T 7.2.1.3 Amplitude Modulation

TPS 7.2.1.3
Solutions
Solutions
2.3 A measurement example
1. Manual operation with analog voltmeter
The amplitude S R (1) of the fundamental harmonic
is greater than the square-wave amplitude A R by a
factor 4/π = 1.27. The formation law for the spectrum
of a symmetrical square-wave signal is:
S
R
4 AR
( n)
=
π ( 2n
−1)
n: 1, 2, 3...
Diagram 2.3-1:
Spectrum of the square-wave signal A R
= 5 V, τ/T P
= 0.5
Table 2.3-1: Spectrum square wave signal
Signal parameter
A R : 5 V
τ/T P : 5/10
f R : 2.00 kHz
n
f
kHz
Analyzer settings
V 1 : 1
b : 500 Hz
f r : 20 kHz
T : 20 s
Measurement
S(n) S R (n)
V 2
V
V
Theory
S (n)
R
V
1 2.0 6.6 1 6.6 6.37
2 4.0 ---- - ---- ----
3 6.0 2.1 1 2.1 2.12
4 8.0 ---- - ---- ----
5 10.0 6.6 5 1.32 1.27
6 12.0 ---- - ---- ----
7 14.0 4.7 5 0.94 0.91
8 16.0 ---- - ---- ----
9 18.0 3.6 5 0.72 0.71
10 20.0 ---- - ---- ----
2. Automatic operation with the XY recorder
or the storage oscilloscope
The reduction in the bandwidth b narrows the
spectral window. The manual frequency setting
thus becomes increasingly difficult, while at the
same time the spectral lines become clearer.
Even when using an oscilloscope as a display unit
which operates (almost) without any inertia, the
spectrum is no longer reproduced with full amplitude.
The reason for this lies in the time law of
electrical communications engineering. The filters
of the analyzer no longer reach the transient
recovery state. If mechanical measuring instruments
subject to inertia are used as display units,
e.g. a multimeter instrument or an XY recorder,
then the lowpass response of the entire system is
further improved. There is practically no pointer
deflection. The following general statements can
be made about the spectrum of the symmetrical
square-wave signal:
– The spectrum has a line structure.
– The spectral lines occur at odd numbered multiples
of the fundamental frequency f R . (3 f R ,
5 f R , 7 f R , ...)
– The amplitudes S R (n) respond inversely proportional
to the odd numbered multiples of the
fundamental frequency.(1/3, 1/5, 1/7, ...). The
envelope curve has the characteristic 1/f.
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