• Power in an FM signal does not vary with modulation
• FM signals do not have an envelope that reproduces the
• The figure below shows a simplified FM generator
• In FM, it is the instantaneous frequency that
varies linearly with message amplitude
• The modulating signal changes the freq. fc of
the carrier signal
• The bandwidth for FM is high
• It is approx. 10x the signal frequency
• Frequency deviation of
the carrier is
proportional to the
amplitude of the
Frequency Modulation Index
• Another term common to FM is the modulation index, as
determined by the formula:
FM for Tone Signals
• Consider a sinusoidal message
• The instantaneous frequency corresponding to
its FM version is
tfAtm mm 2cos)(
• Inst. frequency has upper and lower bounds
FM Modulation using VCO
dttmctAS fccPM cos
fC - Gain of VCO
c - Free Running Frequency of VCO
Corresponding DC bias
Bandwidth of FM is infinite
• As in the case of AM, this time domain representation of the FM signal can be converted to
an equivalent frequency-domain expression that includes the carrier and sidebands. Because
the mathematics required for this conversion are quite complex, we will only consider the
The Jn(x) functions are known as Bessel Functions of the First Kind. Graphs of Jn(x) look like slowly
decreasing sine and cosine functions. The Jn(x) functions are a closely related family of
functions in the same way that sin(nx) and cos(nx) for a family of similar functions.
The zeroth order Bessel function, J0(m) determines the amplitude of the carrier. The nth Bessel
function Jn(m) determines the amplitude of the nth pair of sidebands. There are two
important concepts contained in the expression shown above
The amplitude of the carrier depends on m. the modulation index. This is quite different from
AM, where the amplitude of the carrier was independent of the value of m
There are an infinite number of sidebands. Thus the theoretical bandwidth of FM is infinite.
An infinite bandwidth signal would be very difficult to transmit.
Fortunately, the higher order sidebands in FM have extremely low
amplitude and may be ignored. For example: if the modulation
index is 5, only the first 7 sidebands are significant in value.
Narrowband and Wideband FM
• There are no theoretical limits to the modulation index or
the frequency deviation of an FM signal
• The limits are a practical compromise between signal-to-
noise ratio and bandwidth
• Government regulations limit the bandwidth of FM
transmissions in terms of maximum frequency deviation
and the maximum modulation frequency
Narrow- and Wideband Signals
• Narrowband FM (NBFM) is used for voice transmissions
• Wideband FM (WBFM) is used for most other
• Strict definition of the term narrowband FM refers to a
signal with mf of less than 0.5
FM signal demodulation
• It is more resistant to noise than an AM signal.
• filtering and Limiting the transmitted signal.
• Differentiation to obtain the phase information in the
• There are four ways to implement differentiation:
Phase-Shift or Quadrature Detection
Phase-Locked Loop (PLL)
The PLL consists of three basic components:
A. Phase detector (PD)
B. Low-pass filter (LPF)
C. Voltage controlled oscillator (VCO)
Sout ( t )Sf ( t )
Sphase( t )
SVCO ( t ) = AVCO ·sin [ 0 t + 0( t )]
Sf ( t ) = Af ·cos [ c t + ( t )]
SVCO ( t )
Phase-Locked Loop (PLL)
• A phase detector compares two input signals and produces an
error signal which is proportional to their phase difference.
• If the output phase drifts, the error signal will increase,
driving the VCO phase in the opposite direction so as to
reduce the error. Thus the output phase is locked to the phase
at the other input. This input is called the reference.
• The output is fed through an optional divider back to the
input of the system, producing a negative feedback loop.
Phase-Locked Loop (PLL)
• Analog phase locked loops are generally built
with an analog phase detector, low pass filter
and VCO placed in a negative feedback
configuration. A digital phase locked loop uses
a digital phase detector; it may also have a
divider in the feedback path or in the
reference path, or both, in order to make the
PLL's output signal frequency a rational
multiple of the reference frequency.
Demodulation by Zero Crossing Detection
• Zero crossing detector
• Positive voltage.
• Negative voltage.
• Pulse generator.
• low-pass filter.
• The advantage of zero crossing detection (and
FM-to-AM conversion) is that no source of the
carrier frequency is required to demodulate the
signal. A digital signal can easily be recovered
from a FM signal in this manner.
• Decoding an analog signal may be difficult by this
method, since the signal at the low-pass filter
output does not closely resemble the baseband
Zero crossing detector
higher inst freq
in turn means