# EG7022 Digital Communications Amplitude Of Quadrature Component

### Questions:

A communications link, operates within a bandwidth of 4 kHz.  The signal power at the receiver is -98.0 dBm and the spectral noise density at the receiver is –146 dBm-Hz.  Figure 1.1 shows the eye-diagram for the in-phase amplitude of the signal.  An identical diagram is seen for the quadrature amplitude.   The bit error rate (BER) of the system varies with Eb/N0 as indicated in Figure 1.2.

a)Show that the data-rate is approximately 4 kbit/second.

b)Show that the value of Eb/N0 for this signal is approximately 12 decibels.

c)How many bit-errors would be expected in 1 million bits of this signal?

d)Assuming the signal power, the noise power and the bandwidth remain constant what is the theoretical maximum data-rate that could be sent over this link without bit-errors?

1.Question

e)If the signal power were to fade, what is the maximum symbol-error rate that could occur in this signal due to additive white gaussian noise?

f)Identify the modulation scheme used for this signal.

g)Explain briefly what would happen to the symbol error rate if the amplitude of the in-phase component and the amplitude of the quadrature component were swapped.

2.Question

A communications link uses a Hamming code consisting of four data bits and three parity bits.

a)What advantage has this parity scheme got over a simple scheme that adds just one check-bit per 4-bit data-word?

b)What percentage reduction in the data-rate does this parity scheme impose, compared to sending the data with no check-bits?

c)Assuming errors are evenly spaced throughout the data-stream, what is the maximum bit-error rate that this scheme can successfully deal with?

d)Show that the received codeword contains an error-bit, identify which bit is in error and find the original data-word from the erroneous codeword.

e)State how you would measure the coding gain of the [7,4] Hamming code.

f)For a Hamming code that uses seven parity bits in one codeword, what is the maximum bit-error rate that can be successfully corrected?  (As before, assume that errors are evenly spaced throughout the data-stream)

3.Question

a)According to Maxwell’s equations, what are the two ways to make an electric field?

b)Explain briefly what is meant by a plane wave,

c)A plane wave travels through empty space in the positive z-direction.  State the directions and relative phase of the electric and magnetic field of the wave at any instant of time.

d)A electromagnetic signal of centre frequency 10 GHz and bandwidth 400 MHz travels through a non-magnetic medium which has a relative permittivity equal to 3 – 0.001j.

i.What is the speed of the electromagnetic wave in this material.

ii.Show that the largest value of phase constant,  present in the wave is 370 m-1.

iii.How far can the wave travel through the material before its magnetic field has been reduced to 1% of its original amplitude?

4.Question

a)Figure 4.1 shows a superheterodyne receiver with two local oscillators.  It is to be used to receive various radio stations within the frequency band 4 -12 MHz.  Each radio station has a bandwidth of 100 kHz.  The first filter allows frequencies in the range 10 MHz to 11 MHz to pass, while the second filter allows frequencies 0 – 100 kHz to pass.

Figure 4.1

ii.Over what range of frequencies should the tuneable oscillator be tuneable?

iii.A filter is to be used to block image frequencies.  Where should the filter be placed and what range of frequencies should it block?

iv.What should be the frequency of the second local oscillator (f LO2)?

b)A rectangular metallic waveguide has a cross-section of 5 cm x 3 cm and is filled with polyethylene (relative permittivity = 2.25, relative permeabilty = 1).  A signal containing frequencies 2.5 – 2.8 GHz is fed into the waveguide.

i.What is the dominant range of this waveguide.

ii.What is the difference in speed between the fastest and slowest signals?