analog communication unit5 angle modulation vtu

ANALOG COMMUNICATION (VTU) - 10EC53

UNIT 5

ANGLE MODULATION (FM)-I: Basic definitions, FM, narrow band FM, wide band FM,

transmission bandwidth of FM waves, generation of FM waves: indirect FM and direct FM.

TEXT BOOKS:

1. Communication Systems, Simon Haykins, 5thEdition, John Willey, India Pvt. Ltd, 2009.

2. An Introduction to Analog and Digital Communication, Simon Haykins, John Wiley India

Pvt. Ltd., 2008.

Special Thanks To:

Faculty(Chronological): Arunkumar G (STJIT), Ravitej B (GMIT), Somesh HB (REVA

ITM).

BY:

RAGHUDATHESH G P

Asst Prof

ECE Dept, GMIT

Davangere 577004

Cell: +917411459249

Mail: [email protected]

Quotes:

The end of education is character.

Do not wait for leaders; do it alone, person to person.

My job is not to be easy on people. My job is to make them better.

Design is not just what it looks like and feels like. Design is how it works.

Purity, patience, and perseverance are the three essentials to success, and above all, love.

Meaning is man-created. And because you constantly look for meaning, you start to feel

meaninglessness.

Angle Modulation Raghudathesh G P Asst Professor

Department ECE,GMIT [email protected] Page No - 1

RAGH

UDAT

HESH

G P

ANGLE MODULATION

Definition: It is a process in which either the phase or frequency of the carrier wave is varied in accordance to the modulating or message signal while keeping the amplitude of

the carrier constant.

It is a non-linear process. Types: It is classified into 2 Types:

1. Frequency Modulation (FM): It is a form of angle modulation in which the instantaneous frequency of the carrier wave is varied in accordance to the

modulating or message signal while keeping the amplitude of the carrier constant.

2. Phase Modulation (PM): It is a form of angle modulation in which the phase or

angular argument of the carrier wave is varied in accordance to the

modulating or message signal while keeping the amplitude of the carrier constant.

Angle modulation has several advantages over the amplitude modulation like: 1. Noise reduction 2. Improved system fidelity and 3. Efficient usage of power 4. Can withstand nonlinear distortion and amplitude fading.

Some disadvantages associated with the Angle modulation are: 1. Increased bandwidth requirement and 2. Use of more complex circuits

Angle modulation is being used for the following applications: 1. Radio broadcasting 2. Two way mobile radio 3. Microwave communication 4. TV sound transmission 5. Cellular radio 6. Satellite communication

Frequency Modulation (FM):

Definition: Frequency modulation (FM) is a type of modulation where the frequency of the carrier is varied in accordance with the modulating signal. The amplitude of the

carrier remains constant.

The information bearing signal (the modulating signal) changes the instantaneous frequency of the carrier. Since the amplitude is kept constant, FM modulation is a low

noise process and provides a high quality modulation technique which is used for music

and speech in hi-fidelity broadcasts.



RAGH

UDAT

HESH

G P

Application: In addition to hi-fidelity radio transmission, FM techniques are used for other important consumer applications such as audio synthesis and recording the

luminance portion of a video signal with less distortion.

Devices generating FM waves are VCO and reactance modulator.

Time-domain Representation of Frequency Modulated Waves (FM):

Let the time-domain expression for an angle modulated wave be represented by

------- (1)

Here, = the angle of the modulated carrier and

Ac = the amplitude of the unmodulated carrier and is constant.

In frequency modulation, the carrier frequency is varied in proportion to modulating signal m(t). If m(t) is constant, carrier frequency is constant. If m(t) takes discrete values,

carrier frequency also takes discrete values. If m(t) varies continuously then carrier

frequency also varies continuously.

The frequency at any instant known as the instantaneous frequency fi(t) is defines as,

-------- (2)

The instantaneous frequency fi(t) is varied linearly with the message signal m(t) . Thus, the instantaneous frequency of an FM signal can be represented as

-------- (3)

Here, fc = the frequency of the unmodulated carrier, and

kf = the constant represents the frequency sensitivity of the modulator and has the

unit, Hz/volt.

