Blake Problem Computation

Introduction to Communication System

1.

A receiver has a power bandwidth of 10 kHz. A resistor that matches the receiver input impedance is connected across its antenna terminals. What is the noise power contributed by that resistor in the receiver bandwidth, if the resistor has temperature of 27°C

3.

An AM broadcast transmitter has a carrier power output of 50 kW. What total power would be produce with 80% modulation?

4.

An transmitter generates an LSB signal with a carrier frequency of 8 MHz. What frequencies will appear at the output with a two-tone modulating signal with frequencies of 2 kHz and 3.5 kHz?

5.

An AM transmitter is modulated by two sine waves at 1 kHz and 2.5 kHz, with modulations of 25% and 50% respectively. What is the effective modulation index?

6.

An AM signal has the following characteristics fc = 150 MHz, Ec = 50 V, fm = 3 kHz, Em = 40 V. For this signal, find: (a) the modulation index (b) the bandwidth (c) the peak voltage of the upper side frequencies

7.

An AM transmitter supplies 10 kW of carrier power to a 50 Ω load. It operates at a carrier frequency of 1.2 MHz and is 80% modulated by a 3 kHz sine wave. (a) Calculate the total average power in the signal, in watts and dBW (b) Calculate the RMS voltage of the signal (c) Calculate the peak voltage of the signal

2.

A 300 Ω resistor is connected across the 300 Ω antenna input of a television receiver. The bandwidth of the receiver is 6 MHz and the resistor is at room temperature (293 K or 20°C or 68°F). Find the noise power and noise voltage applied to the receiver input

3.

A diode noise generator is required to produce 10 μV of noise in a receiver with an input impedance of 75 Ω, resistive, and a noise power bandwidth of 200 kHz.(these values are typical of FM broadcast receivers). What must the current through the diode be?

4.

A receiver produces a noise power of 200 mW with no signal. The output level increases to 5 W when a signal is applied. Calculate (S+N)/N as a power ratio and in decibels.

5.

The signal power at the input to an amplifier is 100 μW and the noise power is 1 μW. At the output, the signal power is 1 W and the noise power is 30 mW. What is the amplifier noise figure as a ratio?

8.

An AM transmitter has a carrier power of 50 W at a carrier frequency of 12 MHz. It is modulated at 80% by a 1 kHz sine wave. How much power is contained in the sidebands?

6.

The signal at the input of an amplifier has a S/N of 42 dB. If the amplifier has a noise figure of 6 dB, what is the S/N at the output (in decibels)?

9.

7.

A three-stage amplifier has stages with the ff specs: Stage Power Gain Noise Figure 1 10 2 2 25 4 3 30 5 Calculate the power gain, noise figure and noise temperature of the entire amplifier, assuming matched conditions

CB radio was developed using full-carrier DSB AM. It operates using 40 channels, each 10 kHz wide. When SSBSC is used, the same carrier frequencies are used as with conventional AM, but the transceivers are switchable to either lower or upper sideband. How many channels are available when SSB is used

Angle Modulation

1.

An FM modulator has kf = 30 kHz/V and operates at a carrier frequency of 175 MHz. Find the output frequency for an instantaneous value or the modulating signal equal to: (a) 150 mV (b) -2 V

2.

The same FM modulator as in the previous problem is modulated by a 3 V sine wave. Calculate the deviation

3.

An FM broadcast transmitter operates at its maximum deviation of 75 kHz. Find the modulation index for a sinusoidal modulating signal with a frequency of: (a) 15 kHz (b) 50 Hz

4.

A phase modulator has kp = 2 rad/V. What RMS voltage of a sine wave would cause a peak phase deviation of 60°?

5.

An FM communications transmitter has a maximum frequency deviation of 5 kHz and a range of modulating frequencies from 300 Hz to 3 kHz. What is the maximum phase shift that it produces?

6.

A phase modulation has a sensitivity of kp = 3 rad/V. How much frequency deviation does it produce with a sine-wave input of 2 V peak at a frequency of 1 kHz?

7.

An FM signal has a deviation of 3 kHz and a modulating frequency of 1 kHz. Its total power Pt is 5 W, developed across a 50 Ω resistive load. The carrier frequency is 160 MHz. (a) Calculate the RMS signal voltage Vt

8.

Use Carson’s rule to calculate the bandwidth of the signal used in problem 7

9.

An FM signal has a deviation of 10 kHz and a modulating frequency of 2 kHz. Calculate the modulation index

Radio Frequency Circuits 1.

2.

