ECET412a - Midterm - Lectures 3 and 4

ECET412a

Principles of Communications Course

Joel C. Delos Angeles B.S. ECE 2

Course information

Scope of the course

Principles of Communications

Resources

Lectures posted in Yahoo Group

Course Syllabus

Reading Materials

3

Resources

Course material Course text book:

Carlson, B., Crilly P. (2010). Communications Systems: An Introduction to Signals and Noise in Electrical Communication. 5th ed. Boston: McGraw-Hill.

Additional recommended books Electronic Communications Systems W. Tomasi. Prentice Hall, 4th ed

2001 (or 5th edition, 2004)

Material accessible from course yahoo group: Message Posts

Lecture slides (.ppt, pdf)

Assignments

Joel C. Delos Angeles B.S. ECE Lecture 1: Introduction

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Scope of the course

Course Outline (May change depending on period

time constraints)

Introduction - (Prelims)

Fourier Series, Fourier Transforms and Continuous

Spectra (Prelims)

Signal Transmission and Filtering - (Midterms)

Linear CW Modulation - (Midterms )

Exponential CW Modulation (Finals)

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Lecturer

Course responsible and lecturer and giving

tutorials:

Joel C. Delos Angeles

Office: CEAT CTH 214

Tuesday/Thursday

1:00 to 4:00 PM

Email: [email protected];

[email protected]

ECET412a


Lecture 3

Signal Transmission and Filtering

Primary Reference Book: Carlson Chapter 3

pages 112-124,126-131, 134-136, 137-140,

143-146, 147-151, 153-154,

Midterms

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In Lec 3, we are going to talk about:

Response of LTI Systems

Signal Distortion in Transmission

Transmission Loss and Decibels

Filters and Filtering

Joel C. Delos Angeles B.S. ECE Lecture 3: Signal Transmission and Filtering

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Background

Signal transmission - process whereby an electrical waveform gets from one location to another, ideally arriving without distortion.

Signal filtering operation which purposefully distorts a waveform by altering its spectral content.

Most transmission systems and filters have in common the properties of linearity and time invariance (LTI).

These properties allow us to model both transmission and filtering in the time domain in terms of the impulse response, or in the frequency domain in terms of the frequency response


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Objectives

1. State and apply the inputoutput relations for an LTI system in terms of its impulse response h(t), step response g(t), or transfer function H(f) (Sect. 3.1)

2. Use frequency-domain analysis to obtain an exact or approximate expression for the output of a system (Sect. 3.1).

3. Find H(f) from the block diagram of a simple system (Sect. 3.1).

4. Distinguish between amplitude distortion, delay distortion, linear distortion, and nonlinear distortion (Sect. 3.2)

5. Identify the frequency ranges that yield distortionless transmission for a given channel (Sect. 3.2).

6. Use dB calculations to find the signal power in a cable transmission system with amplifiers (Sect. 3.3).

7. Discuss the characteristics of and requirements for transmission over fiber optic and satellite systems (Sect. 3.3).

8. Identify the characteristics and sketch H(f) and h(t) for an ideal LPF, BPF, or HPF (Sect. 3.4).

9. Find the 3 dB bandwidth of a real LPF, given H(f) (Sect. 3.4).

10. State and apply the bandwidth requirements for pulse transmission (Sect. 3.4).


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RESPONSE OF LTI SYSTEMS

Joel C. Delos Angeles B.S. ECE

Excitation-and-response relationship between input and output

Energy storage elements and other internal effects may cause the output waveform to look quite different from the input

Lecture 3: Signal Transmission and Filtering

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Impulse Response and Superposition


Assume: no internal stored energy so y(t) is due entirely to x(t)

Linear (superposition principle applies):

Time-Invariant


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Define: The systems response to an impulse input

Thus, the superposition integral:

Or, the forced response y(t) is the convolution of the input (t) and the system impulse response h(t)


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System analysis in the time domain thus requires knowledge of the impulse response along with the ability to carry out a convolution. Alternatively, we may calculate first the systems step response

where


Define: unit step function

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Time Response of an nth order system