Substituting Equation (3) in Equation (2), we get

-------- (4)



RAGH

UDAT

HESH

G P

Integrating with respect to t, we get

-------- (5)

In the above representation, the angle of the unmodulated carrier has been assumed be zero at t = 0. The instantaneous phase of the modulated carrier is directly proportional to

the integral of the modulating signal, m(t).

Substituting Equation (5) in Equation (1), we get

-------- (6)

Equation (6) reveals that the envelope of an FM wave is a constant, that is, the amplitudes of the modulated and unmodulated carriers are same, unlike the envelope of AM wave,

which is dependent on the message signal m(t).

In FM, frequency of modulated varies with respect to modulating signal m(t). Figure below illustrates an FM wave along with the unmodulated carrier when the

modulating signal m(t) is a sinusoidal signal.

Time-domain Representation of Phase Modulated Waves (PM Waves):

Phase modulation is a form of angle modulation in which the phase of the modulated carrier is made to vary linearly with the message signal m(t) . That is,

------ (1)

Here,



RAGH

UDAT

HESH

G P

2fct = phase of unmodulated sinusoidal carrier having a frequency fc

kp = constant represents the phase sensitivity of the modulator in radians/volts.

The time-domain expression for a PM wave is

-------- (2)

Unlike in an FM wave, the instantaneous phase of a PM wave varies directly with message signal m(t).

When signal m(t) is time varying, like in frequency modulation, following common features are found in phase modulation:

The zero crossings of a PM wave no longer have a perfect regularity in their spacing like AM waves. This is because instantaneous frequency of PM wave is proportional to time

derivative of m(t).

The envelope of PM wave is a constant equal to the amplitude of the unmodulated carrier.

Figure below illustrates an FM wave along with the unmodulated carrier when the modulating signal m(t) is a sinusoidal signal.

Relationship between Phase Modulation (PM) and Frequency Modulation (FM):

The angle modulated wave is given as

-------- (1)

Here,



RAGH

UDAT

HESH

G P

Ac = the amplitude of the unmodulated carrier and is constant

= Instantaneous total phase angle of the angle modulated wave.

The expression for phase modulated (PM) wave is

-------- (2)

Similarly, the expression for frequency modulated (FM) wave is

-------- (3)

It may be observed from above equations that Phase Modulation (PM) and Frequency Modulation (FM) are closely related to each other because in both the cases there is a

variation in the total phase angle.

In phase modulation (PM), the phase angle varies linearly with baseband signal m(t) whereas in case of Frequency Modulation (FM), the phase angle varies linearly with the

integral of baseband signal m(t).

This means that FM wave may be obtained by using PM. Conversely, PM wave may be obtained by using FM.

To get FM by using PM, we first integrate the baseband signal and then apply to the phase modulator. This process is illustrated with the help of a block diagram shown in

figure below

PM wave may be generated by using frequency modulator by first differentiating modulating or baseband signal m (t) and then applying to the frequency modulator. This

process is illustrated with the help of a block diagram shown in figure below



RAGH

UDAT

HESH

G P

Sinusoidal Frequency Modulation:

Consider a sinusoidal FM modulating signal m(t) = Ac Cos(2fct). FM is a system of modulation in which the instantaneous frequency of the carrier is

varied in proportion with the amplitude of the modulating signal. The amplitude of the

carrier signal remains constant. Thus the information is conveyed via frequency changes.

FM was first practically tried in 1936 as an alternative to AM. FM transmission is more resistant to noise than A.M.

The time domain display of FM wave is as shown in the Figure above. The observations from the Figure are as follows:

1. The amount by which the carrier frequency varies from its unmodulated value is called as "deviation". The deviation () is made proportional to the instantaneous

value of modulating voltage.

2. The rate at which this frequency variation or oscillations takes place is equal to the modulating frequency (fm).



RAGH

UDAT

HESH

G P

3. The amplitude of the FM wave always remains constant. This is the biggest advantage of FM.

Parameters Relating to FM:

Frequency Deviation:

The instantaneous frequency of FM wave is given as,

------ (1)

The instantaneous frequency of FM signal varies with time around the carrier frequency fc. This means that the instantaneous frequency of FM signal varies according to the

modulating signal.

