BLM256 DATA COMMUNICATIONS

TUTORIAL FOR CHAPTER 3

PROBLEM 1:

Given figure shows the effect of eliminating higher-harmonic components of a square

wave and retaining only a few lower harmonic components. What would the signal look

like in the opposite case; that is, retaining all higher harmonics and eliminating a few

lower harmonics?

SOLUTION:

The signal would be low-amplitude, rapidly changing waveform like following signal.

PROBLEM 2:

Given an amplifier with an effective noise temperature of 10,000oK and a 10-MHz

bandwidth, what thermal noise level may we expect at its output?

SOLUTION:

N = 10 log k + 10 log T + 10 log B

= -228.6 dBW + 10 log 104 + 10 log 107

= -228.6 + 40 +70 = - 118.6 dBW

PROBLEM 3:

What is the thermal noise level of a channel with a bandwidth of 10 kHz carrying 1000

watts of power operating at 50oC?

SOLUTION:

N=1.38x10-23x(50+273)x10,000 = 4.5x10-17 watts

PROBLEM 4:

Given a channel with an intended capacity of 20 Mbps, the bandwidth of the channel is 3

MHz. Assuming white thermal noise, what signal to noise ratio is required to achieve

this capacity?

SOLUTION:

C=B log2 (1+SNR)

20x106=3x106x log2 (1+SNR)

log2 (1+SNR)=6.67

1+SNR=102

SNS=101

PROBLEM 5:

If an amplifier has a 30 dB voltage gain, what voltage ratio does the gain represent?

SOLUTION:

For a voltage ratio, we have

NdB=30=20log (V2/V1)

V2/V1=1030/20=101.5=31.6

PROBLEM 6:

If the solid curve in following figure represents sin( 2π ) , what does the dotted curve

represent? That is, the dotted curve can be written in the form A sin( 2πft + φ ) ; what are

A, f , and φ ?

SOLUTION:

2 sin( 4πt + π ); A = 2, f = 2, φ = π

PROBLEM 7:

Assume that the TV picture is to be transmitted over a cannel with 4.5-MHz bandwidth

and a 35-dB signal-to-noise ratio. Find the capacity of the channel (bps).

SOLUTION:

PROBLEM 8:

Suppose a transmitter produced 50 W of power.

a) Express the transmit power in units of dBm and dBW.

b) If the transmitter’s power is applied to a unity gain antenna with a 900-MHz

carrier frequency, which is the received power in dBm at a free space

distance of 100 m?

SOLUTION:

PROBLEM 9 (Chapter 3 Problem 3.7):

SOLUTION:

PROBLEM 10 (Chapter 3 Problem 3.8):

SOLUTION:

PROBLEM 11:

The square wave of Figure 3.7 c, with T=1 ms, is passed through a lowpass filter that passes

frequencies up to 8 kHz with no attenuation.

a) Find the power in the output waveform.

b) Assume that at the filter input there is a thermal noise voltage with N0=0.1 µ Watt /Hz,

find the output signal to noise ratio in dB.

SOLUTION:

PROBLEM 12:

If the received signal level for a particular digital system is -151 dBW and the receiver

system effective noise temperature is 1500 K, what is Eb/N0 for a link transmitting 2400 bps?

SOLUTION:

PROBLEM 13:

What is the channel capacity for a teleprinter channel with a 300 Hz bandwidth and a signalto-noise ratio of 3 dB, where the noise is white thermal noise?

SOLUTION:

PROBLEM 14:

Adigital signaling system is required to operate at 9600 bps.

a) If a signal element encodes a 4 bit word, what is the minimum required bandwidth of

the channel?

b) Repeat part (a) for the case of 8-bit words.

SOLUTION:

PROBLEM 15:

What is the thermal noise level of a channel with a bandwidth of 10 kHz carrying 1000 watts

of power operating at 500C?

