Practice Problems: Modulation Techniques

Question 1:
A telecommunications engineer is designing an AM broadcast transmitter for a commercial radio station. The carrier signal has a power of 50 kW and is modulated by an audio signal. When measurements are taken, the total transmitted power is found to be 62.5 kW.

What is the modulation index of the AM signal?

(a) 0.50
(b) 0.71
(c) 0.85
(d) 0.95

Question 2:
A broadcast engineer is analyzing an FM signal with a carrier frequency of 100 MHz. The modulating signal is a single tone at 5 kHz with a frequency deviation of 75 kHz.

What is the modulation index (β) of this FM signal?

(a) 10
(b) 12
(c) 15
(d) 20

Question 3:
A design engineer is implementing a DSB-SC (Double Sideband Suppressed Carrier) modulator for a communication system. The message signal has a bandwidth of 4 kHz and the carrier frequency is 200 kHz.

What is the bandwidth of the transmitted DSB-SC signal?

(a) 4 kHz
(b) 6 kHz
(c) 8 kHz
(d) 12 kHz

Question 4:
A communications system engineer is designing a VSB (Vestigial Sideband) system for analog television transmission. The video signal has a bandwidth of 4.2 MHz, and the vestigial portion of the lower sideband extends 0.75 MHz below the carrier frequency.

What is the total bandwidth required for the VSB signal?

(a) 4.20 MHz
(b) 4.95 MHz
(c) 5.70 MHz
(d) 8.40 MHz

Question 5:
A RF engineer is analyzing a QPSK (Quadrature Phase Shift Keying) communication system that transmits data at a bit rate of 4 Mbps. Each symbol in QPSK carries 2 bits of information.

What is the symbol rate (baud rate) of this QPSK system?

(a) 1 Msymbols/s
(b) 2 Msymbols/s
(c) 4 Msymbols/s
(d) 8 Msymbols/s

Question 6:
A communications engineer is evaluating an AM signal where the carrier amplitude is 100 V and the modulation index is 0.8. The carrier is modulated by a single-tone sinusoidal signal.

What is the maximum amplitude of the modulated signal envelope?

(a) 120 V
(b) 150 V
(c) 180 V
(d) 200 V

Question 7:
A wireless system designer is implementing a 16-QAM (Quadrature Amplitude Modulation) system. The system operates at a symbol rate of 5 Msymbols/s.

What is the data rate (bit rate) that this 16-QAM system can achieve?

(a) 5 Mbps
(b) 10 Mbps
(c) 15 Mbps
(d) 20 Mbps

Question 8:
A broadcast engineer is working with an FM radio station operating at 98.5 MHz. The station uses a maximum frequency deviation of 75 kHz for music programming, and the highest audio frequency to be transmitted is 15 kHz.

Using Carson's rule, what is the approximate bandwidth required for this FM transmission?

(a) 150 kHz
(b) 180 kHz
(c) 200 kHz
(d) 240 kHz

Question 9:
A satellite communications engineer is designing a BPSK (Binary Phase Shift Keying) system with a bit rate of 10 Mbps. The system uses raised cosine pulse shaping with a roll-off factor of 0.35.

What is the null-to-null bandwidth of the transmitted BPSK signal?

(a) 10.0 MHz
(b) 13.5 MHz
(c) 20.0 MHz
(d) 27.0 MHz

Question 10:
A communications consultant is analyzing an SSB-SC (Single Sideband Suppressed Carrier) system. The message signal has a maximum frequency of 3.4 kHz and a minimum frequency of 300 Hz. Only the upper sideband is transmitted, with a carrier frequency of 9 MHz.

What is the bandwidth occupied by the transmitted SSB-SC signal?

(a) 3.1 kHz
(b) 3.4 kHz
(c) 6.2 kHz
(d) 6.8 kHz

Question 11:
A RF design engineer is working on an AM transmitter that delivers 10 kW of power to the antenna when unmodulated. When the carrier is modulated at 60% modulation depth by a sinusoidal signal, the engineer needs to determine the power consumption.

What is the total power transmitted when the modulation is applied?

(a) 10.0 kW
(b) 11.8 kW
(c) 13.6 kW
(d) 16.0 kW

Question 12:
A cellular network engineer is implementing an 8-PSK (8-ary Phase Shift Keying) modulation scheme for a wireless data link. The system needs to support a data rate of 24 Mbps.

What minimum symbol rate must the system support to achieve this data rate?

(a) 3 Msymbols/s
(b) 6 Msymbols/s
(c) 8 Msymbols/s
(d) 12 Msymbols/s

Question 13:
A test engineer is measuring an AM signal on an oscilloscope and observes that the maximum envelope amplitude is 150 V and the minimum envelope amplitude is 50 V.

What is the percentage modulation of this AM signal?

(a) 33%
(b) 50%
(c) 67%
(d) 75%

Question 14:
A satellite communication engineer is designing an FM system for voice transmission. The audio signal has a maximum frequency of 3 kHz and requires a frequency deviation of 5 kHz for acceptable quality.

What is the deviation ratio (D) for this narrowband FM system?

(a) 0.6
(b) 1.0
(c) 1.67
(d) 2.5

Question 15:
A digital communications engineer is comparing modulation schemes for a new wireless system. The system currently uses QPSK at a symbol rate of 10 Msymbols/s. The engineer proposes switching to 64-QAM at the same symbol rate to increase throughput.

What is the increase in data rate by switching from QPSK to 64-QAM?

(a) 20 Mbps
(b) 30 Mbps
(c) 40 Mbps
(d) 60 Mbps

Question 16:
A power systems communication engineer is implementing a phase modulation (PM) system. The modulating signal is a sinusoid with frequency 1 kHz and amplitude 2 V. The phase sensitivity constant (\(k_p\)) of the modulator is 3 rad/V.

What is the maximum phase deviation of the PM signal?

(a) 2 rad
(b) 3 rad
(c) 5 rad
(d) 6 rad

Question 17:
A telecommunications consultant is analyzing an AM radio station that transmits with a carrier power of 40 kW. The station operates with 100% modulation when transmitting music.

What is the power in each sideband when the modulation is at 100%?

(a) 10 kW
(b) 15 kW
(c) 20 kW
(d) 40 kW

Question 18:
A microwave engineer is designing a communication link using FSK (Frequency Shift Keying) modulation. The mark frequency is 10.2 MHz and the space frequency is 9.8 MHz. The bit rate is 100 kbps.

What is the frequency deviation for this FSK system?

(a) 100 kHz
(b) 200 kHz
(c) 300 kHz
(d) 400 kHz

Question 19:
A broadcast engineer is configuring an FM transmitter with a carrier frequency of 95.5 MHz. The audio input signal has a frequency of 2 kHz and causes a frequency deviation of 30 kHz. The engineer needs to calculate the frequency of the first significant upper sideband component.

What is the frequency of the first upper sideband component?

(a) 95.502 MHz
(b) 95.530 MHz
(c) 97.5 MHz
(d) 125.5 MHz

Question 20:
A systems engineer is evaluating the efficiency of an AM transmitter. The carrier power is 100 W and the transmitter operates with a modulation index of 0.8 for a single-tone modulating signal.

What is the transmission efficiency of this AM system?

(a) 24.2%
(b) 32.0%
(c) 38.5%
(d) 44.4%