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Lecture 1: Introductory Topics

Prof. Park

ELC 222

Essex County College

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Modulation

• Modulation is the process of putting information onto a high-frequency carrier for transmission.

• The low-frequency information is called the intelligence.

• The high-frequency medium is called the carrier.

• The demodulation is the reverse process of modulation.

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Mathematical Representation of Sine Wave

• v = Vp sin(t + )• Where v = instantaneous value• Vp = peak value = angular velocity = 2f = phase angle• AM: Amplitude Modulation• FM: Frequency Modulation• PM: Phase Modulation

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Electrical Noise

• Electrical noise: Any undesired voltages or currents that ultimately end up appearing in a circuit.

• Static: Electrical noise that may occur in the output of a receiver.

• External Noise: Noise introduced by the transmitting medium.

• Internal Noise: Noise introduced by the receiver.

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External Noise

• Human-Made Noise: Noise produced by spark-producing system such as engine ignition systems, fluorescent lights, commutators in electric motors, and power lines.

• Atmospheric Noise: Noise caused by naturally occurring disturbances in the earth’s atmosphere.

• Space Noise: Noise produced outside the earth’s atmosphere.

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Internal Noise

• Thermal Noise: Noise caused by thermal interaction between free electrons and vibrating ions in a conductor.

• Shot Noise: Noise introduced by carriers in the pn junctions of semiconductors

• Excess Noise: Noise occurring at frequencies below 1khz, varying in amplitude inversely proportional to the frequence

• Transit-Time Noise: Noise produced in semiconductors when the transit time of the carriers crossing a junction is close to the signal’s period.

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Thermal Noise

• Thermal Noise: Noise caused by thermal interaction between free electrons and vibrating ions in a conductor.

• Johnson Noise: Another name for thermal noise, first studied by J. B. Johnson in 1928.

• White Noise: Another name for thermal noise because its frequency content is uniform across the spectrum.

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Thermal Noise

• Pn = kTf

• k = Boltzmann’s constant (1.3810-23 J/K)• T = Resistor temperature in kelvin (K) f = Frequency bandwidth of the system• The rms noise voltage en has a maximum at

fRkTen 4

Example 1-4

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Determine the noise voltage produced by a 1Mohm resistor at room temperature (17C) over 1MHz bandwidth.

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A communication system block diagram

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Noise effect on a receiver’s first and second amplifier stages

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Resistance noise generator

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Device noise versus frequency

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Signal-To-Noise Ratio

• Signal-To-Noise Ratio: Relative measure of desired signal power to noise power

• Noise Figure (NF): A figure describing how noisy a device is in decibels

• Noise ratio (NR): A figure describing how noisy a device is as a ratio having no units

NRNS

NSNF

oo

ii1010 log10

/

/log10

Example 1-6

• A transistor amplifier has measured S/R of 10 at its input and 5 at its output.– A) Calculate the NR– B) Calculate the NF

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Noise Due to Amplifiers in cascade

• Friiss’s formula

• NR = NR

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Information and Bandwidth

• Hartley’s Law:

information bandwidth time of transmission• Fourier Analysis: Method of representing

complex repetitive waveforms by sinusoidal components

• Fast Fourier Transform (FFT): A technique for converting time-varying information to its frequency component

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AM vs. FM

AM FM Analog TV

Low Limit 535 kHz 88 MHz

High Limit 1605 kHz 108 MHz

Channel BW 10 kHz 200 kHz 6 MHz

Baseband BW 5 kHz 15 kHz

Max. Stations 107 100

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Example 1-11

• Determine the resonant frequency for the circuit below. Calculate its impedance at f = 12 kHz.

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Example 1-12

• Determine the resonant frequency for the circuit when R1 = 20, R2 = 1, L = 1mH, C = 0.4µF, and ein = 50 mV. Calculate eout at fr and at f = 12 kHz.

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Example 1-13

• A filter circuit has a response as below. Determine (a) bandwidth, (b) Q, (c) L if C = 0.001µF, and (d) total circuit resistance.

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Example 1-14

• A parallel LC tank circuit is made up of an inductor of 3mH and a winding of 2. The capacitance is 0.47µF. Determine (a) fr, (b) Q, (c) Zmax, and (d) BW.