SOLUTION:

PROBLEM 16 (Chapter 3 Problem 3.13,a,b,7):

SOLUTION:

TUTORIAL FOR CHAPTER 3

PROBLEM 1:

Given figure shows the effect of eliminating higher-harmonic components of a square

wave and retaining only a few lower harmonic components. What would the signal look

like in the opposite case; that is, retaining all higher harmonics and eliminating a few

lower harmonics?

SOLUTION:

The signal would be low-amplitude, rapidly changing waveform like following signal.

PROBLEM 2:

Given an amplifier with an effective noise temperature of 10,000oK and a 10-MHz

bandwidth, what thermal noise level may we expect at its output?

SOLUTION:

N = 10 log k + 10 log T + 10 log B

= -228.6 dBW + 10 log 104 + 10 log 107

= -228.6 + 40 +70 = - 118.6 dBW

PROBLEM 3:

What is the thermal noise level of a channel with a bandwidth of 10 kHz carrying 1000

watts of power operating at 50oC?

SOLUTION:

N=1.38x10-23x(50+273)x10,000 = 4.5x10-17 watts

PROBLEM 4:

Given a channel with an intended capacity of 20 Mbps, the bandwidth of the channel is 3

MHz. Assuming white thermal noise, what signal to noise ratio is required to achieve

this capacity?

SOLUTION:

C=B log2 (1+SNR)

20x106=3x106x log2 (1+SNR)

log2 (1+SNR)=6.67

1+SNR=102

SNS=101

PROBLEM 5:

If an amplifier has a 30 dB voltage gain, what voltage ratio does the gain represent?

SOLUTION:

For a voltage ratio, we have

NdB=30=20log (V2/V1)

V2/V1=1030/20=101.5=31.6

PROBLEM 6:

If the solid curve in following figure represents sin( 2π ) , what does the dotted curve

represent? That is, the dotted curve can be written in the form A sin( 2πft + φ ) ; what are

A, f , and φ ?

SOLUTION:

2 sin( 4πt + π ); A = 2, f = 2, φ = π

PROBLEM 7:

Assume that the TV picture is to be transmitted over a cannel with 4.5-MHz bandwidth

and a 35-dB signal-to-noise ratio. Find the capacity of the channel (bps).

SOLUTION:

PROBLEM 8:

Suppose a transmitter produced 50 W of power.

a) Express the transmit power in units of dBm and dBW.

b) If the transmitter’s power is applied to a unity gain antenna with a 900-MHz

carrier frequency, which is the received power in dBm at a free space

distance of 100 m?

SOLUTION:

PROBLEM 9 (Chapter 3 Problem 3.7):

SOLUTION:

PROBLEM 10 (Chapter 3 Problem 3.8):

SOLUTION:

PROBLEM 11:

The square wave of Figure 3.7 c, with T=1 ms, is passed through a lowpass filter that passes

frequencies up to 8 kHz with no attenuation.

a) Find the power in the output waveform.

b) Assume that at the filter input there is a thermal noise voltage with N0=0.1 µ Watt /Hz,

find the output signal to noise ratio in dB.

SOLUTION:

PROBLEM 12:

If the received signal level for a particular digital system is -151 dBW and the receiver

system effective noise temperature is 1500 K, what is Eb/N0 for a link transmitting 2400 bps?

SOLUTION:

PROBLEM 13:

What is the channel capacity for a teleprinter channel with a 300 Hz bandwidth and a signalto-noise ratio of 3 dB, where the noise is white thermal noise?

SOLUTION:

PROBLEM 14:

Adigital signaling system is required to operate at 9600 bps.

a) If a signal element encodes a 4 bit word, what is the minimum required bandwidth of

the channel?

b) Repeat part (a) for the case of 8-bit words.

SOLUTION:

PROBLEM 15:

What is the thermal noise level of a channel with a bandwidth of 10 kHz carrying 1000 watts

of power operating at 500C?

SOLUTION:

PROBLEM 16 (Chapter 3 Problem 3.13,a,b,7):

SOLUTION:

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