A varactor has maximum capacitance of 80 pF and is used in a tuned circuit with a 100 μH inductor. (a) Find the resonant frequency with no tuning voltage applied. (b) Find the tuning voltage necessary for the circuit to resonate at double the frequency found in part (a) A portable radio transmitter has to operate at temperatures from -5°C to 35°C. If the signal is derived from a crystal oscillator with a temperature coefficient of +1 ppm/ degree C and it transmits at exactly 146 MHz at 20°C, find the transmitting frequency at the two extremes of the operating temperature range

3.

Sine-wave signals with frequencies of 10 MHz and 11 MHz are applied to a square-low mixer. What frequencies appear at the output

4.

A phase-locked loop has a VCO with a free-running frequency of 12 MHz. As the frequency of the reference input is gradually raised from zero, the loop locks at 10 MHz and comes out of lock again at 16 MHz. (a) Find the capture range and lock range (b) Suppose that the experiment is repeated, but this time the reference input begins with a very high frequency and steadily moves downward. Predict the frequencies at which lock would be achieved and lost

5.

Configure a simple PLL synthesizer using a 10 MHz crystal so that it will generate the AM broadcast frequencies from 540 to 1700 kHz

6.

A synthesizer has P = 10 and fref = 10 kHz. Find the minimum frequency step size and compare it with that obtained using a fixed divided-by-10 prescaler

Amplitude Modulation 1.

Find the modulation index if a 10 V carrier is amplitude-modulated by three different frequencies with amplitudes of 1 V, 2 V, and 3 V respectively.

2.

CB radio channels are 10 kHz apart. What is the maximum modulation frequency that can be used if a signal is to remain entirely within its assigned channel?

10. When a positive dc voltage of 5 V is applied to an FM modulator its output frequency drops by 100 kHz. Calculate the deviation sensitivity of the modulator 11. A phase modulator with kp = 3 rad/V is modulated by a sine wave an RMS voltage of 4 V at a frequency of 5 kHz. Calculate the phase modulation index

12. A sine wave of frequency 1 kHz phase-modulates a carrier at 123 MHz. The peak deviation is 0.5 rad. Calculate the maximum frequency deviation 13. A phase modulation system operates with a modulation index of 1.5. What is the maximum phase shift in degrees? 14. An FM transmitter has a carrier frequency of 220 MHz. Its modulation index is 3 with a modulating frequency of 5 kHz. The total power output is 100 W into a 5 Ω load. (a) What is the deviation?

5. 6. 7.

An FM broadcast band receiver tunes from 88 to 108 MHz. the IF is 10.7 MHz, and the receiver uses high-side injection. Calculate the range of local oscillator frequencies

8.

A receiver’s IF filter has a shape factor of 2.5 and a bandwidth of 6 kHz at the 6 dB down point. What is its bandwidth at 60 dB down?

15. An FM signal has a deviation of 10 kHz and is modulated by a sine wave with a frequency of 5 kHz. The carrier frequency is 150 MHz and the signal has a total power of 12.5 W, operating into an impedance of 50 Ω. (a) What is the modulation index? (b) How much power is present at the carrier frequency? (c) What is the voltage level of the second sideband below the carrier frequency? (d) What is the bandwidth of the signal, ignoring all components that have less than 1% of the total signal voltage? 16. A frequency modulation system requires a signal-to-noise ratio of 40 dB at the detector output. The modulating frequency is 2 kHz, and the deviation is 50 kHz. Calculate the required minimum S/N at the detector output

An IF transformer operates at 455 kHz. The primary circuit has a Q of 40 and the secondary has a Q of 30. Find (a) the critical coupling factor (b) the optimum coupling factor (c) the bandwidth using the optimum coupling factor A superheterodyne receivers is tuned to a frequency of 5 MHz when the local frequency is 6.65 MHz. What is the IF?

Digital Communications 1.

A telephone line has a bandwidth of 3.2 kHz, and a signal-to-noise ratio of 35 dB. A signal is transmitted down this line using a four-level code. What is the maximum theoretical data rate?

2.

An attempt is made to transmit a baseband frequency of 30 kHz using a digital audio system with a sampling rate of 44.1 kHz. What audible frequency would result?

3.

Calculate the number of levels if the number of bits per sample is (a) 8 (as in telephony) (b) 16 (as in compact disc audio systems)

4.

Find the maximum dynamic range for a linear PCM system using 16bit quantizing

5.

Calculate the minimum data rate needed to transmit audio with a sampling rate of 40 kHz and 14 bits per sample

6.

Convert the 12-bit sample 100110100100 into an 8-bit compressed code

Transmitter 1.

A crystal oscillator is accurate within 0.0005%. How far off frequency could its output be at 27 MHz?

2.

