on the timebase selector knob for a setting
which disables the timbebase generator and connects to an external signal
input instead. 

To save you the search for the electronics book:

If there's a phase shift you'll see a tilted ellipse on the screen. Asjust
the calibrated gain settings for X and Y so the ellipse is as large as the
screen allows.

Center the ellipse horizontally on the screen, carefully, so that the
central vertical axis of the screen passes exactly through the center of
the ellipse. This can be done by moving the figure horizontally until the
maximum extent of it is +X and -X. The value of X, however will not be
used in the calculation. 

Measure the vertical size of the figure. Call it A.

Measure the points of intersection of the figure with the vertical central
axis. Measure the vertical distance between them. Call it B.

sin (phase angle) = B/A

The derivation of this result is a nice exercise for the student. Students
need all the practice we can give them to strengthen their geometrical
thinking.

Do not expect the phase shift to be exactly 90 degrees, since the inductor
has resistance as well as inductance. 

In some cases, lifting of the power line ground can cause unwanted pickup
of 60 and 120 Hz radiation from the environment. Choose a different signal
generator frequency, if possible. If you are using a tubular capacitor, be
sure that the outer foil (the marked lead) is the one closest to ground
(the 'scope ground).

	-- Donald

......................................................................
Dr. Donald E. Simanek                            Office: 717-893-2079
Professor of Physics                                FAX: 717-893-2048
Lock Haven University, Lock Haven, PA. 17745
dsimanek@eagle.lhup.edu                 http://www.lhup.edu/~dsimanek
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