MODULATION:

Modulation is the process of superimposing a low frequency information signal that is to be transmitted on a high frequency carrier signal, by changing one of its characteristics (Amplitude, Frequency or Phase) according to the instantaneous values of the low frequency information signal.

Important terms:-

1. Modulating signal:- It is the Low frequency signal ie. Data or Information signal that is to be transmitted after modulation.
2. Carrier signal:- It is the High frequency signal whose characteristics like(Amplitude, Frequency or Phase) is varied in accordance with the modulating signal.
3. Modulated signal:- It is the carrier signal after modulation.

Modulating signal + Carrier signal = Modulated signal

NEED FOR MODULATION:

To reduce the antenna size:- Usually the transmitting and receiving antenna should have lengths comparable to quarter of the wavelength of the signal to be transmitted. In the case of AF signals, whose frequency is b/w 20Hz and 20 KHz, the wavelength lies b/w 10,000Km and 10Km. Thus the antenna height should be 1/4th of this length, which is not practical. So a HF carrier is modulated with the information signal and transmitted.
To multiplex the a number of signals:- It allows several broadcasting stations to transmit simultaneously at different carrier frequencies.
To increase coverage area:- The coverage area is more for high frequency signals compared to low frequency signals.
To reduce the noise & interference
To reduce equipment complexity




AMPLITUDE MODULATION
In amplitude modulation the amplitude of the carrier wave is varied in accordance with the instantaneous values of the amplitude of the information signal that is to be transmitted. Here the phase angle and frequency are not altered.
Amplitude modulation or AM as it is often called is a form of modulation used for radio transmissions for broadcasting and two way radio communication applications. Although one of the earliest used forms of modulation it is still in widespread use today.
Modulation Index(m):

The depth of modulation, the percentage of modulation or the modulation index is the ratio of peak value of amplitude of modulating wave to the amplitude of the carrier wave.
m= Vm / Vc
Modulation index lies b/w 0 and 1 and it is often expressed as a percentage. So it is called percentage modulation.

Amplitude of AM signal
A = Vc + vm
= Vc + Vm. Sin (ωm t)
= Vc + Vc. m. Sin (ωm t) (since m=Vm/Vc)
= Vc( 1 + m. Sin (ωm t) )

Instantaneous voltage of AM wave
vAM = A Sin (ωc t)
= Vc( 1 + m.Sin (ωm t) ) . Sin (ωc t)
= Vc. Sin (ωc t) + m. Vc . Sin (ωm t) . Sin (ωc t)
= Vc. Sin (ωc t) + (m. Vc /2). [Cos (ωc - ωm)t - Cos (ωc + ωm)t]
= Vc. Sin (2πfc t) + (m. Vc /2). [Cos 2π(fc - fm)t - Cos 2π(fc + fm)t]


The previous result showed that the amplitude modulation had a frequency component at the carrier frequency and two components with the information at the (ωc + ωm) and (ωc - ωm) frequencies. These are called the upper and lower sidebands.
First term {Vc. Sin (ωc t)} à Unmodulated carrier
Second term {(m. Vc /2). [Cos (ωc - ωm)t - Cos (ωc + ωm)t]} à Modulated sidebands
Advantages of Amplitude Modulatio:
There are several advantages of amplitude modulation, and some of these reasons have meant that it is still in widespread use today:
It is simple to implement
it can be demodulated using a circuit consisting of very few components
AM receivers are very cheap as no specialized components are needed.
Disadvantages of amplitude modulation:
Amplitude modulation is a very basic form of modulation, and although its simplicity is one of its major advantages, other more sophisticated systems provide a number of advantages. Accordingly it is worth looking at some of the disadvantages of amplitude modulation.
Less efficiency: It is not efficient in terms of its use of power usage, bandwidth, requiring a bandwidth equal to twice that of the highest audio frequency
Noisy reception: It is prone to high levels of noise because most noise is amplitude based and obviously AM detectors are sensitive to it.
Poor audio quality










FREQUENCY MODULATION
To generate a frequency modulated signal, the frequency of the high frequency carrier is changed in line with the instantaneous values of amplitude of the information signal. Frequency modulation changes the frequency of the carrier wave in response to the amplitude of the original signal. An example of this is shown in the figure below. The higher the amplitude of the modulating signal, the frequency of the transmitted wave is more and as the amplitude of the modulating signal decreases the frequency of the transmitted wave decreases.

Frequency of FM signal
f = fc + fc. K. Vm. Cos (ωm t) ---------------( 1 )
= fc. [1 + K. Vm. Cos (ωm t)]
Here f is the frequency of modulated signal
fc is the carrier frequency
K is a proportionality constant
From the equation, we can see that, a fraction (which is determined by the instantaneous values of amplitude of the information signal and the proportionality constant) of the carrier frequency is added with the carrier frequency. The second term ie. fc. K. Vm. Cos (ωm t) is the deviation from the actual carrier frequency. The maximum deviation can occure when (ωm t) is 0 or 180. ie. When Cos (ωm t) is +1 or -1. So for maximum deviation,
f = fc. [1 ± K.Vm.]
= fc. ± K.Vm.fc
So the maximum deviation is δ = K.Vm.fc

