Communication Systems
Prof. Chngming Kuo
Chapter 6
Single Tone Modulation Comparisons (cont.)
Single-Tone Modulation Comparisons
The forms of DSB, SSB, and conventional AM have been introduced in other modules.
In this module, the modulation is restricted to a single-tone sinusoidal function and the behavior of the different methods is studied.
Single-Tone Modulation Comparisons (cont.)
Both time and frequency domain forms are reviewed, and power comparisons are made.
Results provide certain quantitative criteria for comparing system performance.
DSB :
v t A cosmt cos ct A
2cos c m t A
2cos c m t
SSB :
v t A cos c m t
AM :
v t A 1 m cosmt cos ct
A cos ct mA2
cos c m t mA2
cos c m t
(a) MODULATING SIGNAL (b) MODULATING SPECTRUM
(c) DSB SIGNAL(d) DSB SPECTRUM
(e) SSB SIGNAL
t fmf
c mf fc mf fft
(f) SSB SPECTRUM
c mf fft
(g) AM SIGNAL
f
c mf fc mf f
(h) AM SPECTRUM
t
Power Relationships
Instantaneous Power : p t v2 t R
Average Power : P 1T
p t dt0
T 1RT
v2
0
T t dt Vrms2
R
Peak Envelope Power : Pp Vp
2
2R
AM Single Tone Power Comparisons
Method P pP /pP P
DSB
2
4
A
R
2
2
A
R
2
SSB 2
2
A
R
2
2
A
R
1
AM 2
12 c
mP
2
1 cm P 2
2
(1 )
1 / 2
m
m
AM, m = 0.5 1.125 cP 2.25 cP 2
AM, m = 1 1.5 cP 4 cP 2.667
Example 1
• A single tone modulated DSB signal has peak voltage of 200 V across 50 . Determine average and peak power levels:
P A2
4R 2002
4 50200 W
Pp A2
2R 2002
2 50400 W
Example 2
• An AM transmitter has a carrier power of 1 kW and the antenna input resistance = 50 . Find values of antenna rms voltage and current with no modulation:
P Vrms2 R or
Vrms RP 50 1000 223.6 V
Example 2 (cont.)
• An AM transmitter has a carrier power of 1 kW and the antenna input resistance = 50 . Find values of antenna rms voltage and current with no modulation:
P I rms2 R or
I rms PR
100050
4.472 A
Example 3
• For AM transmitter of Example 2, determine for modulation of 50% and 100%, the average power, peak envelope power, and sideband power.
P 1m2
2
Pc
Pp 1m 2Pc
Example 3: Tabulated Values
Modulation Factor
Average Power
Peak Power Sideband Power
0 1000 W 1000 W 0 50% 1125 W 2250 W 125 W
100% 1500 W 4000 W 500 W
Example 4
50% modulation:
• For transmitter of Examples 2 and 3, find antenna rms voltage and current for 50% and 100% modulation.
Vrms RP 50 1125 237.2 V
I rms P R 1125 50 4.743 A
Example 4 (cont.)100% modulation:
Vrms RP 50 1500 273.9 V
I rms P R 1500 50 5.477 A
Summary With single-tone modulation, DSB peak power is
twice the average power. With single-tone modulation, SSB peak and average
powers are the same. For complex waveforms, peak power may be much greater.
With single-tone modulation, AM average power is 1.5 times carrier power.
With single-tone modulation, AM peak power is 4 times carrier power.