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Home , Amplitude modulation, Demodulation

ENSC327 Communications Systems 3.

Jie Liang School of Engineering Science Simon Fraser University

1 Outline  Overview of Modulation  What is modulation?  Why modulation?  Overview of analog modulation  History of AM & FM Broadcast  Linear Modulation: 

2 Overview of Modulation  What is modulation?  The process of varying a carrier signal in order to use that signal to convey information. Why modulation? 1. Reducing the size of the antennas : The optimal antenna size is related to wavelength: Voice signal: 3 kHz

3 Overview of Modulation  Why modulation?  2. Allowing transmission of more than one signal in the same channel ( )

 3. Allowing better trade-off between and signal-to-noise ratio (SNR)

4 Analog modulation  The input message is continuous in time and value  Continuous- modulation (focus of this course)  A parameter of a high-freq carrier is varied in accordance with the message signal

If a sinusoidal carrier is used, the modulated carrier is:

Linear modulation : A(t) is linearly related to the message. AM, DSB, SSB :  : Φ(t) is linearly related the message. Freq. modulation : d Φ(t)/dt is linearly related to the message.

5 Analog modulation

 Linear modulation (Amplitude modulation)

Angle modulation:  Message

 Carrier

 Phase modulation

 Freq modulation 6 Problems to be studied

 For each modulation scheme, we will study the following topics:  How does the modulator work?  How does the demodulator work?  What is the required bandwidth ?  What is the power efficiency?  What is the performance in the presence of noise ?

7 Outline  Overview of Modulation  What is modulation?  Why modulation?  Overview of analog modulation  History of AM & FM Radio Broadcast  Linear Modulation:  Amplitude modulation

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Spark-gap AM FM 1895 by Marconi 1906 by Fessenden 1931 by Armstrong (Canadian )

Marconi in Newfoundland. 9 Early History of Radio

 1887: Heinrich Hertz first detected radio .  1894: invented spark transmitter with antenna in Bologna, Italy.  1897: Marconi formed his company in Britain at age 23, awarded patent for “ telegraph”.  1905-06: (A Canadian) invented a continuous-wave voice transmitter, first voice broadcast in Christmas Eve 1906.  1906: patented his tube, had visited the Fessenden lab in 1903 and stole the design for a "spade " (de Forest sued Armstrong over the basic regenerative patent from 1915 to 1930, and was finally awarded the basic radio patent, causing him to become known as the "father of radio."  1912-1933: Edwin Armstrong invented the (1912), the Superheterodyne Circuit (1918), the Superregenerative Circuit (1922) and the complete FM System (1933). He spent almost his entire adult life in litigation over his patents and ultimately committed suicide by jumping to his death from a high- rise in New York City in 1954.  1912: Due to Titanic disaster, all ships were required to have with 2 operators and auxiliary power and all must be licensed.  1920: The first licensed commercial AM radio services. 10 AM and FM Radio

 AM radio ranges from 535 to 1605 kHz  The bandwidth of each station is 10 kHz.

The FM radio band goes from 88 to 108 MHz  The bandwidth of each FM station is 200 kHz  FM has much better quality than AM

We will learn in this course how these numbers are chosen.

11 Other Usages of Spectrum

 TV Band:  54-88 MHz: Channel 2 to 6.  174-216MHz: Channel 7 to 13  450-800MHz Ultra-high (UHF) TV

 GSM: 400, 800, 900, 1800, 1900MHz  IEEE 802.11b/g (Wi-Fi): 2.4 - 2.4835 GHz  Also used by ovens, cordless phones, medical and scientific equipment, as well as Bluetooth devices.  UWB (Ultra Wideband): 3.1 - 10.6GHz  Opened up by FCC in 2002.  Signal bandwidth > 500MHz  Extremely low emission level  Many potential applications  Currently a hot research topic 12 Outline  Overview of Modulation  History of AM & FM Radio Broadcast  Linear Modulation:  Amplitude modulation:  AM wave   Spectrum  Power Efficiency  Single tone modulation  Measure of modulation factor in time domain and freq domain

13 Amplitude Modulation (AM)  An amplitude-modulated (AM) wave is given by:

s(t) = Ac [1+ kam(t)]cos(2π ctf ) m(t :) Message signal to be transmitted. M(t) usually has zero mean .

ka : Amplitude sensitivity (system parameter).

Ac : Amplitude of the carrier.

fc : Carrier frequency.

 The amplitude of the carrier is a function of m(t).

14 s(t) = Ac [1+ kam(t)]cos(2π ctf ) AM Percentage Modulation k m t ×  The Percentage Modulation of an AM system is max a ( ) 100

 Example: m(t) = cos(2π 0tf ) s(t) s(t)

max kam(t) = 5.0 or 50% max kam(t) =1 or 100% Observation: k m t >  Over-modulation: when max a ( ) 1

max kam(t) = 5.1 or 150%. Observation: 15 Amplitude Modulation (AM)  The Most Attractive Feature of AM: The message can be recovered from the envelope of the AM wave if the following conditions are satisfied:

.1 max kam(t) <1 for all t.

.2 fc >> W (W : message bandwidth)

 Non-sinusoidal messages: AM wave if If max kam(t) > 1 Message signal

AM wave if

max kam(t) <1

16 Demodulation of AM:  The following simple circuit can be used to recovered the message from the AM envelope:  The : only allows the positive part to pass.  The lowpass RC circuit: tracks the envelope  The carrier freq. must be large enough  The RC time constant must be set carefully  too large: discharge too slow, won’t track  too small: discharge too fast, too much

Good RC RC too large RC too small 17 Spectrum of AM

 Let M(f) be the FT of m(t), then the FT of the AM signal is

Ac ka Ac S( f ) = []δ ( f − fc ) +δ ( f + fc ) + []M ( f − fc ) + M ( f + fc ) 2 2  Proof :

18 Spectrum of AM

 Assume the message is a lowpass signal:

AM

19 Bandwidth of AM

 Assuming the bandwidth of the original lowpass signal is W  In AM, the low-pass signal M(f) is shifted to both fc and –fc:   Bandwidth of the AM signal is  Upper (USB) :  Lower sideband (LSB):  Disadvantages of AM:

20 s(t) = Ac [1+ kam(t)]cos(2π ctf ) Power Efficiency of AM T 1 2 Pm = m (t)dt is message power, Assuming m(t) has zero average , and lim ∫−T T →∞ 2T k 2 P total sideband power = a m then the power efficiency of AM system is: 2 total power 1+ ka Pm  Proof:

21 Power Efficiency of AM

22 Power Efficiency of AM 1 1 P = A2k 2 P P = A2 [1+ k 2 P ]. sb 2 c a m T 2 c a m

  The power efficiency is:

 If ka approaches ∞,

23 A Special Case: Single Tone Modulation

 If the message is a single frequency signal:

m(t) = Am cos(2πfmt)

 The AM wave: s(t) = Ac [1+ kam(t)]cos(2π ctf )

 To use envelope detector, need µ < 1. 2  The power efficiency becomes: µ 2 + 2  Proof: µ

24 A Special Case: Single Tone Modulation µ 2 Power Efficiency = 2 + µ 2

 µ  ∞: Eff  1 (leads to DSB, studied later)  If envelope detector is used, µ < 1:  For sinusoidal signals, the max power efficiency of AM is

0.35

0.3

0.25

0.2

0.15 Efficiency

0.1

0.05

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Modulation Index 25 Modulation factor µ Time-Domain Measurement of Modulation Factor

 How to measure the modulation factor from oscilloscope display? (Part of Lab 2)

s(t) = Ac [1+ µm(t)]cos(2π ctf )

If m(t) is chosen in [-1, 1], then E − E µ = max min -Emin Emax + Emin -Emax Proof:

26 Measurement of Modulation Factor  Spectrum analyzer (SA): a device to examine the spectral composition of a signals:  Can be used to measure the power at each frequency.  dBm: SA usually measures power in dBm unit (w.r.t. 1mW): P = x 10log 10 (See Page 459 of book) 1mW

P1 : carrier power ( dBm )

P2 : sideband power of each side ( dBm )

 How to measure the modulation factor from Spectrum Analyzer screen? (Part of Lab 2) 27 Frequency Domain Measurement of Modulation Factor  The modulation factor from Spectrum Analyzer screen: P −P − 1 2 20 If m(t) = Am cos(2πfmt), then µ = 2×10 . Proof:

28 Summary of AM

s(t) = Ac [1+ kam(t)]cos(2π ctf )  Advantage: Simple demodulation  Envelope detector  Disadvantages:  Low power efficiency:  Carrier power is wasted  Waste of bandwidth:  Bandwidth is twice of the message.  USB and LSB has same information  Measurement of modulation factor  Concepts:  Percentage Modulation  Modulation factor (index): for single tone messages only.

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