NUMERICAL SHEET 2

ANALOG MODUULATION: AMPLITUDE,FREQUENCY,PHASE

1. The rms value of a carrier voltage after amplitude modulation to a depth of 40% by a sinusoidal

modulating voltage is 35V. Calculate the rms value of a carrier voltage when amplitude

modulated to a depth of 80%. (60.81V)

2. A radio telephone transmitter using amplitude modulation has unmodulated carrier output

power of 20kW and can be modulated to a maximum depth of 80% by a sinusoidal modulating

voltage without causing overloading. Find a value to which unmodulated carrier power power

may be increased without resulting in overloading if the maximum permissible modulation index

is 60%.

3. A radio transmitter radiates 10kW with the carrier unmodulated and 11.25kW when the carrier

is modulated by a sinusoidal voltage. Calculate the modulation index. Another sine wave is

capable of producing 30% modulation. If both the sine when simultaneously modulate the

carrier, determine total radiation power. (0.58, 11.7kW)

4. An FM wave is represented by the voltage equation: v = 20 sin(5x10^8t+4sin1500t).

Find the carrier and modulating frequency, the modulation index and maximum deviation of

FM. What power will this FM voltage dissipate in a 20Ω resistance?

(fc=7.96x10^7 Hz, fm=238.7 Hz, mf=4, fd=955Hz, P=10W)

5. A 20kHz 5V carrier is modulated by a 500Hz sine wave. The maximum frequency deviation is

15kHz and the same ‘m’ is obtained for both FM and PM. Write expressions for this modulated

wave for FM and PM. Next if the modulating frequency is increased to 3000Hz, other things

remaining the same, write the new expressions for FM and PM.

(v = 5 sin(1.25x10^8t+30 sin 3141t), Case2 FM: (v = 5 sin(1.25x10^8t+5 sin 3141t))

6. A sinusoidal carrier voltage of amplitude 80 volts and frequency 800kHz is amplitude modulated

by a sinusoidal voltage of frequency 15kHz resulting in minimum modulated carrier amplitude of

72 volts. Compute the sideband frequencies and the modulation index.

(785kHz, 815kHz, ma = 0.1)

7. A sinusoidal carrier voltage of frequency 1MHz is amplitude modulated by a sinusoidal voltage

of frequency 10KHz resulting in maximum and minimum modulated carrier amplitude of 85 and

75 volts respectively. Calculate the unmodulated carrier amplitude and the modulation index

and the amplitude of each sideband. (80V, 0.0625, 2.5V)

8. A broadcasting radio transmitter radiates 10kW when the modulation percentage is 60%. How

much of this is the carrier power? (8.47kW)

9. The antenna current of an AM transmitter is 8A when only carrier is sent us it increases to 8.93A

when the carrier is modulated by a single sine wave. Find the percentage modulation.

Determine the antenna current when the percent of modulation changes to 0.8 (70.1%, 9.19A)

10. A certain transmitter radiates with carrier unmodulated and 10.125kW with carrier sinusoidally

modulated. Calculate the modulation index, percent of modulation. If another sine wave

corresponding to 40% modulation is transmitted simultaneously, determine the total radiated

power. (0.5, 10.84kW)

11. In an FM system, when the AF is 500Hz and the AF voltage is 2.4V, the deviation is 4.8kHz. if the

AF voltage is now increased to 7.2V, what is the new deviation? If the AF voltage is raised to 10V

while the AF is dropped to 200Hz, what is the deviation? Find modulation index in each case.

(dev = 14.4kHz, mf1=9.6, mf2=28.8, mf3=100)

12. What is the bandwidth required for an FM signal in which the modulating frequency is 2kHz and

the maximum deviation is 10kHz. (mf=5, 24kHz)

13. A 2500kHz carrier is modulated by audio signal with frequency span of 50-15000Hz. What are

the frequencies of lower and upper sidebands? What bandwidth of RF amplifier is required to

handle the output?

(2500.05-2515kHz, 2499.95-2485kHz)

14. An AM wave is represented by the equation: v = 5(1+0.6cos 6280t) sin 211x10^4t volts.

i. What are the minimum and maximum amplitudes of the AM wave?

Ii. What frequency components are included in the modulated wave and what is the amplitude

of each component?

(8V, 2V; 335kHz, 336kHz, 337kHz; 1.5V, 5V, 1.5V)

15. A 50kW carrier is to be modulated to a level of 80% and 10%. What is the total sideband in each

case? (16kW, 0.25kW)

16. The load current in the transmitting antenna of an unmodulated AM transmitter is 8A. What will

be the antenna current when modulation is 40%? (8.31A)

17. The rms value of carrier voltage is 100V. After amplitude modulation by a sinusoidal af voltage,

the rms value becomes 110V. Calculate the modulation index. (0.648)

18. An AM wave consists of the following components:

carrier component = 5V peak value, LSB = 2.5V peak value, USB = 2.5V peak value.

If the AM wave drives a 2kΩ resister, find the power delivered to the resister by--

carrier, LSB, USB component. What is the total power delivered?

(6.25mW, 1.562kW, 9.374kW).

19. A carrier wave of frequency 10MHz and peak value 10V is amplitude modulated by 5KHz sine

wave of amplitude 6V. Determine the modulation index and draw the amplitude spectrum.

(0.6, 10.005, 9.995MHz)

20. Determine the modulation index, and plot the sinusoidal FM wave for which Ec(max) = 10V,

Em(max) = 3V, k = 2000Hz/V, fm = 1KHz and fc = 20KHz. On the same sets of axes, plot the

modulating function. The plot should extend over two cycles of the modulating function.`

(6, e(t) = 10 cos (4Πx10^4t + 6sin 2Πxq0^3t) )

21. A modulating signal given by Em(t) = 3 cos(2Πx10^3t-90°)volts is used to phase modulate a

carrier for which Ec(max) = 10V and fc = 20KHz. The phase deviation constant is K = 2 rad/V. Plot

the modulated waveform over 2 cycles of the modulating function.

(e(t) = 10 cos (4Πx10^4t+6sin2Πx10^3t).