Transcript Exponential Carrier Wave Modulation

Questions

Q: Envelope detection was pretty hard to comprehend. Why doesn’t the
envelope detection work on SSB modulation?
a x  1  x ln a 

1
1
( x ln a)2  ( x ln a)3...
2!
3!
Substituting the expression of the envelope to the series expression of
square root reveals that it can not be simplified to the form
A(t )  KAm sin(mt )
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Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Mathematica® output
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Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Questions (cont.)

Q: ... What puzzles me still is how the synchronous detection works. Must
be something about autocorrelation…
ANS: Multiplication with the carrier frequency produces twice the carrier
and around DC-converted components. The latter one is the detected wave

… it would be nice to hear about real life applications between all those
theoretical slides …
ANS: have a look on interesting demos! (http://www.williamsonlabs.com/home.htm)

For me, the most important lesson is that the signals that look awkward and
strange at first sight, can be oftentimes divided in smaller parts and then
make some sense of them. For example phasor presentation visualizes
well what is really happening in amplitude or phase modulation.
Comment: It is easier to understand if one can consider topics from
various point of views
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Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Analysis of de-tuned resonant circuit

Capacitance part of a resonant circuit can be made to be a
function of modulation voltage m(t).
fCC  1 / (2 LC ) Resonance frequency
fCC [ x (t )]  1 / {2 LC[ x (t )]} De-tuned resonance frequency
C[ x (t )]  C0  Cx (t ) Capacitance diode
fCC [ x (t )]  fC (1  Cx (t ) / C0 )1/ 2 , fC  1 / (2 LC0 )

That can be simplified by the series expansion
kx 3k 2 x 2
(1 - kx )  1  
... kx  1
2
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fCC [ x(t )]  fC (1  Cx(t ) / C0 )1/2
1/ 2
L
1 Cx(t ) O 1 d (t )

M
P
2 dt
N2 C Q
C
 fC 1 
0
 (t )  2f t  2
C
4
z
f C x (  )d
2C0 t

f
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Note that this applies for a
relatively small modulation
index
Remember that the
instantaneous frequency is
the derivative of the phase
LP-filter is an approximation of the ideal
integrator
Zin->
<-Zout
Vin
Vout
H ( f )Vin ( f )  Vout ( f )
H ( f )  I ( f ) Z out ( f ) /[ I ( f ) Z in ( f )]  Z out ( f ) / Z in ( f )
( j C ) 1
1
H( f ) 

R  ( j C ) 1 j RC  1
1
H( f ) 
,   1
j RC
Ideal integrator is defined by
t
 Vin ( f ) 1
Vout ( f )  …  vin ( )d   
 Vin (0) ( f )
 
 j 2 f 2
Vout ( f ) V
in ( t ) 
5
(t )
1
1

 (f )
j 2 f 2
… (t   d )   exp( j d )
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen