Angle Modulation:
In Angle Modulation angle of carrier is varied according to the amplitude of modulation signal. There are
two types of angle modulation.
1) Frequency Modulation (FM): instantaneous frequency of carrier is varied according to
modulating signals, and FM is also called constant envelop.
S (t) = A0 Cos [θ (t)]  A0 Cos [ωc t + θ0]
Where instantaneous phase of frequency represents as: ω i = dθ/dt
Let’s define some parameters for Frequency Modulation:
Message Signal
m (t)
FM Signal SFM (t) = Ac Cos [2πfc t + 2πk ∫ m (t) dt] 
SFM (t) = Ac Cos [2πfc t +kfAm/fm Sin (2πfmt)]
and power in FM signal is PFM = Ac2/2
In FM frequency modulation index is representing as follows: βi = kfAm/W = Δf / W
where W = highest frequency component in message signal and AM = peak value of
modulating signal.
βf = frequency modulation index is equal to
βf = kfAm/W = Δf / W
where Am = peak value of modulation signal,
Δf = peak frequency deviation of the transmitter, W = max bandwidth of the modulating
signal or W = fmax if modulating signal is a low pass signal.
The Narrow Band Frequency Modulator:
In the narrow band frequency modulation kf g(t) << π/2 let’s consider the general equation
to understand the spectrum of the narrowband FM as follows
SFM (t) = A Cos (ωc t) Cos ( kf g(t)) - A Sin (ωc t) Sin( kf g(t))
Se (ω) = A /2 π [δ (ω - ωc) + δ (ω + ωc)] – f[A kf /2][G (ω + ωc) - G (ω - ωc)]
The Wide Band Frequency Modulator:
In the wide band frequency modulation kf g(t) > π/2 let’s consider the general equation to
understand the spectrum of the wideband FM as follows
SFM (t) = A Cos (ωc t) Cos ( kf g(t)) - A Sin (ωc t) Sin( kf g(t))
The resulting signal function is represent as
SFM (t) = Am Cos (ωc t+ βf Sin (ωm t))
By applying the trigonometric identity we got
SFM (t) = Am Cos (ωc t) Cos (βf Sin (ωm t)) - Am Sin (ωc t) Sin (βf Sin (ωm t))
Let’s look at the approximation of FM bandwidth
Upper band is equal to (fc +- fm) and upper bandwidth BT = 2 (βf + 1) fm
Lower bound of the bandwidth BT = 2 Δ f
There are two main methods of FM modulation:
I)
Direct Method in direct method the carrier frequency fc varied according to the message signal
m (t) furthermore the Voltage Control Oscillator (VCO) varies with baseband amplitude. In
this process Varactor (Voltage variable capacitor) or VCO is used to control the frequency of
carrier with respect to massage signal in order to generate FM signal. There is one problem
when we move narrowband FM to wideband FM carrier frequency fc is no longer stable so in
order to solve that problem the Phase Lock Loop is used because there is restoration comes
up.
II) Indirect Method in indirect method there are two further consideration balanced modulator
generates narrowband FM signal and frequency multiplication. The indirect method
purposed by Armstrong and it is approximation of narrowband FM (Carrier + SSB (90 degree
out of phase) SFM (t) = [Ac Cos (2πfc t)] – [Ac θ (t)Sin (2πfmt)]  Ac Cos (2πfc t + θ (t)) and
SFM (t) = Ac Cos [2πfc t + 2πk ∫ m (t) dt] the problem of this method is phase noise in the
system, which kills the system
2) Phase Modulation (PM): in the phase modulation instantaneous phase of carrier is varied
according to modulating signals. Let’s look at the sinusoidal carrier signals.
Where in Phase Modulation the following parameters are represent follows
PM signal = SPM (t) = Ac Cos [2πfc t + kθ m (t)]
Phase Modulation index = βθ = kθ Am and power represent in PM signal is PPM = Ac2/2
the bandwidth of phase modulation is Bf = 2Δf FM signal can be generated by first
integrating m (t) and then give input to the phase modulator.
There is very interesting relationship between FM and PM, frequency modulation is just
product of integrated message signal with phase modulator, but on the other hand phase
modulation is product of differentiated message signal with frequency modulator. The
method described above represents as follows
FM = PM ∫ m (t) and PM = FM d/dt m (t)
Now let’s look at the spectrum of frequency modulator carrier
SFM (t) = Ac Cos [ωc t + kf ∫ m (t) dt] the general equation for a FM carrier is follows
SFM (t) = A Cos (ωc t) Cos ( kf g(t)) - A Sin (ωc t) Sin( kf g(t))
βp = phase modulation index is equal to
βp = kθ Am = Δθ where Δθ is equal to peak phase deviation of the transmitter
FM demodulation: There are two methods use to detect the frequency modulation
Frequency to amplitude converter circuit and Frequency discriminators further there are several
techniques for detection of FM.
