C4_AM

1Assoc Prof. Dr. Ho Van KhuongTele. Dept., HCMUT

Email: [email protected]

Linear CW Modulation

2Continuous Wave Modulation (1)

Modulation is the systematic alteration of one waveform, called thecarrier, according to the characteristics of another waveform, themodulating signal or message. The goal is to produce an informationbearing modulated waveform best suited to the given communication task.

Analog modulation methods can be divided into 2 main classes:continuous-wave modulation and pulse coded modulation. Furthermore,

1. CW-modulation (continuous-wave) can be:a) Linear CW-modulation

AM amplitude modulationDSB double sideband modulationVSB vestigial sideband modulationSSB single sideband modulation


b) Exponential CW-modulationFM frequency modulationPM phase modulation

2) Pulse coded modulation (for discrete signals) can be:PAM pulse coded amplitude modulationPDM pulse delay modulationPPM pulse position modulation

CW modulation includes a high frequency sinusoidal signal, pulsemodulation contains a square wave.


Example of Analog Modulation Methods

E.g., applications of AM signals: commercial broadcasting, multiplexing of telephone signals, short wave military and amateur communications.


Assumptions:Assumptions of information signal x(t) are as follows Bandlimited:

Normalized:

Tone Modulation:

6AM Modulation (1)

AM-Signal in time domain:

where fc is carrier frequency,Ac is the amplitude of the unmodulated carrier, > 0: modulation index.

AM-signal (modulated envelope):

Envelope reproduces the shape of x(t) if

7AM Modulation (2)

100 % modulation: = 1

Overmodulation: > 1: It causes phase reversals and envelope distortion.

8AM Modulation (3)

AM-Signal in Frequency Domain

Here, we have written out only the positive-frequency half. Negativefrequency half will be the hermitian image of the above equation.

The bandwidth of the modulated signal is twice the bandwidth ofmodulating (message) signal: BT = 2W.

9AM Modulation (4)

Power of AM-Signal:Average transmitted power is:

When fc >> W, second term averages to zero. Ifand

Then,

This can be represented by using the power of unmodulated carrier Pcand the power per sideband Psb:

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AM Modulation (5)

It follows from the condition | x(t)| 1 that

Consequently, at least 50% of the total transmitted power resides in acarrier term thats independent of x(t) and thus conveys no messageinformation.

AM-signal is not practical for transmitting DC-component or signals with significant low frequency content.

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DSB-Modulation (1)

DSB: double-sideband suppressed-carrier modulation: two sidebands, suppressed carrier

In frequency domain:

Like AM-spectrum without carrierBandwidth BT = 2WPhase reversal whenever x(t) crosses 0.

In Time domain:Envelope:

Phase:

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DSB-Modulation (2)

Note: Envelope itself cannot be used for detection because of the phasereversal

Detection is more difficult than in the case of AM DSB conserves power but requires complicated demodulation

circuitry, whereas AM requires increased power to permit simple envelope detection.

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DSB-Modulation (3)

Power of DSB-signal:All of the average transmitted power is used for information transition.

The peak envelope power is the limiting factor in the transmittersAmax2 (Amax = max A(t) ).

If Amax2 is fixed and other factors are equal, a DSB-transmitter produces four times the sideband power of an AM-transmitter. Since the transmission range is proportional to the power per sideband, DSB provide 4 times longer path length.

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Tone Modulation and Phasor Analysis (1)Setting

DSB:

AM:

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Tone Modulation and Phasor Analysis (2)

Phasor analysis is helpful for studying effects of transmission distortion and interference:

Example: Consider tone-modulated AM with Am = 2/3. The phasor diagram is constructed as (including carrier phasor and two sideband phasors):

The phasor sum equals the envelope Ac(1 + 2/3 cosmt)

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Tone Modulation and Phasor Analysis (3)

Suppose that a transmission channel completely removes the lower sideband, then we obtain a phasor as:

Now the envelope becomes:

Therefore, the envelop distortion can be determined. Also, the amplitude distortion produces a time-varying phase (t).

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SSB-Modulation (1)

SSB: Single-sideband (suppressed-sideband)

AM is wasteful of both power and bandwidth, DSB is wasteful ofbandwidth.

In the case of real baseband signals, the positive frequencies contains all the information of the signal.

=> The upper and lower sidebands of DSB are symmetric about the carrier frequency, so either one contains all the message information.

USSB: Lower sideband is removed.

LSSB: Upper sideband is removed.

In both cases, the bandwidth is

and the transmitted power is

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SSB-Modulation (2)

SSB spectra:

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SSB-Modulation (3)

Tone-modulation:

Note: Pure sine wave with frequency fc fmEnvelope is constant => envelope detection does not work.

