29
The frequency is the reciprocal of the period =
1/dT. First determine the period as described in
the previous chapter, then use a hand-held
calculator to divide "1" by the period. If your
calculator has a 1/x key, just enter the period and
press the 1/x key to obtain the frequency.
However, remember the powers of ten, these
are listed in the Table below as a reminder.
Period in s Reciprocal = Hz (= 1/s)
In ms = 10-3 s = kHz
In µs = 10-6 s = MHz
The accuracy of this measurement is limited by
the accuracy of the time base.
2.3.5 Measurement of phase displacement
The phase displacement or phase angle between
two signals can be determined either in dual-
trace mode or in X-Y mode.
a) Dual trace mode
This method of measurement can be used to
work on various signal waveforms up to a
maximum frequency of 40 MHz.
To measure the phase angle, proceed as
follows:
1. Set up the oscilloscope as described under
heading 2.2.4 for dual-trace mode. Connect
one signal to CH 1 and the other signal to CH 2.
Note:
To avoid measuring errors, use identical, acc-
urately compensated probes or coaxial cables of
identical length/type to ensure identical delay
times.
2. You will then see two in-phase points on both
curve traces on the screen. If the signals have
a sine-wave shape, find a point that is as close
as possible or, best of all, actually on the
datum line (horizontal centre line). The
slope of the curve trace is at its steepest at
this point and here it is possible to determine
a position on the X-axis with maximum
accuracy.
3. In the figure below, these points of the two
sine-wave signals are identified as P1 and P2.
To obtain the phase difference, the displace-
ment is measured as the distance P1-P2 which
is then expressed as a ratio to distance P1-P1’.
Fig. 17
4. The phase angle is expressed in angular
degrees and must be determined from the
measured distances. One period corresponds to
exactly 360º. The phase angle phi is obtained as
follows:
1-P2 1 DIV
Phi = — x 360° from the fig. = — x 360° = 60°
P1-P1’ 6 DIV
b) X-Y mode (Lissajous method)
This method is used exclusively in the case of
sine curves. Measurements are possible up to
500 kHz max. which is the bandwidth of the
horizontal amplifier.
Using this method, proceed as follows:
1. Set the TIME/DIV knob to the right-hand stop
and do not forget to reduce the intensity
(brightness).
2. Make sure that the POSITION knob for
channel 2 (17) is pushed in, otherwise this
would give a phase displacement of 180º.
3. Connect one measuring signal to the CH 1 or
X input and the other measuring signal to the
CH 2 or Y input.
4. Use the CH 2 POSITION knob (17) and the
VOLTS/DIV knob (13) to adjust the vertical
sweep so that the amplitude covers 6 DIVs
and is above the 100% marker line (horizon-
tal; the number "100" is on the left-hand
edge of the graticule) and the bottom
touches the 0% line.
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