Slope Detector: in slope detection the received signal vin (t) is passing through a limiter to get v1 (t)
then it went through differentiator to become v2 (t). Finally, the signal passes through envelope detector
to receive the message signal vout (t). For better understanding let us form a block diagram.
vin (t)
Limiter
v1 (t)
Differentiator
Envelope
v2 (t)
vout (t)
Detector
v1 (t) = V1 Cos (2πfc t + θ (t))  V1 Cos [2πfc t + 2πkf ∫ m (t) dt]
v2 (t) = V1 [2πfc t + dθ / dt] Sin (2πfc t + θ (t))
vout (t) = V1 [2πfc t + dθ (t) / dt]  V12πfc + V12πkf m (t)
Zero crossing Detector: The second method of FM demodulation is Zero Crossing Detector, which is
easy to explain with diagram. In zero crossing method the received signal is passing through limiter than
differentiator follows by Mono stable vibrator and at the end passed through the Low pass filter. The
zero crossing method counts the number of zeros in the received signal by monitoring the amplitude of
the signal. From the zero crossing method we obtained the pulse train, which represent the receiving
signal. After we differentiate to see where the pulses are and we get the location of start point. Infect
we found out where are the zero crossing means where are the frequency high I have close pulses and
where ever the frequency low the pulses are apart from each others. Then Mono-stable multi-vibrator
average out the impulses by passing through the low pass filter I obtained my modulated signal.
vin (t)
Limiter
v1 (t)
Differentiator
v2 (t)
Mono stable
Multi vibrator
v3 (t)
Low Pass
Filter
vout (t)
Phase Lock Loop for FM detection: The third and the popular method of FM detection is Phase Lock
Loop in this method the internal voltage controlled oscillator (VCO) is provider to generate own
frequency of the modulated FM signal, which is passing through phase detector to check the phase of
the signal with respect to own generated signal and its job to minimized the error. If phase detector not
be able to minimize the error it will track the phase of the input to the oscillator. Finally, the input signal
passed through low pass filter to detect the demodulated signal. The figure below is describe further
Input FM signal Phase
Loop Amplifier
m (t) demodulated output signal
And Low Pass
Filter
Detector
Voltage
Controlled
Oscillator
Quadrature Detection: Fourth method of FM detection is Quadrature Detection, which is the one of the
most popular detection technique. It can be implemented on IC at a very low cost and the phase
difference between original FM signal and the signal at the output of the phase shift network is
detected. In this FM detection method the output of phase detector will be proportional to the
instantaneous frequency of the input FM signal.
Input FM signal
X
Low Pass
Filter
m (t) demodulated
Output signal
Phase Shifter Network
Phase response function: φ (f) = - π/2 + 2πK (f - fc) and the instantaneous frequency f (t) = fc + kfm (t)
Let’s see what happed at the product detector
Vφ (t) = ρ2Ac2 Cos (φ (fi (t)))
Vφ (t) = ρ2Ac2 Cos (π/2 + 2πK ((fi (t) - fc)
Vφ (t) = ρ2Ac2 Sin (2πK kfm (t))
The simplified small angle is follows
V0 (t) = ρ2Ac2 (2πK kfm (t)) == Cm (t)
AM vs. FM
Amplitude Modulation (AM): In AM, there is a linear relationship between the quality of the received
signal and power of the received. In modern AM systems, susceptibility to fading has been improved
through the use of in-band pilot tones which are transmitted along with the standard AM signal. The
modern AM receiver is able to monitor the pilot tone and rapidly adjust the receiver gain to compensate
for the amplitude fluctuations. AM signals are able to occupy less bandwidth as compared to FM signals,
since the transmission system is linear. In AM it is critical to maintain linearity between the applied
message and the amplitude of the transmitted signal, thus linear class A or AB amplifiers are used. In AM
systems, all of the interferes are received at once and must be discriminated after the demodulation
process.
Frequency Modulation (FM):
In FM, the signals have all their information in the phase or frequency of the carrier. This provides a
nonlinear and very rapid improvement in reception quality once a certain minimum received signal
called FM threshold is achieved. FM has noise immunity when compared to AM. FM signals are less
susceptible to atmospheric and impulse noise, which tend to cause rapid fluctuations in the atmosphere
of the received radio signal. Message amplitude variations do not carry information in FM, so burst
noise does not affect FM system performance as much as in AM systems. Small-scale fading can cause
rapid functions in the received signal, thus FM offers superior qualitative performance in fading when
compared to AM. In FM system, it is possible to tradeoff bandwidth occupancy for improved noise
performance. Unlike AM in an FM system the modulation index, and hence bandwidth occupancy can be
varied to obtain greater signal- to noise performance. Under certain conditions the FM signal to noise
ratio improves 6dB for each doubling of bandwidth occupancy. An FM signal is a constant envelope
signal, and so the transmitted power of the message signals. The constant envelope of the transmitted
signal allows efficient class C power amplifiers to be used for RF power amplification of FM. Frequency
modulation exhibits capture effect characteristics. If two signals in the same frequency band are
available at an FM receiver, the one appearing at the higher received signal level is accepted and
demodulated, while the weaker one is rejected. Thus an FM system is very resistant to co-channel
interference and provides excellent subjective received quality.