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.