Definition: The instantaneous frequency of FM signal varies with time around the carrier frequency fc. The maximum change in the instantaneous frequency of the average

frequency face is called frequency deviation.

This maximum change in instantaneous frequency fi from the average or carrier frequency fc depends upon the magnitude and sign of kf m(t).

This means that the frequency deviation would be either positive or negative depending upon the sign of kf m(t).

However, the amount of frequency deviation in both these cases is given by the maximum magnitude i.e. .

Maximum frequency deviation is generally denoted by . Thus, it is given as,

The frequency deviation is a useful parameter for determining the bandwidth of FM signals.

The Figure below illustrates the concept of frequency deviation



RAGH

UDAT

HESH

G P

Modulation Index:

Definition: The ratio of frequency deviation to the modulating frequency is called as modulation index.

The modulation index of an FM wave is given as,

------- (1)

The modulation index (mf) is very important in FM because it decides the bandwidth of the FM wave.

The modulation index also decides the number of sidebands having significant amplitudes.

In AM the maximum value of the modulation index m is 1. But for FM the modulation index can be greater than 1.

Percentage Modulation of FM Wave:

Definition: The ration of actual frequency deviation to the maximum allowable frequency deviation.

The Percentage Modulation is given as follows,

Deviation Ration:

Definition: The modulation index corresponding to the maximum deviation and maximum modulating frequency is called as the deviation ratio.

Deviation ratio is given as follows,

In FM broadcasting the maximum value of deviation is limited to 75 kHz. The maximum modulating frequency is limited to 15 kHz.



RAGH

UDAT

HESH

G P

Transmission Bandwidth of FM waves:

An FM wave consists of infinite number of side bands hence the bandwidth is theoretically infinite.

In practice, the FM wave is effectively limited to a finite number of side band frequencies compatible with a small amount of distortion.

There are many ways to find the bandwidth of the FM wave. 1. Carsons Rule. 2. Universal Curve.

1. Carsons Rule:

In singletone modulation, for the smaller values of modulation index the bandwidth is approximated as 2fm.

For the higher values of modulation index, the bandwidth is considered as slightly greater than the total deviation 2f.

Thus the Bandwidth for sinusoidal modulation is defined as:

For non-sinusoidal modulation, a factor called Deviation ratio (D) is considered. Deviation ratio, D = ( f / W ), where W is the bandwidth of the message signal and the

corresponding bandwidth of the FM signal is,

2. Universal Curve:

An accurate method of bandwidth assessment is done by retaining the maximum number of significant side frequencies with amplitudes greater than 1% of the unmodulated

carrier wave.

Thus the bandwidth is defined as the 99 percent bandwidth of an FM wave as the separation between the two frequencies beyond which none of the side-band frequencies

is greater than 1% of the carrier amplitude obtained when the modulation is removed.



RAGH

UDAT

HESH

G P

Here, fm = modulation frequency and

n = number of pairs of side-frequencies such that |Jn()| > 0.01.

The value of nmax varies with modulation index and can be determined from the Bessel coefficients. The table 5.2 shows the number of significant side frequencies for different

values of modulation index.

From the universal curve, for a given message signal frequency and modulation index the ratio (B/ f ) is obtained from the curve. Then the bandwidth is calculated as:

Mathematical Expression for Single-Tone Frequency Modulation:

Expression for a modulating signal is,



RAGH

UDAT

HESH

G P

------- (1)

Expression for a Carrier signal is,

--------- (2)

Expression for a FM modulated wave is, ------- (3)

We know that the instantaneous frequency of the modulated signal is given as

--------- (4)

Putting the value of m (t) from (1) into (4), we get

-------- (5)

But we know that frequency deviation is given as

------- (6)

Substituting (6) in (5) we get,

------- (7)

The total phase angle of the modulated wave is given as

Putting the value of from equation (7), we get

------- (8)



RAGH

UDAT

HESH

G P

But, modulation index is given as

Therefore, putting the value of mf in equation (8) we obtain

Substituting this value of in equation (3), we get the expression for single-tone FM wave

-------- (9)

This is the required mathematical expression for single tone FM wave.