The order n is equal to the number of energy-storage elements (below is 1st order)

The step response (input is a step function)


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Time Response of an 1st order system


The impulse response (when input is an impulse)

One can now find the response y(t) to an arbitrary input x(t)


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Time Response of an 1st order system


Let x(t) = A for 0 < t < , then the response is


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System Gain and Phase Shift


Since Ay/Ax = |H(f0)| and any frequency f0, then H(f) is the amplitude ratio as a function of frequency or the amplitude response or gain

arg H(f) represents the system phase shift since y x = arg H(f0)

Plots of |H(f0)| and arg H(f0) versus frequency gives the systems frequency response


ECET412a


Lecture 4

Linear Continuous-Wave Modulation

Primary Reference Book: Carlson Chapter 4

Midterms

Joel C. Delos Angeles B.S. ECE Lecture 4: Linear CW Modulation

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In Lec 4, we are going to talk about:

Bandpass Signals and Systems

DSB Amplitude Modulation

Modulators and Transmitters

Suppressed-Sideband AM

Frequency Conversion and Demodulation


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Background

Modulation - the systematic alteration of one waveform, called the carrier, according to the characteristics of another waveform, the modulating signal or message, to produce an information-bearing modulated wave with properties best suited to the given communication task.

CW modulation systems the carrier is a sinusoidal wave modulated by an analog signal (e.g. AM, FM)

Linear CW modulation involves direct frequency translation of the message spectrum


Background - Modulation

Modulating Signal + Carrier Wave

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Modulation Benefits and Applications

Joel C. Delos Angeles B.S. ECE Lecture 1: Introduction

1) For Efficient Transmission antennas for line-of-sight requires at least 1/10 of signal wavelength

2) To overcome hardware limitations minimize cost if fractional bandwidth (absolute bandwidth / center frequency) is kept within 1 to 10%

3) To reduce noise and interference (wideband noise reduction using much greater transmission bandwidth than the bandwidth of modulating signal)

4) For frequency assignment

5) For multiplexing / multiple access

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Objectives

1. Given a bandpass signal, find its envelope and phase, in-phase and quadrature components, and lowpass equivalent signal and spectrum (Sect. 4.1).

2. State and apply the fractional-bandwidth rule of thumb for bandpass systems (Sect. 4.1).

3. Sketch the waveform and envelope of an AM or DSB signal, and identify the spectral properties of AM, DSB, SSB, and VSB (Sects. 4.2 and 4.4).

4. Construct the line spectrum, and find the sideband power and total power of an AM, DSB, SSB or VSB signal with tone modulation (Sects. 4.2 and 4.4).

5. Distinguish between product, power-law, and balanced modulators, and analyze a modulation system (Sect. 4.3).

6. Identify the characteristics of synchronous, homodyne, and envelope detection (Sect. 4.5).


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BANDPASS SIGNALS AND SYSTEMS

Applying Fourier frequency translation or modulation property:

Most long-haul transmission systems have a bandpass frequency response.

The properties of the transmission system are similar to those of a bandpass filter, and any signal transmitted on such a system must have a bandpass spectrum.


Arbitrary message waveform x(t) with spectrum X(f):

Fall-back position for ease of analysis is tone modulation:

What is the spectrum of a tone message signal?

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Analog Message Conventions


In general, multiplying the message by cos 2fCt in the time domain translates its spectrum to frequency fc

Note how the shape of X(f) is preserved in the graph of Xbp(f); the modulated signal occupies BT = 2W Hz of spectrum.

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Analog Message Conventions


Bandpass signal

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Bandpass Signals


envelope

phase

envelope

phase phase phase

envelope

phase

bandpass condition

Simplest bandpass system

or immediately from ylp(t)

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Bandpass Transmission


Voltage Transfer Function H(f)

where the resonant frequency f0 and quality factor Q are related to the element values by

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Bandpass Transmission Tuned Circuit


3-dB (half-power) bandwidth

since practical tuned circuits typically have 10 < Q < 100 then 0.01 f0 < B < 0.10 f0

Antennas in radio systems produce considerable distortion when the frequency range is small compared to the carrier frequency fC.

