Digital Signal Processing Reference
In-Depth Information
•
To what extent are sinusoidal signals of different frequencies allowed
to pass? In this context the amplitudes of u
out
and u
in
within the frequen-
cy range in question are compared with each other (Û
out
/Û
in
).
•
How great is the time delay between u
out
and u
in
? This is determined
via the phase difference
Δϕ
between u
out
and u
in
.
Note:
In the case of all
non
-sinusoidal test signals and modern analysis procedures - as
they will be described in the following - the problem is mostly reduced to the two
measurements of amplitude and phase curve. The only difference is that all the
frequencies in which we are interested are given to the input at the same time.
If you do not have computer-aided modern processes available you should note the
following tricks and tips:
(d)
Always trigger the input signal and do not change the amplitude of u
in
(if possible,
select Û
in
= 1V) during the entire measurement series.
(e)
Turn the frequency range to be examined manually on the function generator and
note the area where the amplitude of u
in
changes most strongly. Make most of the
measurements in this area.
(f)
Select for the measurement of the amplitudes (Û
out
depending on the frequency)
such a large time base that the sinusoidal alternating current appears as a “bar” on
the screen. The amplitude can be most easily determined in this way. (See Illustra-
tion 103, top).
(g)
To measure the phase difference
set exactly a half period of the input signal u
in
by means of the uncalibrated time base regulator, which can be set as desired.
T/2 is for example 10 cm on the screen scale and corresponds to an angle of
Δϕ
π
rad.
Now read the phase difference
(or time shift) between the zero crossings of u
out
and u
in
and you obtain (initially) x cm. Finally, by means of the
rule of three
using
a pocket calculator determine the phase difference
Δϕ
Δϕ
in rad for every x value. If
u
out
is
trailing
as in Illustration 103 (bottom)
Δϕ
is
positive
, otherwise it is negative.
For complete and careful measurement with evaluation you require roughly 2 hours. To
awaken your enthusiasm for modern computer-based processing - for the same measure-
ment and evaluation with a much greater degree of precision you need only a fraction of
a second!
Sweep
It is possible to get a quicker overview of the frequency-dependent behaviour of output
amplitude Û
out
by means of the sweep signal (Illustration 104). Here the idea is as fol-
lows. Instead of setting the frequency range continuously by hand from the lower starting
frequency f
start
to the upper stop frequency f
stop
this is carried out in the instrument by
means of a Voltage Controlled Oscillator VCO.
