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Concept of Instantaneous Frequency Angle Modulation

Lesson 10 EEE 352 Analog Communication Systems Mansoor Khan CIIT EE Department Islamabad Campus

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 carrier keeping phase and frequency of carrier constant the resulting modulation is AM or Amplitude Modulation. • If the information is carried as the variation in phase or frequency of the signal 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 the resulting 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 the resulting modulation is PM(phase modulation).

Angle Modulation • Entails both frequency modulation (FM) and phase modulation (PM). • Angle modulation results whenever the phase angle (ө) of a sinusoidal wave is varied with respect to time.

Angle Modulation • An angle-modulated wave can be expressed mathematically as :

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

Angle Modulation • If the frequency of the carrier is varied directly in accordance with the modulating signal , FM result.

• If the phase of the carrier is varied directly in accordance with the modulating signal , PM result.

AM and FM Modulation (a) Carrier wave.

(b) Sinusoidal modulating signal. (c) Amplitude-modulated signal.

(d) Frequency modulated signal.

EEE 352

Angle Modulation vs. AM • Properties of amplitude modulation – Amplitude modulation is linear • just move to new frequency band, spectrum shape does not change. 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

Angle Modulation Applications • Applications – FM radio broadcast – Two-way mobile radio – Cellular radio – Microwave and satellite communications

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

(t ) A cos(c t 0 ) • Now, let us consider a generalized form of sinusoidal signals

(t ) A cos (t ) • Because the two angles are tangential to each other over this small interval • The frequency is actually the slope of its angle over this interval

• The instantaneous frequency,

• Or

d i (t ) dt t

(t ) i ( )d

• We can see the possibility of transmitting the information of m(t) by modifying the angle θ of a carrier. • Such technique of modulation where the angle of carrier is varied in some manner with a modulating signal is known as angle modulation or Exponential modulation

• Two most extensively studied angle modulation schemes are phase modulation (PM) and frequency modulation (FM) • In PM the angle is varied linearly with m(t)

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

Phase Modulation • In PM angle varies according to message signal

(t ) c t 0 k p m(t ) • Assuming the initial phase to be zero

(t ) c t k p m(t ) • Phase modulated signal will be

PM (t ) A cos(c t k p m(t ))

• The instantaneous frequency is now

d i (t ) c k p m (t ) dt • Therefore in PM the instantaneous frequency varies proportionally to the derivative of the modulating signals or to the variation of the modulating signal

Frequency Modulation • In FM we modify the instantaneous frequency directly with the amplitude of m(t) as

i (t ) c k f m(t ) • Therefore the angle is

(t )

t

c

k f m( ) d

c t k f

t

m( )d

• Frequency modulated signal can be written as t

FM (t ) A cos(ct k f m( )d )

Example 5.1 (cont)

Example 5.1 (cont)

Example 5.2 (cont)

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 remain constant i.e

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Lesson 10 EEE 352 Analog Communication Systems Mansoor Khan CIIT EE Department Islamabad Campus

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 carrier keeping phase and frequency of carrier constant the resulting modulation is AM or Amplitude Modulation. • If the information is carried as the variation in phase or frequency of the signal 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 the resulting 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 the resulting modulation is PM(phase modulation).

Angle Modulation • Entails both frequency modulation (FM) and phase modulation (PM). • Angle modulation results whenever the phase angle (ө) of a sinusoidal wave is varied with respect to time.

Angle Modulation • An angle-modulated wave can be expressed mathematically as :

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

Angle Modulation • If the frequency of the carrier is varied directly in accordance with the modulating signal , FM result.

• If the phase of the carrier is varied directly in accordance with the modulating signal , PM result.

AM and FM Modulation (a) Carrier wave.

(b) Sinusoidal modulating signal. (c) Amplitude-modulated signal.

(d) Frequency modulated signal.

EEE 352

Angle Modulation vs. AM • Properties of amplitude modulation – Amplitude modulation is linear • just move to new frequency band, spectrum shape does not change. 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

Angle Modulation Applications • Applications – FM radio broadcast – Two-way mobile radio – Cellular radio – Microwave and satellite communications

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

(t ) A cos(c t 0 ) • Now, let us consider a generalized form of sinusoidal signals

(t ) A cos (t ) • Because the two angles are tangential to each other over this small interval • The frequency is actually the slope of its angle over this interval

• The instantaneous frequency,

• Or

d i (t ) dt t

(t ) i ( )d

• We can see the possibility of transmitting the information of m(t) by modifying the angle θ of a carrier. • Such technique of modulation where the angle of carrier is varied in some manner with a modulating signal is known as angle modulation or Exponential modulation

• Two most extensively studied angle modulation schemes are phase modulation (PM) and frequency modulation (FM) • In PM the angle is varied linearly with m(t)

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

Phase Modulation • In PM angle varies according to message signal

(t ) c t 0 k p m(t ) • Assuming the initial phase to be zero

(t ) c t k p m(t ) • Phase modulated signal will be

PM (t ) A cos(c t k p m(t ))

• The instantaneous frequency is now

d i (t ) c k p m (t ) dt • Therefore in PM the instantaneous frequency varies proportionally to the derivative of the modulating signals or to the variation of the modulating signal

Frequency Modulation • In FM we modify the instantaneous frequency directly with the amplitude of m(t) as

i (t ) c k f m(t ) • Therefore the angle is

(t )

t

c

k f m( ) d

c t k f

t

m( )d

• Frequency modulated signal can be written as t

FM (t ) A cos(ct k f m( )d )

Example 5.1 (cont)

Example 5.1 (cont)

Example 5.2 (cont)

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 remain constant i.e

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