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Hilbert Transform (1)

Hilbert transform is useful when analysing the SSB modulation. We will also see in what follows the relationship between Hilbert transform and analytic signals.

In the following, we are using a quadrature filter with transfer function:

The corresponding impulse response is

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Now, let the input signal to a quadrature filter be x(t). Then, the outputsignal x(t) is defined to be the Hilbert-transform of x(t):

The quadrature filter is non-causal, so it is not realizable. It can be,however, well approximated over a finite frequency band.

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Hilbert-transform properties:

A signal x(t) and its Hilbert transform x(t) have the same amplitude spectrum. In addition, the energy or power in a signal and in its Hilbert transform are also equal.

If x(t) is the Hilbert transform of x(t), then - x(t) is the Hilberttransform of x(t). i.e., that two successive frequency shifts of -90degrees result in a total shift of 180 degrees.

A signal x(t) and its Hilbert transform x(t) are orthogonal.

Hilbert transforms are useful in analyzing SSB signals.

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Examples:(a) The Hilbert-transform for a sinusoidal signal corresponds to 90phase-shift:

(b) The Hilbert-transform of a rectangular pulse is:

Then,

(See more on p. 123, [1])

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SSB Modulation: Analysis with Arbitrary Message (1)

We begin with the general DSB-modulated signal:

The idea is to use the method of low-pass equivalent signals:

We assume that the sideband filters are ideal:

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Then, the output of the ideal filter:

Frequency domain waveform of SSB signal:

Time-domain waveform of SSB signal:

A signal under the form is called an analytic signal.

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Lowpass bandpass transformation yields:

This means that we can represent the SSB-modulated signal with in-phase and quadrature-phase components as:

The SSB envelope is:

Due to the complexity of the above expression, it is a difficult task tosketch SSB waveforms or to determine the peak envelope power.

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Example: SSB with pulse modulation

SSB envelope A(t) exhibits infinite peaks (horns) at t = 0 and t = , the instants when x(t) has stepwise discontinuties.

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Remarks:

Whenever the SSB modulating signal has abrupt transitions, the Hilbert transform contains sharp peaks. In practice, the message needs to be lowpass filtered before SSB modulation.

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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Analytic Signal

An analytic signal, in general, is a signal which has only positivefrequency components. Thus, its frequency spectrum is zero when f < 0.

An analytic signal is also defined as:

(this is also called pre-envelope of a real signal).

Analytic signals are used in the analysis of SSB modulation. SSB modulation can be studied as follows: first, we form the analytic lowpass signal, then we apply a frequency translation (at carrier frequency):

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VSB Modulation (1)VSB (Vestigial sideband): A compromise between DSB and SSB:

Bandwidth closer to SSB Easier to implement than SSB The message can include also small frequencies

Consider a modulation signal of very large bandwidth having significantlow frequency content (e.g., television video, facsimile, high-speed datasignals). Bandwidth conservation argues for the use of SSB, but practical SSB signals have poor low-frequency response (due to non-ideality of practical filters). On the other hand, DSB works quite well for low message frequencies, but the transmission bandwidth is twice that of SSB. The compromise is VSB.

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VSB Modulation (2)

One sideband is passed almost completely, while just a trace, or a vestige, of the other sideband is included.

If we take the USB case, the sideband filter transfer function H(f) has to fulfil:

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VSB Modulation (3)

The filter transition band is symmetric with respect to fc in a way that:

Usually, we want that the transfer function HT(f) of the total chain (transmitter + receiver) is symmetric in a way that:

The processing of the vestigial sideband can be done either in the transmitter or in the receiver. Then, this calls for a little bit wider vestigial sideband in the other end. The processing can also be shared equally between the transmitter and the receiver.

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VSB Modulation (4)

VSB signal in time domain

The transmitted power is not easy to be determined exactly but it isbounded by:

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VSB Modulation (5)

VSB+C (VSB & carrier)Time domain waveform:

In-phase and quadrature-phase components are given by

The envelope is

Hence, if is not too large and not too small, then

Envelope detection works.

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VSB Modulation (6)

In practice, we have to find a compromise between the following: Envelope distortion (related to the demodulation complexity) Power efficiency Bandwidth

Usually, practical solutions are found empirically.

In practice, VSB+C is used in traditional TV broadcasting systems, such as NTSC, PAL and SECAM.

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I/Q Modulation or QAMQAM: Quadrature Amplitude Modulation.

The general representation of a bandpas signal consists of two independent components (in-phase and quadrature-phase components). Based on this, it is possible to modulate two independent messages, x1(t) and x2(t), into one carrier => QAM signal:

Assuming that the bandwidths of the two messages are the same, thebandwidth of the QAM signal equals the DSB bandwidth. Then, if it is necessary to transmit two messages, QAM has the SSB bandwidth efficiency.This QAM modulation principle is used commonly as follows:

PAL and NTSC colour TV systems are partially based on QAM QAM is used extensively in digital communications (will be studied

later)

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Frequency Conversion and Linear Demodulation

Demodulation (for AM, DSB, SSB and VSB) implies downward frequency translation in order to recover the original message.

Demodulators fall into two categories: Envelope (non-coherent) detectors. Synchronous (coherent) detectors.

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Envelope Detection (for AM)

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Synchronous Detection (1)

The local oscillator signal is synchronized in phase and frequency with the carrier.

A generalized AM-/DSB-/SSB-/VSB-signal:

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Synchronous Detection (2)

Here, KD is a detector specific constant. If needed, the DC-term can be filtered out.

It should be noted that the synchronous detector attenuates the quadrature-phase component completely.

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Synchronous Detection of a VSB Signal

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Carrier Synchronization

In a good-quality synchronous detection, the local oscillator signal is exactly synchronized to the carrier in both frequency and phase. The synchronization can be based on:

1. Carrier (if present, the envelope detection is usually used).2. Partially attenuated carrier.3. Pilot-signal that is synchronized to the carrier (e.g., half of th carrier frequency).4. Short carrier burst that is repeated from time to time.

In practice, a phase-locked loop (PLL) is used to lock the local oscillator phase and frequency to the received pilot-signal.

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Phase & Frequency Errors in Synchronous Detection (1)

The local oscillator signal:

DSB with sine wave modulation demodulated signal:

SSB with sine wave modulation demodulated signal:

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If the LO phase is drifting: 0, = 0 with SSB, the phase errors appear as delay distortion (extreme case:

delay of 90 degrees output signal becomes the Hilbert transform of the input signal). However, human ear can tolerate rather high delay distortions no serious effect in speech signals

with DSB, the amplitude is varying 0 ... KD (if phase error is + or 90 degrees, the amplitude vanishes completely) an apparent fading effect.

If the LO frequency is drifting: 0, = 0 with SSB the frequency is changing the harmonic structure of

speech is distorted, tolerable error 10 Hz. with DSB, a pair of frequency tones is produced worse than with

SSB.

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Summary: phase and frequency synchronization requirements are rather modest for voice transmission via SSB. But in data, facsimile and video systems with suppressed carrier, careful synchronization is a must. Consequently, TV broadcasting employs VSB+C rather than suppressed carrier VSB.

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Synchronization Errors in QAM

In the case of QAM, the in-phase and quadrature modulated signals can be separated only if the local oscillator is well synchronized to the carrier.

Phase error in local oscillator causes leakage. For instance, 900 phase error changes the I to Q signal and vice versa.

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Slide Number 1Continuous Wave Modulation (1)Continuous Wave Modulation (2)Continuous Wave Modulation (3)Continuous Wave Modulation (4)AM Modulation (1)AM Modulation (2)AM Modulation (3)AM Modulation (4)AM Modulation (5)Slide Number 11DSB-Modulation (1)DSB-Modulation (2)DSB-Modulation (3)Tone Modulation and Phasor Analysis (1)Tone Modulation and Phasor Analysis (2)Tone Modulation and Phasor Analysis (3)SSB-Modulation (1)SSB-Modulation (2)SSB-Modulation (3)Hilbert Transform (1)Hilbert Transform (2)Hilbert Transform (3)Hilbert Transform (4)SSB Modulation: Analysis with Arbitrary Message (1)SSB Modulation: Analysis with Arbitrary Message (2)SSB Modulation: Analysis with Arbitrary Message (3)SSB Modulation: Analysis with Arbitrary Message (4)SSB Modulation: Analysis with Arbitrary Message (5)SSB Modulation: Analysis with Arbitrary Message (6)Analytic Signal VSB Modulation (1)VSB Modulation (2)VSB Modulation (3)VSB Modulation (4)VSB Modulation (5)VSB Modulation (6)I/Q Modulation or QAM Slide Number 39Frequency Conversion and Linear DemodulationEnvelope Detection (for AM)Synchronous Detection (1)Synchronous Detection (2)Synchronous Detection of a VSB SignalCarrier Synchronization Phase & Frequency Errors in Synchronous Detection (1)Phase & Frequency Errors in Synchronous Detection (2)Phase & Frequency Errors in Synchronous Detection (3)Synchronization Errors in QAMSlide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54

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