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COMMUNICATION SYSTEM EECB353 Chapter 3 Part I ANGLE MODULATION

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### COMMUNICATION SYSTEM EECB353Chapter 3 Part IANGLE MODULATION

Dept of Electrical Engineering

Universiti Tenaga Nasional

Introduction

- Amplitude Modulation (AM) – Amplitude of the carrier varies accordingly to the message signal.
- Angle Modulation (FM and PM) – Angle of the carrier varies accordingly to the message signal while amplitude of the carrier is constant.

where m(t) = angle modulated waveform

Vc = peak carrier amplitude

c = carrier radian frequency (=2fc)

(t) = instantaneous phase deviation (radians)

(1)

Introduction

- Angle modulation as a function of modulating signal can be expressed mathematically as

(t) = F [vm(t)] (2)

where vm(t) = Vmsin(mt)

Vm = peak modulating signal amplitude

m = modulating signal radian frequency (=2fm)

Figure: Angle modulation vs amplitude modulation

Introduction

- Whenever the frequency of a carrier varied, the phase is also varied and vice versa.
- Thus, FM and PM must both occur whenever either form of angle modulation is performed.
- If the freq of the carrier is varied directly in accordance with the modulating signal, FM results.
- If the phase of the carrier is varied directly in accordance with the modulating signal, PM results.
- Therefore, direct FM is indirect PM and direct PM is indirect FM.
- DirectFM/PM – frequency/phaseof the constant amplitude carrier is varied proportionally to the amplitude of the modulating signal at a rate equal to the frequency of the modulating signal.

Introduction

- How carrier freq, fc change in accordance to modulating signal vm(t)?

- +ve increase in modulating signal amplitude causes increase in carrier freq.
- Deacrease (or –ve increase) in modulating signal amplitude causes decrease in carrier freq.

Figure: Angle modulated wave in frequency domain

Mathematical Analysis

Instantaneous phase deviation = = (3)

Instantaneous frequency deviation = = (4)

where Kpand Kf are constant (deviation sensitivity of phase and freq)

- For a modulating signal,
- Phase modulation,

(5)

- Frequency modulation,

(6)

Modulating signal

FM

PM

Figure : Phase and Frequency Modulation of sinusoidal carrier by a single-freq modulatingsignal.

The phase deviation of modulator o/p is prop. to m(t). The freq deviation is prop. to the derivative of the phase deviation, thus the i is max when the slope of m(t) is max and min when the slope of m(t) is min

FM

Freq. deviation is prop. to m(t), thus the i is max when the m(t) is max and min when m(t) is min

Note that m(t) is not shown along with the modulator o/p. It would not be possible to distinguish the PM and FM o/p

Accos 2fct

PM

FM

Output of PM and FM modulators for a sinusoidal, Accos 2fct

Comparison of PM and FM modulator outputs for a unit-step input.

(a) Message signal. (b) Unmodulated carrier. (c) Phase modulator output (kp = ½). (d) Frequency modulator output.

PM

i =fc for t<t0 and t>t0

The phase of unmodulated carrier is advanced by kp=/2 rads for t>t0 giving rise to a signal that is discontinues at t=t0

FM

i =fc for t<t0 and,

= fc+ fdfor t>t0

The modulator o/p phase is, however, continues at t=t0

Mathematical Analysis

- For FM – maximum freq deviation (change in the carrier freq) occurs during the maximum +ve and –ve peaks of the modulating signal i.e freq deviation to the amplitude of the modulating signal.
- For PM – maximum freq deviation occurs during zero crossings of the modulating signal i.e freq deviation to the slope or first derivative of modulating signal.
- For FM and PM – rate of freq change is equal to the modulating signal freq.
- Example : A transmitter operates on a frequency of 915 MHz. The maximum FM deviation is +/- 12.5 kHz. What are the maximum and minimum frequencies that occur during modulation?
- Example : A phase modulator has Kp= 2 rad/V. What voltage of sinewave would cause a peak phase deviation of 60 degrees ?

Phase Deviation and Modulation Index, m

Kf = deviation sensitivity for frequency

Kp = deviation sensitivity for phase

m = modulation index and peak phase deviation, ∆Ѳ rad

Frequency Deviation and Percent Modulation

- Frequency Deviation – the change in frequency that occurs in the carrier when it is acted on by a modulating-signal frequency.
- Typically given as a peak frequency shift in hertz (f).
- The peak-to-peak freq deviation (2f) is called carrier swing.
- For FM, the deviation sensitivity, Kf is often given in hertz/volt. Thus, the peak freq deviation can be expressed mathematically as:

Frequency Deviation and Percent Modulation

- With PM, modulation index and peak phase deviation are directly proportional to the amplitude of the modulating signal and unaffected by its frequency.
- With FM, both modulation index and freq deviation are directly proportional to the amplitude of the modulating signal, and modulation index is inversely proportional to its freq.
- Percent Modulation – the ratio of actual freq deviation to the maximum freq deviation allowed in percentage form.

% modulation = (27)

Examples

- Determine the peak frequency deviation (f) and modulation index (m) for an FM modulator with a deviation sensitivity, Kf = 5kHz/V and a modulating signal vm(t) = 2 cos(22000t).
- Determine the peak phase deviation (m) for a PM modulator with a deviation sensitivity Kp = 2.5rad/V and a modulating signal vm(t) = 2 cos(22000t).
- Below is the angle modulated signal produced after FM modulator;

Determine:

- Modulation index
- Peak frequency deviation

Examples

4. For a direct FM modulation, an information signal, is used to modulate a carrier, . For a deviation sensitivity of 2.5rad/s/V, calculate

- The peak frequency deviation in Hz
- The modulation index
- The percent modulation for maximum frequency deviation of 75kHz
- Using part (b), the deviation sensitivity for the indirect PM
- The carrier swing
- Write out the mathematical expression of the FM wave

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