SPECTRUM ANALYSIS OF SINUSOIDAL FM WAVE:

The Expression for FM wave with sinusoidal modulation is given by

--------- (1)

From this expanded form, we see that the in-phase and quadrature components of the FM wave

s(t) for the case of sinusoidal modulation are as follows:

-------- (2)

------- (3)

The complex envelope of the FM wave equals

----- (4)

But expressing FM wave s(t) in terms of complex envelope as,

------- (5)



RAGH

UDAT

HESH

G P

Expanding in the form of complex Fourier series as:

------ (6)

Here cn = complex Fourier coefficient and is given as,

------ (7)

Let

Differentiating the above equation wrt t we get,

------ (i)

Also,

As,

Let Let

Then Then ------ (ii)

Substituting equations (i) and (ii) in (7) we get,

------- (8)

But, nth order Bessel function of 1

st kind with argument is given by,

-------- (9)

Comparing equations (7) and (8) we get,

------ (10)

Substituting equations (10) in (6) we get,



RAGH

UDAT

HESH

G P

------ (11)

Substituting equations (11) in (4) we get,

------ (12)

This is the desired form for the Fourier series representation of the single tone FM wave s(t) for

an arbitrary value of . The discrete spectrum s(t) is obtained by taking the Fourier transforms of

both sides of Equation (12) thus

---- (13)

In Figure below we have plotted the Bessel function versus the moulation index for n =

0, 1, 2, 3, 4.

These plots show that for fixed n, alternates between positive and negative values for

increasing and that | |approaches zero as approaches infinity. Note also that for fixed ,

we have

------- (14)

Properties of FM:

Property 1:- Narrowband FM:



RAGH

UDAT

HESH

G P

It is a class of FM wave having smaller bandwidth. For small values of the modulation index compared to one radian, FM wave assumes a

narrow band.

This narrowband wave essentially consisting of a carrier, an upper sideband (frequency component) and a lower sideband (frequency component).

With this property for smaller values of we have,

---------------- (1)

Expression of FM wave having Bessel function as,

----------------- (2)

Substituting equation (1) in (2) we get,

----- (3)

Thus from above equation we conclude that for smaller values of , the FM wave s(t) may be closely approximated by the sum of a carrier of amplitude Ac, an upper side

frequency component of amplitude Ac/2 and a lower side frequency component of

amplitude Ac/2 with a phase-shift of equal to 1800 (represented by minus sign).

Hence an FM wave so characterized is said to be narrow band. Application: Speech transmission like FM mobile communication such as police

wireless, ambulance etc.

Property 2:- Wideband FM:

It is a class of FM wave having infinite bandwidth. For large values of the modulation index compared to one radian, FM wave (in theory)

contains a carrier and an infinite number of sidebands (side-frequency components)

located symmetrically around the carrier.

It is mathematically represented as,



RAGH

UDAT

HESH

G P

Here the amplitude of the carrier component contained in a wideband FM wave varies with the modulation index in accordance with J0().

Application: In high quality music transmission like entertainment broadcasting applications such as TV, FM radio etc.

Property 3:- Constant Average Power:

The envelope of an FM wave is constant, so that the average power of such a wave dissipated in

a 1-ohm resister is also constant.

An FM wave s(t) defined as below which have a constant envelope equal to Ac.

-------------- (1)

Thus the average power dissipated in 1-ohm resister is,

-------- (2)

As RL=1 Thus,

------- (3)

But the Amplitude of the envelope of FM wave is constant thus, the power dissipated in 1-ohm

resister is also constant.

It is also possible to express the transmitted power in the form of series expansion as follows,

Advantages of FM over AM:

The frequency modulation (FM) has the following advantages over AM:

1. FM receivers may be fitted with amplitude limiters to remove the amplitude variations caused by noise. This makes FM reception a good deal more immure to noise than AM

reception.

2. It is possible to reduce noise still further by increasing the frequency-deviation. This is a feature which AM does not have because it is not possible to exceed 100 percent

modulation without causing severe distortion.

3. Standard Frequency Allocations provide a guard band between commercial FM stations. Due to this, there is less adjacent-channel interference than in AM.