Let the instantaneous voltage of FM wave be
vFM = A.Sinθ
We have to find the expression for θ to write the complete o/p equation. For finding θ we need ω.
ω = 2πf
ie f = ω/ 2π and fc = ωc /2π
Substitute in equation (1)
(ω/ 2π) = (ωc /2π) [1 + K. Vm. Cos (ωm t)]
ω = ωc [1 + K. Vm. Cos (ωm t)]

θ = ∫ ω. dt
= ∫ ωc [1 + K. Vm. Cos (ωm t)]. dt
= ωc. ∫ [1 + K. Vm. Cos (ωm t)]. dt
= ωc. [ t + { K. Vm. Sin (ωm t) / ωm }]
= ωc. t + {K. Vm. 2 π fc. Sin (ωm t) / 2 π fm }
= ωc. t + (K. Vm. fc. / fm). Sin (ωm t)
= ωc. t + (δ / fm). Sin (ωm t) (because, δ = K.Vm.fc)
The term (δ / fm) is the modulation index in the case of FM.
ie. mf = Maximum deviation / Modulating frequency
= (δ / fm)
So, θ = ωc. t + mf. Sin (ωm t)
vFM = A.Sinθ
= A. Sin { ωc. t + mf. Sin (ωm t) }
Equation involves Sine of a Sine function. So we have to expand using Bessel’s function. The result after expansion is given by
vFM = A. { J0. mf. Sin (ωc t) + J2. mf. [ Sin (ωc.+ ωm.)t + Sin (ωc.- ωm.)t ]
+ J3. mf. [ Sin (ωc.+ 2. ωm.)t + Sin (ωc.- 2. ωm.)t ]
+ J4. mf. [ Sin (ωc.+ 3. ωm.)t + Sin (ωc.- 3. ωm.)t ]
+ J5. mf. [ Sin (ωc.+ 4. ωm.)t + Sin (ωc.- 4. ωm.)t ]
+ ..................
The FM wave consists of a carrier and infinite number of side bands, each preceded by J coefficients. They are separated from the carrier by fm, 2fm, 3fm, 4fm,.... and thus have a recurring frequency of FM.
Advantages of frequency modulation, FM over AM
Resilience to signal level variations: The modulation is carried only as variations in frequency. This means that any signal level variations will not affect the audio output, provided that the signal does not fall to a level where the receiver cannot detect. As a result this makes FM ideal for mobile radio communication applications including more general two-way radio communication or portable applications where signal levels are likely to vary considerably.
Immune to noise: It is for this reason that FM is used for high quality broadcast transmissions. The main reasons for the decrease in noise, in the case of FM are
i. FM is used in VHF and UHF range where noise is less, but AM uses MF and HF range.
ii. Amplitude limiters can be used in FM receivers which remove any amplitude variations due to noise.
iii. In FM, Guard Bands are available, which avoids co-channel interference.

It is possible to use efficient RF amplifiers with frequency modulated signals: It is possible to use non-linear RF amplifiers to amplify FM signals in a transmitter and these are more efficient than the linear ones required for signals with any amplitude variations (e.g. AM and SSB). This means that for a given power output, less battery power is required and this makes the use of FM more viable for portable two-way radio applications.
Security: FM receivers are complex which provides some sort of secrecy to the information.

Disadvantages of frequency modulation:
Large BW requirement: Since there are infinite numbers of side bands in FM, the band width requirement is more.
Complexity of equipments: FM transmitters and receivers are complex.
Small area of reception: Since the reception is limited to line of sight (LOS) the area of reception is smaller than AM.

PHASE MODULATION
In phase modulation the phase of the carrier is shifted according to the instantaneous values of amplitude of the modulating signal keeping the amplitude of carrier constant.

Frequency modulation requires the oscillator frequency to deviate both above and below the carrier frequency. During the process of frequency modulation, the peaks of each successive cycle in the modulated waveform occur at times other than they would if the carrier were unmodulated. This is actually an incidental phase shift that takes place along with the frequency shift in fm.
Just the opposite action takes place in phase modulation. The information signal is applied to a phase modulator in PM. The resultant wave from the phase modulator shifts in phase according to the instantaneous values of amplitude of the modulating signal. Notice that the time period of each successive cycle varies in the modulated wave according to the information signal variations. Since frequency is a function of time period per cycle, we can see that such a phase shift in the carrier will cause its frequency to change. The frequency change in FM is vital, but in PM it is merely incidental. The amount of frequency change has nothing to do with the resultant modulated wave shape in PM.
If the phase in the equation of carrier v = A. Sin ( ) is varied so that its magnitude is proportional to the instantaneous values of amplitude of the modulating signal, the resultant wave is phase modulated.
The phase modulated signal is given by the expression,
v = A. Sin { ωc. t + Фm. Sin (ωm t) }
Here Фm is the maximum value of phase change ( in radians) that can take place. This is multiplied by the modulating signal term Sin (ωm t) so that we get a phase change from - Фm to +Фm according to the amplitude variations in the modulating signal.
The modulation index ( mf ) of PM is same to the maximum phase change Фm
mf = Фm
So the phase modulated signal is given by,
v = A. Sin { ωc. t + mp. Sin (ωm t) }