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PPT – Angle Modulations PowerPoint presentation | free to view - id: 1c6fe2-ZDc1Z

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Angle Modulations

Angle Modulations

where

Thus,

Angle Modulations

Phase Modulation (PM)

So that

phase modulation index

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Frequency Modulation (FM)

frequency deviation

Since

PM

Therefore,

Thus,

Angle Modulations

Frequency Modulation (FM)

Assume that

Therefore,

Thus,

Angle Modulations

Angle Modulations

Illustrative AM, FM, and PM waveforms

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Narrowband PM and FM

From

we can rewrite xc(t)

where

and

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Narrowband PM and FM

Assume that

so that

Thus,

in which

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Tone Modulation

Assume that

Since

PM

and

FM

Therefore,

modulation index

where

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Narrowband Tone Modulation

From

Therefore,

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Arbitrary FM with Tone Modulation

From

Bessel Functions

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Arbitrary FM with Tone Modulation

Since

Therefore,

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Arbitrary FM with Tone Modulation

Angle Modulations

Bessel Functions

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Bessel Functions

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Bessel Functions

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Properties of Bessel functions

1. J0(?) varies with the modulation index

2. The number of sideband lines depends on ?

3. Large ? means large bandwidth

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Tone-modulation line spectra

FM or PM with fm fixed

FM with Amf fixed

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FM phasor diagram

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Transmission Bandwidth

max. deviation(f)

deviation ratio(D)

max. modulating freq(W)

Carsons Rule

BT 2(f W) 2(D1)W for D gtgt 1 or D ltlt1

Majority of FM, 2 lt D lt 10

BT 2(f 2W) 2(D2)W for D gt 2

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Transmission Bandwidth Example

Commercial FM broadcast

A maximum frequency deviation 75

kHz Bandwidth, W 15 kHz

Thus, deviation ration, D 75kHz/15kHz 5 BT

2(52)15 kHz 210 kHz

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FM and PM Generation

- Direct FM and VCO
- Indirect FM

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Direct FM

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Direct FM

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Indirect FM

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FM and PM Detection

- FM-to-AM conversion
- Phase-shift discrimination
- Zero-crossing detection

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FM to AM conversion

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Phase-shift discrimination

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FM and PM Detection

- FM-to-AM conversion
- Phase-shift discrimination
- Zero-crossing detection

Assignment 4

1. The signal shown below amplitude modulates a

carrier of frequency 1 MHz

(a) If the modulation is DSBSC, sketch the

modulated waveform and its spectrum. (b) If the

modulation is DSBTC sketch the modulated

waveform. Assume that the amplitude of the

carrier is 1 and the modulation index is 0.5.

(c) The modulated signal of Problem (a) forms

the input to an envelope detector. Sketch

the output of the detector. (d) For the modulated

signal of Problem (b), sketch the output of an

envelope detector.

s(t)

S(f)

1

1

t(msec)

f(kHz)

0.1

-0.1

-0.8

-15-10 -5

5 10 15

2. Consider tone-modulation FM with Ac 100,

Amf 8 kHz, and fm 4 kHz. Draw the line

spectrum for fc 30 kHz and for fc 11 kHz

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Mid-term

- FS
- FT
- Linear Systems (filters)
- Convolution
- AM FM