A transmitter has a carrier power output of 10 W at an efficiency of 70%. How much power must be supplied by the modulating amplifier for 100% modulation?

3.

A transmitter operates from a 12 V supply, with a collector current of 2A. The modulation transformer has turns ratio of 4:1. What is the load impedance seen by the audio amplifier?

4.

A collector-modulated Class C amplifier has a carrier output power Pc of 100 W and an efficiency of 70%. Calculate the supply power and the transistor power dissipation with 100% modulation.

5.

An AM transmitter is required to produce 10 W of carrier power when operating from a 15 V supply. What is the required load impedance as seen from the collector?

6.

The power amplifier of an AM transmitter has an output carrier power of 25 W and an efficiency of 70% and is collector-modulated. How much audio power will have to be supplied to this stage for 100% modulation?

7.

A transmitter uses twelve modules in its solid-state output stage. Calculate the power reduction (in decibels) that would occur if one module fails

8.

An AM transmitter operates into a 50 Ω resistive load. The RMS voltage measured at the output is 250 V without modulation and 300 V with modulation, using the true RMS reading meter. Find: (a) the power with modulation (b) the power without modulation (c) the modulation index (d) the peak voltage with modulation (e) the overall efficiency with modulation if the transmitter allows 3 kW from the AC line when modulated

Receivers 1.

A tuned circuit tunes the AM radio broadcast band (from 540 to 1700 kHz). If its bandwidth is 10 kHz at 540 kHz, what is it at 1700 kHz?

2.

A receiver has a sensitivity of 0.5 μV and a blocking dynamic range of 70 dB. What is the strongest signal that can be present along with a 0.5 μV signal without blocking taking place?

3.

An FM detector produces a peak-to-peak output voltage of 1.2 V from an FM signal that is modulated to 10 kHz deviation by a sine wave. What is the detector sensitivity?

4.

A PLL FM detector uses a VCO with kf = 100 kHz/V. If it receives an FM signal with a deviation of 75 kHz and sine-wave modulation, what is the RMS output voltage from the detector?

The telephone System 1.

A local loop has a resistance of 1 kΩ, and the telephone connected to it has an off-hook resistance of 200 Ω. Calculate the loop current and the voltage across the telephone when the phone is (a) on hook (b) off hook

2.

A telephone signal takes 2 ms to reach its destination Calculate the via net loss required for an acceptable amount of echo

Data Transmission 1.

Calculate the maximum efficiency of an asynchronous communication system using ASCII with seven data bits, one start bit, one stop bit, and one parity bit

2.

How many Hamming bits are required for a block length of 21 message bits?

Digital Modulation and Modems 1.

A radio channel has a bandwidth of 10 kHz and a signal-to-noise ratio of 15 dB. What is the maximum data rate that can be transmitted: (a) using any system? (b) using a code with four possible states?

2.

A modulator transmits symbols, each of which has sixty-four different possible states, 10,000 times per second. Calculate the band rate and bit rate.

3.

The North American TDMA digital cell phone standards transmit at 24.3 kilo baud using DQPSK. What is the channel data rate?

4.

A modem uses sixteen different phase angles and four different amplifiers. How many bit does it transmit for each symbol?

5.

A typical dial-up telephone connection has a bandwidth of 3 kHz and a signal-to-noise ratio of 30 dB. Calculate the Shannon limit

Multiplexing and Multiple-Access 1.

How many of each of the following signals would fit into a 1 MHz spectrum allocation? (a) voice, with a maximum frequency of 4 kHz,

modulated using SSBSC AM (b) the same voice signal using DSB full-carrier AM (c) High-fidelity music with a maximum baseband frequency of 15 kHz, using wideband FM with a maximum duration of 75 kHz (d) A bit stream at 56 kbps, using QPSK modulation and assuming a noiseless channel

2.

3.

A voice transmission occupies a channel 30 kHz wide. Suppose a spread-spectrum system is used to increase its bandwidth to 10 MHz. If the signal has a total signal power of 110 dBm at the receiver input and the system noise temperature referred to the same point is 300 K, calculate the signal-to-noise ratio for both systems.

The critical frequency at a particular time is 11.6 MHz. What is the MUF for a transmitting station if the required angle of incidence for propagation to a desired destination is 70°?

7.

A taxi company uses a central dispatcher, with an antenna at the top of a 15 m tower, to communicate with taxicabs. The taxi antenna are on the roofs of the cars, approximately 1.5 m above the ground. Calculate the maximum communication distance: (a) between the dispatcher and a taxi (b) between two taxis

8.

Find the propagation loss for a signal at 800 MHz, with a transmitting antenna height of 30 m, over a distance of 10 km, using (a) the freespace model (b) the mobile-propagation model

9.

