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Concept of InstantaneousFrequency

Angle Modulation

Lesson 10EEE 352 Analog Communication Systems

Mansoor KhanCIIT EE DepartmentIslamabad Campus

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Angle Modulation Information in a modulation process is carried by a carrier signal in the

form of variation in any one of the three parameters: amplitude,frequency or phase.

If modulating signal is carried by the variations in the amplitude of carrierkeeping phase and frequency of carrier constant the resulting modulationis AM or Amplitude Modulation.

If the information is carried as the variation in phase or frequency of thesignal while maintaining the amplitude of carrier constant, the type of modulation is angle modulation .

Angle Modulation is further divided into two categories:I. If frequency of carrier is varied with respect to instantaneous amplitude

of modulating signal while keeping other parameters constant theresulting modulation is FM(frequency modulation).

II. If phase of carrier is varied with respect to instantaneous amplitude of modulating signal while keeping other parameters constant theresulting modulation is PM(phase modulation).

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Angle Modulation

Entails both frequency modulation (FM)and phase modulation (PM) .

Angle modulation results whenever thephase angle ( ) of a sinusoidal wave isvaried with respect to time.

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Angle Modulation

An angle-modulated wave can be expressedmathematically as :

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Angle Modulation

With angle modulation, it is necessary that (t)be prescribed function of the modulated signal.

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Angle Modulation

If the frequency of the carrier is varieddirectly in accordance with the modulatingsignal , FM result.

If the phase of the carrier is varied directlyin accordance with the modulating signal ,PM result.

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EEE 352

AM and FM Modulation

(a) Carrier wave.

(b) Sinusoidal modulating sign al.

(c) Amplitude-modulated signal.

(d) Frequency modulated signal.

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Angle Modulation vs. AM

Properties of amplitude modulation Amplitude modulation is linear

just move to new frequency band, spectrum shape does notchange. No new frequencies generated.

Bandwidth 2W

Properties of angle modulation

They are nonlinear spectrum shape does change, new frequencies generated.

Bandwidth is usually much larger than 2W

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Angle Modulation Applications

Applications FM radio broadcast

Two-way mobile radio Cellular radio Microwave and satellite communications

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When we say that a signal is sinusoidal, it is given by

Now, let us consider a generalized form of sinusoidal signals

Because the two angles are tangential to each other over thissmall interval

The frequency is actually the slope of its angle over thisinterval

)cos()( 0 t At c

)(cos)( t At

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The instantaneous frequency,

Or

We can see the possibility of transmitting the information of m(t) by modifying the angle of a carrier.

Such technique of modulation where the angle of carrier isvaried in some manner with a modulating signal is known asangle modulation or Exponential modulation

dt d

t i

)(

t

i d t )()(

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Two most extensively studied angle modulation schemes arephase modulation (PM) and frequency modulation (FM)

In PM the angle is varied linearly with m(t)

In FM we modify the instantaneous frequency directly withthe amplitude of m(t)

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Phase Modulation

In PM angle varies according to message signal

Assuming the initial phase to be zero

Phase modulated signal will be

)()( 0 t mk t t pc

)()( t mk t t pc

))(cos()( t mk t At pcPM

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The instantaneous frequency is now

Therefore in PM the instantaneous frequency variesproportionally to the derivative of the modulating signals orto the variation of the modulating signal

)()( t mk dt d

t pci

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Frequency Modulation

In FM we modify the instantaneous frequency directly withthe amplitude of m(t) as

Therefore the angle is

)()( t mk t f ci

t

f c d mk t )()(

t

f c d mk t )(

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Frequency modulated signal can be written as

))(cos()(t

f cFM d mk t At

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Example 5.1 (cont)

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Example 5.1 (cont)

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Example 5.2 (cont)

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Power of Angle Modulated Waves

Amplitude of Angle modulated schemes (FM +PM)regardless of kf or kp remains constant.

Hence power of FM and PM always remainconstant i.e