16
Subject to change without notice
Phase difference measurement in DUAL mode
t
= horizontal spacing of the zero transitions in div.
T
= horizontal spacing for one period in div.
In the example illustrated,
t
= 3div. and
T
= 10div. The
phase difference in degrees is calculated from
Relatively small phase angles at not too high frequencies
can be measured more accurately in the X-Y mode with
Lissajous figures.
Measurement of an amplitude modulation
The momentary amplitude u at time t of a HF-carrier
voltage, which is amplitude modulated without distortion
by a sinusoidal AF voltage, is in accordance with the
equation
u = U
T
· sin
Ω
Ω
Ω
Ω
Ω
t + 0,5m · U
T
· cos(
Ω−ω
Ω−ω
Ω−ω
Ω−ω
Ω−ω
)t
−−−−−
0,5m · U
T
· cos(
Ω
Ω
Ω
Ω
Ω
+
ω
ωω
ω
ω
)t
where
U
T
= unmodulated carrier amplitude
Ω
Ω
Ω
Ω
Ω
=
2
πππππ
F
= angular carrier frequency
ω
ωω
ω
ω
=
2
πππππ
f
= modulation angular frequency
m
= modulation factor (i.a.
≤
1 100%).
The lower side frequency
F
−
f
and the upper side frequency
F+f
arise because of the modulation apart from the carrier
frequency
F
.
Amplitude and frequency spectrum for AM display (
m
= 50%)
The display of the amplitude-modulated HF oscillation can
be evaluated with the oscilloscope provided the frequency
spectrum is inside the oscilloscope bandwidth. The time
base is set so that several wave of the modulation
frequency are visible. Strictly speaking, triggering should
be external with modulation frequency (from the AF
generator or a demodulator). However, internal triggering
is frequently possible with normal triggering (
AT/NORM.
button depressed) using a suitable
LEVEL
setting and
possibly also using the time variable adjustment.
Oscilloscope setting for a signal according to figure 2:
Depress no buttons.
Y: CH. I; 20mV/div.; AC
.
TIME/DIV.:
0.2ms/div.
Triggering:
NORMAL
; with
LEVEL
-setting; internal (or
external) triggering.
Figure 2
Amplitude modulated oscillation:
F
= 1 MHz;
f
= 1 kHz;
m
= 50 %;
U
T
= 28.3 mV
rms
.
If the two values
a
and
b
are read from the screen, the
modulation factor is calculated from
where
a = U
T
(1+m)
and
b = U
T
(1
−−−−−
m)
.....
The variable controls for amplitude and time can be set
arbitrarily in the modulation factor measurement. Their
position does not influence the result.
Triggering and time base
Time related amplitude changes on a measuring signal
(AC voltage) are displayable in Yt-mode. In this mode the
signal voltage deflects the beam in vertical direction while
the timebase generator moves the beam from the left to
the right of the screen (time deflection).
Normally there are periodically repeating waveforms to be
displayed. Therefore the time base must repeat the time
deflection periodically too. To produce a stationary display,
the time base must only be triggered if the signal height
and slope condition coincide with the former time base
start conditions. A DC voltage signal can not be triggered
as it is a constant signal with no slope.
Triggering can be performed by the measuring signal itself
(internal triggering) or by an external supplied but
synchronous voltage (external triggering).
The trigger voltage should have a certain minimum
amplitude. This value is called the trigger threshold. It is
measured with a sine signal. When the trigger voltage is
taken internally from the test signal, the trigger threshold
can be stated as vertical display height in div., through
which the time base generator starts, the display is stable,
and the trigger LED lights.
t
T
ϕ°
ϕ°
ϕ°
ϕ°
ϕ°
=
·
360°
=
3
10
·
360°
=
108°
3
10
·
2
πππππ
=
t
T
arc
ϕ°
ϕ°
ϕ°
ϕ°
ϕ°
=
·
2
πππππ
=
1,885 rad
Figure 1
m • U
T
U
T
a
b
a
−−−−−
b
a + b
a
−−−−−
b
a + b
m =
· 100 [%]
m =
or
U
U
U
T
T
T
0 . 5 m •
0 . 5 m •
F – f
F + f
