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Unformatted text preview: t frequency ( at l east over a small band). This scheme suffers from
t he fact t hat t he slope of H (w) of a t uned circuit is linear only over a small band,
a nd therefore causes considerable distortion in t he o utput. T his fault can partially
be corrected by a balanced discriminator t hat uses two resonant circuits, one t uned
above a nd t he o ther t uned below We.
These days, a p hase-locked l oop ( PLL), whose performance is s uperior to
any of t he m ethods discussed here (especially in t he large noise environment) has
become very popular as a demodulator of angle modulated signals because of its
reasonable cost. More discussion a bout m odulation a nd d emodulation of angle
modulated signals appears in reference 4.
A Historical Note I n t he twenties, broadcasting was in its infancy. However, t here was a constant
search for techniques t hat would reduce noise (static). Now, since t he noise power
is p roportional t o t he m odulated signal bandwidth (sidebands), a ttempts were focused on finding a modulation scheme to reduce t he b andwidth. I t was rumored
t hat a new method h ad b een discovered for eliminating sidebands (no sidebands, no
bandwidth!). T he c oncept of FM, where t he c arrier frequency would be varied in
proportion to t he message m (t), a ppeared quite intriguing. T he c arrier frequency
w(t) would be varied with time so t hat w(t) = We + k m(t), where k is a n a rbitrary
c onstant. T he c arrier frequency will remain within t he b and from We - kmp t o 4 Continuous-Time Signal Analysis: T he Fourier Transform 300 + k mp. T he s pectrum, centered a t We, would have a bandwidth 2 kmp, which is
controlled by t he a rbitrary c onstant k. B y using a n a rbitrarily small k, we could
make t he i nformation bandwidth arbitrarily small. This was a passport t o communication heaven. Unfortunately, t he e xperimental results showed t hat s omething
was seriously wrong somewhere. T he F M b andwidth was found t o b e always greater
t han ( at b est e qual to) t he AM b andwidth. In some cases, its bandwidth was several
times t hat of AM.
Careful a nalysis by Carson showed t hat t he F M b andwidth could never be
smaller t han t hat of AM; a t b est equal t o t hat of AM. Unfortunately, Carson did
n ot recognize t he c ompensating advantage of F M in its ability t o s uppress noise.
W ithout any justification, he states, " Thus, F M introduces inherent distortion a nd
has no compensa.ting advantages whatsoever."5 I n his later p aper he says: " In fact,
as more a nd m ore schemes are analyzed a nd t ested, and as t he essential n ature
of t he problem i s clearly perceivable, we a re unavoidably forced t o t he conclusion
t hat s tatic, like t he poor, will always be with us.,,6 This opinion of one o f t he a blest
mathematicians o f t he day in t he communication industry set back t he development
of FM. T he nois€-suppressing advantage of F M was later proved by Major Edwin
H. A rmstrong 7 , a b rilliant engineer whose contributions to t he field o f r adio systems
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