Designing reasonably distortionless bandpass amplifier is difficult if B is too small or too large compared to fC.

Thus rule of thumb for fractional bandwidth

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Bandpass Transmission Tuned Circuit


Otherwise, the signal distortion may be beyond the scope of practical equalizers.

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Bandpass Transmission


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Bandpass Signals - Bandwidth


1. Absolute bandwidth. This is where 100% of the energy is confined between some frequency range of fa -> fb. (If we have ideal filters and unlimited time signals)

2. 3 dB / half-power bandwidth. The frequency(s) where the signal power starts to decrease by 3 dB.

3. Noise equivalent bandwidth. Equal to the total signal power over all frequencies divided by the value of the power spectral density at fC.

4. Null-to-null bandwidth. Frequency spacing between a signal spectrums first set of zero crossings.

5. Occupied bandwidth. This is an FCC definition, which states, The frequency bandwidth such that, below its lower and above its upper frequency limits, the mean powers radiated are each equal to 0.5 percent of the total mean power radiated by a given emission. In other words, 99% of the energy is contained in the signals bandwidth.

6. Relative power spectrum bandwidth. This is where the level of power outside the bandwidth limits is reduced to some value relative to its maximum level. This is usually specified in negative decibels (dB). For example, consider a broadcast FM signal with a maximum carrier power of 1000 watts and relative power spectrum bandwidth of -40 dB (i.e., 1/10,000). Thus we would expect the stations power emission to not exceed 0.1 W outside of fC 100 kHz.

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Bandpass Transmission - Bandwidth


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DOUBLE-SIDEBAND AM


Two types of DSB Standard AM

DSB-Suppressed Carrier (DSB-SC)

AM Signals and Spectra

The envelope of the modulated carrier has the same shape as the message or modulating signal x(t)

where AC is the unmodulated carrier amplitude

and is the modulation index

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The signals envelope is then

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1 AC [ 1 + x(t) ] does not go negative

100% modulation

= 1

Amin = 0; Amax = 2 Ac

Overmodulation ( > 1)

causes phase reversals and envelope distortion

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Frequency Domain (positive-side only)

NOTE: Transmission bandwidth is twice the baseband bandwidth. BT is an important consideration in comparing modulation systems

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Average transmitted power of AM signal

from

we have

assuming the message has zero dc component, the average of x(t) =0; carrier average is also equal to zero

NOTE: Transmission bandwidth is twice the baseband bandwidth

0 0 0 0

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If the average power of the message or modulating signal is

then

In terms of power of each sideband (upper and lower)

where


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PC = power of the unmodulated carrier (note when = 0; no modulation)

PSB = power of each sideband

The modulation constraint |x(t)| 1 makes


At least 50% (often close to 2/3) of the total transmitted power is wasted carrier power

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DSB-SC Signals and Spectra



The wasted carrier power can be eliminated by setting = 1 and suppressing the unmodulated carrier-frequency component

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For standard AM, xC(t) has no time-varying phase (i.e. the value of xC(t) is always positive and (t) is zero

Its in-phase and quadrature components are

However for DSB-SC:

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The envelope takes on the form of |x(t)| rather than x(t) as in standard AM

Full recovery of the message requires knowledge of the phase reversals a simple envelope detector will not suffice (circuit complexity)

The trade-off is that all of the average transmitted power goes to information-bearing sidebands (efficiency), thus

DSB conserves power but requires complicated demodulation circuitry whereas AM requires increased power to permit simple envelope detection.

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In practice, transmitters are limited by its peak envelope power A2max

Under maximum modulation conditions, for DSB, Amax = AC; for AM Amax = 2AC

Thus for AM

and for DSB-SC

yields

If is Amax is fixed and other factors are equal, a DSB transmitter produces 4x the sideband power of an AM transmitter.

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DSB AM : Exercises


1) Consider a radio transmitter rated for ST 3kW and A2max 8 kW. Let the modulating signal be a tone with so with Am = 1.

a) Find the modulating signal power Sx

b) If the modulation is DSB, find the maximum possible power per sideband (hint: use both the formula for ST and the one for PSB/A

2max and choose the smaller value allowed for PSB

c) If the modulation is AM with 100% modulation, find the maximum allowed PSB (again use the two specifications to get the lower value)

d) How far will the DSB signal travel compared to the AM signal?

z

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DSB AM : Exercises


2) Let the modulating signal be a square wave that switches periodically between x(t) = 1 and x(t) = -1. a) Sketch xC(t) when the modulation is AM with = 0.5

b) with AM with = 1

c) with DSB

3) Suppose a voice signal has |x(t)|max = 1 and Sx= 1/5. Calculate the values of ST and A

2max needed to get

PSB = 10 W for

a. DSB

b. AM with = 1

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Tone Modulation


Tone-modulated DSB waveform

Line spectra for tone-modulated DSB

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Tone Modulation


Tone-modulated AM waveform

Line spectra for tone-modulated AM

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DSB-AM: Exercises


1) AM DSBFC signal with carrier 100 KHz and a maximum modulating signal frequency of 5 KHz

a. Frequency limits of upper and lower sidebands

b. Spectral Bandwidth

c. Draw frequency spectrum

d. Repeat a to c if tone input to AM modulator is 3 KHz

2) Input to a conventional AM modulator is a 500 KHz carrier with amplitude 20 V. Modulating signal input is 10 KHz that is of sufficient amplitude to cause a change in the output wave of +/- 7.5 V, Determine

a. Upper and lower side frequencies

b. Modulation coefficient /percent modulation

c. Peak amplitude of modulated carrier

d. Upper and lower side frequency voltages

e. Maximum and Minimum amplitudes of the envelope

f. Expression for the modulated wave

g. Draw the output spectrum

h. Sketch the output envelope (i.e. time-domain)

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DSB-AM: Exercises


3) AM DSBFC signal with carrier 100 KHz and a maximum modulating signal frequency of 5 KHz with peak unmodulated carrier of 10 volts, load resistance of 10 ohms, and 100% modulation

a. Power of carrier, upper and lower sidebands

b. Total sideband power

c. Total power in the modulated wave if index is 0.5

d. Draw the power spectrum

e. Repeat a to d if modulation coefficient is 0.3

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MODULATORS AND TRANSMITTERS

Time-varying or nonlinear systems since LTI systems do not produce new frequency components

Modulators

Product Modulator (low-level)

Square-law Modulator (low-level)

Switching Modulator (high-level)

A modulator is a component inside a transmitter/transceiver


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Product Modulators


Product:

Schematic Diagram with Analog Multiplier

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Product Modulators


Variable Transconductance Multiplier:

Input voltage v1 is applied to a differential amplifier whose gain depends on the transconductance of the transistors which, in turn, varies with the total emitter current

Input v2 controls the emitter current by means of a voltage-to-current converter, so the differential output equals Kv1v2

Most analog multipliers are limited to low power levels and relatively low frequencies (low-level modulator)

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Low-level AM Modulator


Modulation takes place prior to the output element of the final stage of the transmitter - less modulating signal power is required to achieve a high percentage

of modulation

Emitter modulator

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The modulating signal varies the gain of the amplifier at a sinusoidal rate equal to the frequency of the modulating signal

Coupling capacitor C2 removes the modulating signal frequency from the waveform, producing a symmetrical AM envelope at Vout

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For a low-level AM modulator with modulation coefficient of 0.8, quiescent voltage gain of 100, and an input carrier frequency of 500 KHz with an amplitude VC = 5 mV and a 1 KHz modulating signal, determine:

a) Maximum and minimum voltage gains

b) Maximum and minimum amplitudes for Vout c) The output AM envelope

d) The output signal AM equation

e) The output signal spectrum

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Square-law Modulators


Field-effect transistor as the nonlinear element and a parallel RLC circuit as the filter.

