csd hcmut chapter7!8!2012
TRANSCRIPT
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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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(Suppressed-Carrier) DSB (2)
DSB transmitted power:
Product DSB modulator:
Balanced modulator:
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(Suppressed-Carrier) DSB (3)
Ring modulator:
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(Suppressed-Carrier) DSB (4)
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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(Suppressed-Carrier) DSB (5)
Using pilot carrier:
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(Suppressed-Carrier) SSB (1)
SSB signals and spectra:
SSB bandwidth and power:
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(Suppressed-Carrier) SSB (2)
SSB modulator:
Based on DSB and filter:
Two-step SSB modulator:
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(Suppressed-Carrier) SSB (3)
Phase-shift method:
HQ(f): 90o phase shifter
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(Suppressed-Carrier) SSB (4)
Weaver method:
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(Suppressed-Carrier) SSB (5)
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)