RAGH

UDAT

HESH

G P

4. FM broadcasts operate in the upper VHF and UHF frequency ranges at which there happens to be less noise than in the MF and HF ranges occupied by AM broadcasts.

5. The amplitude of the FM wave is constant, It is thus independent of the modulation depth, whereas in AM, modulation depth governs the transmitted power. This permits the

use of low-level modulation in FM transmitter and use of efficient class C amplifiers in

all stages following the modulator. Further since all amplifiers handle constant power, the

average power handled equals the peak power. In AM transmitter the maximum power is

four times the average power. Finally in FM, all the transmitted power is useful where as

in AM, most of the power is carrier power which does not contain any information.

Note:

In general, FM is considered to be superior to AM. Although both modulation types are suitable for transmitting information from one place to another and both are capable of

equivalent fidelity and intelligibility, FM typically offers some significant benefits over

AM.

Disadvantages of FM over AM:

1. A much wider channel typically 200 KHz is required in FM as against only 10 kHz in AM broadcast. This forms serious limitation of FM.

2. FM transmitting and receiving equipments particularly used for modulation and demodulation tend to be more complex and hence more costly.

Comparison of FM and AM System:

Sl.No FM AM

1 Amplitude of FM wave is constant. It is

independent of the modulation index.

Amplitude of AM wave will change

with the modulating voltage.

2 Transmitted power remains constant. It

is independent of mf.

Transmitted power is dependent on the

modulation index.

3 All the transmitted power is useful. Carrier power and one sideband power

are useless.

4 FM receivers are immune to noise. AM receivers are not immune to noise.

5 AM receivers are not immune to noise,

5. It is possible to decrease noise further

by increasing deviation.

This feature is absent in AM.

6 Bandwidth = . The bandwidth depends on modulation index.

BW = 2fm. It is not dependent on the

modulation index.

7 BW is large. Hence, wide channel is

required.

BW is much less than FM.



RAGH

UDAT

HESH

G P

8 Space wave is used for propagation. So,

radius of transmission is limited to line

of sight.

Ground wave and sky wave propagation

is used. Therefore, larger area is covered

than FM.

9 Hence, it is possible to operate several

transmitters on same frequency.

Not possible to operate more channels

on the same frequency.

10 FM transmission and reception

equipment are more complex.

AM equipments are less complex.

11 The number of sidebands having

significant amplitudes depends on

modulation index mf.

Number of sidebands in AM will be

constant and equal to 2.

12 The information is contained in the

frequency variation of the carrier.

The information is contained in the

amplitude variation of the carrier.

13 FM wave:

AM wave:

14 Application: Radio, TV broadcasting,

police wireless, point to point

communicators.

Applications: Radio and TV

broadcasting.

Comparison Of Angle Modulated And Amplitude Modulated Wave:

Figure below shows a single-tone modulating signal, a carrier signal, amplitude-modulated (AM) wave and angle-modulated (i.e. FM and PM) waves.



RAGH

UDAT

HESH

G P

On comparison, we note the following differences between two techniques: 1. The envelope of FM wave or PM wave is constant and is equal to the unmodulated

carrier amplitude. On the other hand, the envelope of AM wave is dependent on the

modulating signal m(t).

2. The zero crossings (i.e. the instants of time at which the waveform changes from negative to a positive value or vice-versa) of a FM wave or a PM wave no longer

exhibit a perfect regularity in their spacing like AM wave. Thus this makes the

instantaneous frequency of the angle modulated wave depend upon time.

Note:

The primary benefit of FM over AM is its superior noise immunity. Noise is interference to a signal generated by lightning, motors, automotive ignition

systems, and any power line switching that produces transients. Such noise is typically

narrow spikes of voltage with very broad frequency content. They add to a signal and

interfere with it. If the noise signals are strong enough, they can completely obliterate the

information signal.

FM Generation:

The FM modulator circuits used for generating FM signals may be put into two categories as under:

1. The direct method or parameter variation method. 2. The Indirect method or the Armstrong method.

The classification of FM generation methods is shown in figure below

The direct method or parameter variation method:

In this method, the baseband or modulating signal directly modulates the carrier.