Assume the nonlinear element approximates the square-law transfer curve

Can be used at higher frequencies

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Square-law Modulators


We just need a bandpass filter (BPF) with

center frequency = ? and bandwidth = ?

Thus,

The last term is the desired AM wave provided it can be separated from the rest (AC = a1 and = 2a2/a1)

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Balanced Modulators: DSB-SC


Two AM modulators arranged in a balanced configuration to cancel out the carrier.

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Balanced Modulators: DSB-SC


Ring Modulator

A square-wave carrier c(t) with frequency causes the

diodes to switch on and off.

Functionally, multiplying x(t) with c(t):

We just need a bandpass filter (BPF) with

center frequency = ? and bandwidth = ?

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Medium-Power AM Modulator


Collector modulator

Consider: without applied modulating signal

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Medium-Power AM Modulator


When modulating signal is applied:

1) The modulating signal adds to and subtracts from the DC supply VCC and the output voltage waveform swings from a maximum value (2Vcc) to a minimum value Vce(sat) 0

2) The operation is as before only this time, there is a slow time-varying power supply

3) What is the stage after this?

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Switching Modulators


The active device, typically a transistor, serves as a switch driven at the carrier frequency, closing briefly every 1/fC sec.

The RLC load, called a tank circuit, is tuned to resonate at fC, so the switching action causes the tank circuit to ring sinusoidally.

The steady-state load voltage in absence of modulation is then v(t) = V cos Ct

Adding the message to the supply voltage, say via transformer, gives v(t) = [V + Nx(t)] cos Ct

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Switching Modulators


In view of the heavy filtering required, square-law modulators are used primarily for low-level modulation, i.e., at power levels lower than the transmitted value.

Substantial linear amplification becomes necessary to bring the power up to ST

But RF power amplifiers of the required linearity are not without problems of their own, and it often is better to employ high-level modulation if is ST to be large

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Low-level AM Transmitters


Preamplifier (linear voltage amplifier with high input impedance) - raises source signal amplitude to a usable level with minimum nonlinear distortion and as little thermal noise as possible

Modulating signal driver (linear amplifier) - amplifies the information signal to an adequate level to sufficiently drive the modulator

RF carrier oscillator - generates stable carrier signal

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Low-level AM Transmitters


Buffer amplifier (low-gain, high-input impedance linear amplifier) - isolates the oscillator from the high-power amplifiers

Intermediate and final power amplifiers (push-pull modulators) requires linearity with low-level transmitters to maintain symmetry in the AM envelope

Coupling network - matches output impedance of the final amplifier to the transmission line/antenna

Applications in low-power, low-capacity systems: wireless intercoms, remote-control units, pagers and short-range walkie-talkies

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High-level AM Transmitters


Addition of power amplifier (To provide higher power modulating signal necessary to achieve 100% modulation)

The modulator circuit has three primary functions:

Provide the circuitry necessary for modulation to occur

Act as the final power amplifier

Frequency up-converter: translates low-frequency information signals to RF signals

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SUPPRESSED SIDEBAND AM

Conventional amplitude modulation is wasteful of both transmission power and bandwidth

Suppressing the carrier reduces the transmission power

Either one of the sidebands contains ALL of the message information

Suppressing one sideband, in whole or part, reduces transmission bandwidth and leads to single-sideband modulation (SSB) or vestigial-sideband modulation (VSB)


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SSB Signals and Spectra


Time-domain representation is not immediately obvious save for the special case of tone modulation

Note: Unlike AM and DSB, the amplitude of the modulated signal is constant. So envelope (peak) detection wont work to demodulate SSB

For the general case where the input modulating signal x(t) is not a tone, the modulated signal is expressed as

where is the Hilbert transform of x(t)

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SSB is not appropriate for pulse transmission, digital data, or similar applications, and more suitable modulating signals (such as audio waveforms) should

still be lowpass filtered before modulation in order to smooth out any abrupt transitions that might cause excessive horns or smearing

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Time-domain of modulated output when modulating signal input is a pulse