An automobile travels at 60 km/hr. Find the time between fades if the car uses: (a) a cell phone at 800 MHz (b) a PCS phone at 1900 MHz

A frequency-hopping spread-spectrum system hops to each of 100 frequencies every 10 seconds. How long does it spends on each frequency?

Multiplexing and Multiple-Access 1.

6.

A coaxial cable has a capacitance of 90 pF/m and a characteristic impedance of 50 Ω. Find the inductance of a 1m length

2.

Find the characteristic impedance of each of the following lines: (a) an open-wire line with conductors 3 mm in diameter separated by 10 mm (b) a coaxial cable using a solid polyethylene dielectric having Er = 2.3, with an inner conductor 2 mm in diameter and an outer conductor 8 mm in inside diameter

10. A metropolitan area of 1000 square km is to be covered by cells with a radius of 2 km. How many cell sites would be required, assuming hexagonal cells?

3.

Find the velocity factor and propagation velocity for a cable with a Teflon dielectric (Er = 2.1)

1.

Calculate the length of a half-wave dipole for an operating frequency of 20 MHz.

4.

What length of standard RG – 8/V coaxial cable would be required to obtain a 45° phase shift at 200 MHz

2.

A dipole antenna has a radiation resistance of 67 Ω and a loss resistance of 5 Ω, measured at the feed point. Calculate the efficiency

5.

A 50 Ω line is terminated in a 25 Ω resistance. Find the SWR

3.

Two antennas have gains of 5.3 dBi and 4.5 dBd respectively. Which has greater gain?

6.

A generator sends 50 mW down a 50 Ω line. The generator is matched to the line, but the load is not. If the coefficient of reflection is 0.5 how much power is reflected and how much is dissipated in the load?

4.

The ERP of a transmitting station is specified as 17 W in a given direction. Express this as an EIRP in dBm so that it can be used with the path loss equation

7.

A transmitter supplies 50 W to a load through a line with an SWR of 2:1. Find the power absorbed by the load.

5.

8.

A series tuned circuit operating at a frequency of 1 GHz is to be constructed from a shorted section of air dielectric coaxial cable. What length should be used?

A helical antenna with eight turns is to be constructed for a frequency of 1.2 GHz (a) Calculate the optimum diameter and spacing for the antenna and find the total length of the antenna (b) Calculate the antenna gain in dBi (c) Calculate the beamwidth

6.

A parabolic antenna has a diameter of 3 m. An efficiency of 60%, and operates at a frequency of 4 GHz. Calculate its gain and beamwidth

7.

Calculate the length of a practical half-wave dipole for a frequency of 15 MHz

8.

A transmitter with a power output of 100 watts is connected to a dipole antenna with a radiation resistance of 75 Ω and an ohmic resistance of 2 Ω (a) How much power is radiated into space?

9.

Given that a half-wave dipole has a gain of 2.14 dBi, calculate the electric field strength at a distance of 10 km in free space in the direction of maximum radiation from a half-wave dipole that is fed by means of lossless, matched line, by a 15 W transmitter

9.

A transmitter is required to deliver 100W to an antenna through 45 m of coaxial cable with a loss of 4 dB/100 m. What must be the output power of the transmitter, assuming the line is matched?

10. A TDR display shows a discontinuity 1.4 μs from the start. If the line has a velocity factor of 0.8, How far is the fault form the reflectometer? 11. Two adjacent minima on a slotted line are 23 cm apart. Find the wavelength and frequency, assuming a velocity factor of 95% 12. The forward power in a transmission line is 150 W, and the reverse power is 20 W. Calculate the SWR on the line

Antennas

10. Calculate

the length of a quarter-wave monopole antenna for a frequency of 1000 kHz

Radio-wave Propagation 1.

Find the characteristic impedance of polyethylene which has a dielectric constant of 2.3

2.

The dielectric strength of air is about 3 MV/m. Arcing is likely to take place at field strengths greater than that. What is the maximum power density of an electromagnetic wave in air?

3.

A power of 100 W is supplied to an isotropic radiator. What is the power density at a point 10 km away?

4.

Find the electric field strength for the signal in the previous problem

5.

A radio wave moves from air (Er = 1) to glass (Er = 7.8). Its angle of incidence is 30°. What is the angle of refraction?

Microwave Devices 1.

Find the cutoff frequency for the TE10 mode in an air-dielectric waveguide with an inside cross section of 2 cm by 4 cm. Over what frequency range is the dominant mode the only one that will propagate?

2.

Find the group velocity for the waveguide in problem 1 at a frequency of 5 GHz