RAGH

UDAT

HESH

G P

The carrier signal is generated with the help of an oscillator circuit.

The Indirect method or the Armstrong method:

In this method, a narrow band FM is generated and then frequency multipliers are used to increase the frequency deviation which results in Wide-band FM.

The direct method or parameter variation method:

In direct FM generation, the instantaneous frequency of the carrier is changed directly in proportion with the message signal.

For this a device called voltage controlled oscillator (VCO) is used. A VCO can be implemented by using a sinusoidal oscillator with a tuned circuit having a

high value of Q. The frequency of this oscillator is .changed by incremental variation in

the reactive components involved in the tuned circuit.

If L or C of a tuned circuit of an oscillator is changed in accordance with the amplitude of modulating signal then FM can be obtained across the tuned circuit as shown in. Figure

below

A two or three terminal device is placed across the tuned circuit. The reactance of the device is varied proportional to modulating signal voltage. This will vary the frequency

of the oscillator to produce FM. The devices used are FET, transistor or varactor diode.

An example of direct FM is shown in Figure above which uses a Hartley oscillator along with a varactor diode. The varactor diode is reverse biased. Its capacitance is dependent

on the reverse voltage applied across it. This capacitance is shown by the capacitor C (t)

in Figure below.



RAGH

UDAT

HESH

G P

Frequency of oscillations of the Hartley oscillator shown in Figure above is given by

--------- (1)

Here, . That means C(t) is the effective capacitance of the fixed tuned circuit capacitance C and the varactor diode capacitance

Let the relation between the modulating voltage m (t) = 0 and the capacitance C (t) be represented as follows:

-------- (2)

Here C = total capacitance when x (t)=0 and kc is the sensitivity of the varactor capacitance to change in voltage.

Substituting expression for C (t) in Equation (1) we get,

Let

which is the oscillator frequency in absence of the modulating signal

m(t)=0.

-------- (3)



RAGH

UDAT

HESH

G P

If the maximum change in the capacitance corresponding to the modulating wave is assumed to be small as compared to the unmodulated capacitance C then Equation (3) for

fi (t) can be approximated as follows:

Let defining

= frequency sensitivity of the modulator. Then,

------- (4)

Disadvantage of direct method:

1. In the direct method of FM generation, we have to use the LC oscillator. The LC oscillator frequency is not stable enough. Therefore it is not possible to use such

oscillators for the communication or broadcast purpose.

2. We have to use a scheme in which we can use the crystal oscillator to control the carrier frequency.

3. We have to use the automatic frequency control scheme.

Frequency Stabilized FM Generator:

Figure above shows the automatic frequency stabilized FM generator. The output of VCO is applied to the mixer along with that of a crystal oscillator. At the Mixer output we get the following four frequency components.



RAGH

UDAT

HESH

G P

Out of them only the difference term is extracted by using a bandpass filter after the mixer.

This mixer output is then applied to a frequency discriminator and a low pass filter. Frequency Discriminator: This is a special type of device which produces an output

voltage; the amplitude of which is proportional directly to the frequency of its input.

The low pass filter that follows the frequency discriminator will eliminate the ripple contents in the output of the frequency discriminator to produce a ripple free control

voltage at its output.

When fVCO = fcr then output of mixer = fcr - fVCO = 0. Hence the output voltage of frequency discriminator is zero and hence the control voltage at the output of the low

pass filter is zero.

Thus this circuit will maintain the VCO frequency constant equal to the crystal oscillator frequency fcr.

If the VCO frequency deviates above or below fcr then the dc control voltage at the output of the low pass filter will be adjusted automatically to bring fvco close to fcr.

Indirect or Armstrong Method of FM Generation:

Generation of a narrow-band FM wave:

Consider the expression for an FM wave S1(t) for the general case of a modulating wave m(t), which is given as below,

------- (1)

Here, f1 = carrier frequency

A = carrier amplitude.