A perfect cutoff at f=fC cannot be synthesized, so a real sideband filter will either pass a portion of the undesired sideband or attenuate a portion of the desired sideband (the former is Vestigial Sideband)

Fortunately, many modulating signals have little or no frequency content their spectra having holes at zero frequency

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SSB Generation


It may not be possible to obtain a sufficiently high carrier frequency with a given message spectrum. For these cases the modulation process can be carried out in two (or more) steps

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SSB Generation


An SSB signal consists of two DSB waveforms with quadrature carriers and modulating signals x(t) and bypassing the need for sideband filters

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SSB Generation: Phase-Shift Method


Exercise: Let x(t) = cos mt

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SSB Generation: Weavers Modulator


Consider a modulating signal of very large bandwidth having significant low-frequency content (analog TV video, fax, and high-speed data signals

Bandwidth conservation argues for SSB, but practical SSB systems have poor low-frequency response

DSB works quite well for low message frequencies but the transmission bandwidth is twice that of SSB

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Vestigial SB Signals and Spectra


Suppose an AM (DSB-FC) wave is applied to a vestigial sideband filter the modulation scheme is termed VSB plus carrier (VSB + C)

Used for television video transmission.

The unsuppressed carrier allows for envelope detection (an approximation), as in AM while retaining the bandwidth conservation of SSB.

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Vestigial SB Signals and Spectra


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FREQUENCY CONVERSION AND DEMODULATION

Demodulation implies downward frequency translation in order to recover the message from the modulated wave.

Types of demodulators

Synchronous detectors

Envelope detectors

Frequency translation, or conversion, is also used to shift a modulated signal to new carrier frequency (up or down) for amplification or other processing.


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Frequency Conversion

Frequency conversion starts with multiplication by a sinusoid

With appropriate filtering, the signal is up-converted or down-converted. The operation itself is termed heterodyning or mixing.


Frequency converter or mixer

?? Sketch the output spectrum

cos 1t

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Frequency Conversion

Below is a simplified transponder in a satellite relay that provides two-way communication between two ground stations.

Different carrier frequencies, 6 GHz and 4 GHz, are used on the uplink and downlink to prevent self-oscillation due to positive feedback from the transmitting side to the receiving side.

A frequency converter translates the spectrum of the amplified uplink signal to the passband of the downlink amplifier.


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Synchronous Detection

All types of linear modulation (AM,DSB,SSB) can be detected by a product demodulator

Synchronous or coherent assumes that the local oscillator (LO) is exactly synchronized (in-phase) with the carrier


0 0

General AM equation

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Synchronous Detection: VSB ??

Baseband and corresponding VSB spectra

Frequency-translated signal prior to filtering shows recovery of original baseband modulating signal


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Synchronous Detection: Challenge

The crux of the problem is synchronization synchronizing an oscillator (LO) in the receiver that is not even present in the incoming signal if carrier is supressed. Thus, suppressed-carrier systems may have a small amount of carrier reinserted in xC(t) at the transmitter

This pilot carrier is picked off at the receiver by a narrow bandpass filter, amplified, and used in place of a LO (local oscillator)

In practice, the amplified pilot serves to synchronize a separate oscillator rather than be used directly (using a phase-locked loop)


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Envelope Detection

Synchronous detectors are best for weak signal reception

In most cases, the envelope detector is much simpler and more suitable (if a carrier is present)


R2C2 acts as a DC block to remove the bias of the unmodulated carrier component.

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Envelope Detection

Some DSB and SSB demodulators employ the method of envelope reconstruction. The addition (reinsertion) of a large, locally generated carrier to the incoming signal reconstructs the envelope for recovery by an envelope detector.

This method eliminates signal multiplication but does not get around the synchronization problem, for the local carrier must be as well synchronized as the LO in a product demodulator.


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The Superheterodyne Receiver


Intermediate Freq (IF) = 455 KHz (standard for AM)

Preselectors function is to reject image frequencies

ECET412a - Midterm - Lectures 3 and 4

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