Transcript of ANGLE MODULATION 1. Introduction 2 Another class of modulation methods are frequency and phase...
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- ANGLE MODULATION 1
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- Introduction 2 Another class of modulation methods are
frequency and phase modulation which referred to as angle-
modulation methods. In frequency-modulation (FM), the frequency of
a carrier wave is changed by the message signal. In
phase-modulation (PM), the phase of the carrier is changed
according to the variations in the message signal.
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- Introduction 3 For all AM modulation schemes Modulated spectrum
is the frequency translated message spectrum Transmission BW never
exceeds twice the message BW In Angle modulation Modulated spectrum
is not a translated copy of the message spectrum. Transmission BW
is usually much greater than twice the message BW. The major
benefit of the FM and PM modulation is their high degree of noise
immunity.
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- Introduction 4 Consider a sinusoid, A c cos ( c t+ ) where A c
is the (constant) amplitude, c is the (constant) frequency and is
the initial phase. In the AM modulation, the condition that A c be
a constant is relaxing and the amplitude become a function of the
message signal m(t). the frequency and the phase remain constant
and dont change or effect by the m(t).
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- Introduction 5 In the FM and PM modulation, A c is a constant
but c t+ , instead of being constants it will be a function of
m(t). We must extend the concept of a sinusoid to a generalized
function whose frequency vary with time
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- Generalized Sinusoidal Signal 6 Let us consider a generalized
sinusoidal signal given as A c cos ( (t) ) where the (t) is the
instantaneous angle and is a function of t. The generalized angle
for the conventional sinusoid A c cos ( c t+ ) is (t) = c t+
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- Angle Modulated signal 7 So for angle modulation, the modulated
carrier represented by S angle_mod (t) = A c cos ( (t) ) where A c
is a constant amplitude and (t) is a function of the message signal
m(t). We define the instantaneous radian frequency of the angle
modulated wave i (t) as:
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- Phase Modulation (PM) 9 In phase modulation the angle is varied
linearly with the message signal m(t) as (t) = c t + k p m(t) where
k p is the phase deviation or sensitivity constant. Thus the phase
modulated signal is defined as: S PM (t) = A c cos ( c t + k p m(t)
) The instantaneous radian frequency of S PM (t) is
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- Example 10 If the message signal m(t) = a cos ( m t) is used to
phase modulate the carrier A c cos ( c t) Find the PM modulated
signal S PM (t) = A c cos ( c t + a k p cos ( m t) )
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- Frequency Modulation (FM) 11 In frequency modulation the angle
is varied linearly with the integral of message signal m(t) as
where k f is the frequency deviation or sensitivity constant. Thus
the frequency modulated signal is defined as: The instantaneous
radian frequency of S FM (t) is
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- Example 12 If the message signal m(t) = a cos ( m t) is used to
phase modulate the carrier A c cos ( c t) Find the FM modulated
signal
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- Example 13 In a frequency modulation process m(t) be a periodic
triangular wave with m max (t) =1 and m min (t)=-1 the carrier
frequency is 100 kHz k f = 10 4 Hz/volt find the maximum and
minimum values of the instantaneous frequency f i_max (t) = 100 *10
3 + 10 4 * 1= 100 *10 3 + 10 4 =110 kHz f i_min (t) = 100 *10 3 +
10 4 * -1 = 100 *10 3 - 10 4 =90 kHz
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- The Relationship Between FM and PM 14 There is a close relation
between FM and PM modulations. An FM modulated wave can be
generated by first integrating the message signal m(t) with respect
to time t and thus using the resulting signal as the input to a
phase modulation. A PM modulated wave can be generated by first
differentiating m(t) with respect to time t and then using the
resulting signal as the input to a frequency modulator
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- Bandwidth 16 The FM modulated wave is not band-limited. It has
an infinite bandwidth and is not related to the modulating signal
spectrum in any simple way, as was the case in AM modulation.
Although the theoretical bandwidth of an FM wave is infinite, the
most of the modulated signal power resides in a finite bandwidth.
There are two distinct possibilities in terms of bandwidth:
narrow-band FM and wide-band FM.
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- Single-Tone Frequency Modulation 17 Consider a sinusoidal
modulating signal defined as m(t) = A m cos( 2 f m t) So, the
instantaneous frequency (in Hertz) of the FM signal is f i (t) =f c
+ k f A m cos( 2 f m t) = f c + f cos( 2 f m t) where f is called
the frequency deviation given by f =k f A m The resultant FM signal
is is the modulation index
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- Single-Tone Frequency Modulation 18 The frequency deviation
factor indicates the amount of frequency change in the FM signal
from the carrier frequency f c on either side of it. Thus FM signal
will have the frequency components between (fc - f ) to (fc +f ).
The modulation index, represents the phase deviation of the FM
signal and is measured in radians. Depending on the value of , FM
signal can be classified into two types: 1. Narrow band FM ( >
1).
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