The angular argument of is related to m(t) by

------ (2)

Here k1 = frequency sensitivity of the modulator. Provided that the angle is small compared to one radian for all t, we may use the

following approximations:



RAGH

UDAT

HESH

G P

------ (3)

Thus, Equation (1) is expanded as,

---- (4)

Substituting Equation (3) in (4) we get,

----- (5)

Substituting Equation (2) in (5) we get,

------ (6)

Equation (6) defines a narrow-band FM wave. We may use this equation to set up the scheme shown in Figure below for the generation

of a narrow-band FM wave.



RAGH

UDAT

HESH

G P

The scaling factor 2k1 is taken care of by the product modulator. the part of the frequency modulator that lies inside the dashed rectangle in Figure above represents a

narrow-band phase modulator.

The modulated wave produced by the narrow-band modulator of Figure above differs from an ideal FM wave in two respects:

1. The envelope contains a residual amplitude modulation and, therefore, varies with time.

2. For a sinusoidal modulating wave, the phase of the FM wave contains harmonic distortion in the form of third- and higher-order harmonics of the modulation

frequency fm.

But by restricting the modulation index to 0.3 rad, the effect of residual AM and harmonic PM are limited to negligible levels.

Step2: frequency multiplication:

Basically, a frequency multiplier consists of a nonlinear device (e.g, diode or transistor) followed by a band-pass filter, as in Figure below

The nonlinear device used is a memory less device. If the input to the nonlinear device is an FM wave with frequency, fc and deviation, f1

then its output v(t) will consist of dc component and n frequency modulated waves

with carrier frequencies, fc, 2fc, 3fc, nfc and frequency deviations a f1, 2f1 , 3f1

, ........ nf1 respectively.

The band pass filter is designed in such a way that it passes: 1. The FM wave centered at the frequency, nfc with frequency deviation nf1 and 2. To suppress all other FM components.

Thus the frequency multiplier can be used to generate a wide band FM wave from a narrow band FM wave.

Step3: Generation of WBFM using Indirect Method:

In indirect method a NBFM wave is generated first and frequency multiplication is next used to increase the frequency deviation to the desired level. The narrow band FM wave

is generated using a narrow band phase modulator and an oscillator. The narrow band FM



RAGH

UDAT

HESH

G P

wave is then passed through a frequency multiplier to obtain the wide band FM wave, as

shown in the figure below,

We may generate a wideband FM wave S(t) with carrier frequency fc = nf1, and frequency deviation f = n f1, as desired.

Hence, we may write,

--------- (7)

Here,

In other words, the wideband frequency modulator of Figure above has a frequency sensitivity n times that of the narrow-band frequency modulator, where n is the frequency

multiplication ratio. In Figure above we show a crystal-controlled oscillator as the source

of carrier; this is done for frequency stability.

Problems:

1. In a FM system, the modulating frequency frn = 1 kHz, the modulating voltage Am = 2 volt and

the deviation is 6 kHz. If the modulating voltage is raised to 4 volt then what is the new

deviation? If the modulating voltage is further increased to 8 volt and modulating frequency is

reduced to 500 Hz what will be deviation? Calculate the modulation index in each case.

Comment on the result.

Solution:

Given: frn = 1 kHz, Am = 2 v,

Determining the frequency sensitivity of the modulator:



RAGH

UDAT

HESH

G P

i) Determining the frequency deviation when signal amplitude increased to 4V

ii) Determining the frequency deviation when signal amplitude increased to 8V and modulating

frequency is reduced to 500 Hz

iii) Calculations of modulation index for each case:

Expression for modulation index is:

a) and frn = 1 kHz thus,

b) and frn = 1 kHz thus,

c) and frn = 500Hz thus,

Comment: The modulation index is dependent on the value of deviation as well as the

modulating frequency.

2. What is the bandwidth required for a FM signal if the modulating frequency is 1 kHz and the

maximum deviation is 10 kHz? What is BW required for a DSBFC (AM) transmission?



RAGH

UDAT

HESH

G P

Solution:

Given: frn = 1 kHz and

Expression for bandwidth of a FM signal is given by Carsons rule:

Expression for bandwidth of a DSBSC(AM) signal is given by:

Analysis: The above result shows that for the transmission of same signal the BW required for

FM is very much higher than that of an AM system.



RAGH

UDAT

HESH

G P

analog communication unit5 angle modulation vtu

Documents