csd hcmut chapter7!8!2012

7/29/2019 Csd Hcmut Chapter7!8!2012

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Dept. of Telecomm. Eng.Faculty of EEE

CSD2012DHT, HCMUT1

Chapter 7:

Analog Modulators


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References

[1] J. J. Carr,RF Components and Circuits, Newnes, 2002.


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Analog Modulation

Amplitude Modulation:

Standard amplitude modulation (AM) with carrier.

Suppressed-carrier double-sideband modulation (DSB).

Single-sideband modulation (SSB).

Vestige-sideband modulation (VSB).

Frequency Modulation

Phase Modulation


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Standard AM (1)

AM signal and spectra:

The AM signal is:

where is positive constant called AM modulation index, x(t) is message,

Accosctis carrier signal.


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Standard AM (2)

Message spectrum with bandwidth W:

AM spectrum: AM bandwidth is 2W


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Standard AM (3)

AM transmitted power:

where Pc represents unmodulated carrier power:

and Psb represents power per sideband:

where Sx is average message power.

Iffc >>W and 1, then the message can be extracted fromxc(t) by a

simple envelope detector.


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Standard AM (4)

Product modulator for AM:

Using Multiplier:


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Standard AM (5)

Using square-law element:


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Standard AM (6)

We assumed that the nonlinear element approximates the square

law transfer curve:

Thus, with

High-level modulation using class C amplifier:


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Standard AM (7)

AM demodulation:

Synchronous detection (coherent detection): The oscillator ofdemodulator is exactly synchronized (both phase and frequency) with

the carrier.

Using PLL for carrier synchronization.


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Standard AM (8)

Envelop detection:


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(Suppressed-Carrier) DSB (1)

DSB signal and spectra: The wasted carrier power in AM can be

eliminated by setting = 1 and suppressing the carrier-frequency

component. The resulting DSB signal is:


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DSB transmitted power:

Product DSB modulator:

Balanced modulator:


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Ring modulator:


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DSB demodulator:

Synchronous detection (coherent detection): As AM demodulator.

Required carrier synchronization.

Envelope reconstruction (for suppressed carrier modulation):

Required carrier synchronization.


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Using pilot carrier:


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(Suppressed-Carrier) SSB (1)

SSB signals and spectra:

SSB bandwidth and power:


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SSB modulator:

Based on DSB and filter:

Two-step SSB modulator:


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Phase-shift method:

HQ(f): 90o phase shifter


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Dept. of Telecomm. Eng.

Faculty of EEE

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Weaver method:


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SSB demodulator: Similar to DSB demodulator.


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Carrier Synchronization for Coherent Detection (1)

Squaring loop:


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Carrier Synchronization for Coherent Detection (2)

Costas loop:


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PM/ FM (1)

PM and FM signals: Considering a signal with time-varying phase:

The total instantaneous angle:

Therefore:

Ifc(t) contains the message informationx(t), then it is exponential

modulation (or angle modulation).

The phase modulation (PM) is defined by

so that


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PM/ FM (2)

The constant

( 180o) represents the maximum phase shift (or PM

index, or phase deviation) produced byx(t).

In the case offrequency modulation (FM), the instantaneous frequency is

defined as:

The constant frequencyf called frequency deviation, represents themaximum shift off(t) relative to the carrier frequencyfc

By definition:

where

Then, the FM signal has and integration yields the PM:


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PM/ FM (3)

Ift0 is selected such that (t0) = 0, then

Therefore, The FM signal is written as:


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PM/ FM (4)


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PM/ FM (5)

Average transmitted power (for PM and FM): regardless of

messagex(t):

Narrowband PM and FM: Representing the exponential modulation

as:

where

If

so that


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PM/ FM (6)

Then the spectrum ofxc(t) in term of the message spectrum is:

where

Therefore, we conclude that if the message has bandwidth ofW


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PM/ FM (7)

The parameter is the modulation index for PM and FM in the case of

tone modulation.

Narrowband PM/FM tone modulation requires


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PM/ FM (8)

For arbitrary (wideband PM/FM tone modulation):

using

The coefficientJn() are Bessel function of first kind.


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PM/ FM (9)

Finally, we obtain:

Using the property:

Then, we obtain the compact form:


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PM/ FM (10)

Selected values ofJn()


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PM/ FM (11)

Bandwidth of PM/FM tone modulation: According to Carsons

rule:

where


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PM/ FM (12)

Direct FM and VCO:


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PM/ FM (13)


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PM/ FM (14)

Phase modulators and indirect FM:

Narrowband phase modulator:

Indirect FM transmitter:


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PM/ FM (15)

FM/PM detector (demodulator) using PLL:


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PM/ FM (16)

csd hcmut chapter7!8!2012

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