ENSC327 Communications Systems 3. Amplitude Modulation
School of Engineering Science Simon Fraser University
1 Outline
Some Required Background Overview of Modulation What is modulation? Why modulation? Overview of analog modulation History of AM & FM Radio Broadcast Linear Modulation: Amplitude modulation
2 Some Required Background
Basics of sinusoidal signals: amplitude, frequency, phase.
RC Circuits, Natural Response. Assume initial voltage to be ( ). Recall from ENSC-220, what is ( )? 𝑒𝑒𝑜𝑜 𝑡𝑡0 𝑒𝑒𝑜𝑜 𝑡𝑡
Fourier Transform of cos 2 or a complex exponential. Properties of FT, e.g., shift in frequency, Parseval’s theorem. 𝜋𝜋𝑓𝑓𝑐𝑐𝑡𝑡 Definition of Bandwidth (BW) (see Lecture 2) 3 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
4 Overview of Modulation
Why modulation? 2. Allowing transmission of more than one signal in the same channel (multiplexing)
3. Allowing better trade-off between bandwidth and signal-to-noise ratio (SNR)
5 Analog modulation
The input message is continuous in time and value Continuous-wave 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 Angle modulation: Phase modulation: Φ(t) is linearly related the message. Freq. modulation: dΦ(t)/dt is linearly related to the message.
6 Analog modulation
Linear modulation Message
(Amplitude modulation)
Angle modulation: Message
Carrier
Phase modulation
Freq modulation 7 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?
Spark-gap transmitter 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 waves. 1894: Guglielmo Marconi invented spark transmitter with antenna in Bologna, Italy. 1897: Marconi formed his company in Britain at age 23, awarded patent for “wireless telegraph”. 1905-06: Reginald Fessenden invented a continuous-wave voice transmitter, first voice broadcast in Christmas Eve 1906. (See the attachment). 1906: Lee de Forest patented his audion tube (a triode device that could detect and amplify electric signals).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 Regenerative Circuit (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 radios with 2 operators and auxiliary power and all transmitters 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 frequency (UHF) TV
GSM: 400, 800, 900, 1800, 1900MHz (primary band used in Canada) IEEE 802.11b/g (Wi-Fi): 2.4 - 2.4835 GHz Also used by microwave 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 Amplitude Modulation (AM) An amplitude-modulated (AM) wave is given by:
s(t) = Ac [1+ kam(t)]cos(2πfct)
m(t) : Message signal (Usually has zero mean) = cos( ): Carrier signal
𝒄𝒄 𝒄𝒄 𝒄𝒄ka𝒕𝒕 : 𝑨𝑨Modulation𝟐𝟐 𝝅𝝅 𝒇𝒇 Sensitivity𝒕𝒕
Ac : Carrier Amplitude
fc : Carrier Frequency
In AM modulation, the amplitude of the modulated
signal varies as a function of m(t). 13 Amplitude Modulation (Cont.)
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)
Example: Message signal
AM wave if
max kam(t) >1 AM signal if max kam(t) <1
14 Example m = 2 cos(200 ), c = cos(2000 ), = 0.5. Plot the AM modulated signal, s(t).
𝑡𝑡 𝜋𝜋 𝑡𝑡 𝑡𝑡 𝜋𝜋 𝑡𝑡 𝑘𝑘𝑎𝑎
15 Percentage Modulation
s(t) = Ac [1+ kam(t)]cos(2πfct)
The Percentage Modulation of an AM system max kam(t) ×100% Example: m(t) = cos(2πf0t) s(t) s(t)
max kam(t) = 0.5 or 50% max kam(t) =1 or 100% Observation: The message can be recovered from the positive envelope.
Over-modulation: When max k a m ( t ) > 1 for some values of t.
max kam(t) =1.5 or 150%. Observation: The positive envelope is different from the message. 16 Example
A message, m(t), and the AM modulated signal s(t) are given below. Find the percentage modulation and the value of “x” shown on the graph of s(t). Assume = 1.
𝐴𝐴𝑐𝑐
17 Demodulation of AM: Envelope Detector
The following simple circuit can be used to recover the message from the AM envelope (big advantage of AM): The diode: only allows the positive part of the signal 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 distortion
Good RC RC too large RC too small 18 Spectrum of AM
Let M(f) be the FT of m(t), then the FT of the AM signal is A k A S( f ) = c [δ ( f − f ) +δ ( f + f )]+ a c [M ( f − f ) + M ( f + f )] 2 c c 2 c c Proof:
19 A k A S( f ) = c [δ ( f − f ) +δ ( f + f )]+ a c [M ( f − f ) + M ( f + f )] Example 2 c c 2 c c
Assume the message is a lowpass signal the spectrum below. Plot the spectrum of the AM signal:
AM
20 Bandwidth of AM
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 sideband (USB): Lower sideband (LSB): Disadvantages of AM:
21 Power Efficiency of AM
s(t) = Ac [1+ kam(t)]cos(2πfct) T 1 2 Assuming m(t) has zero average , and Pm = m (t)dt is message power, lim ∫−T T →∞ 2T then the power efficiency of AM system is:
total sideband power k 2 P = a m 2 total power 1+ ka Pm
Proof:
22 Example
For the special case of single tone modulation, i.e., when the message is a single sinusoidal (m ( t ) = A m cos( 2 π f m t ) ), we have:
s(t) = Ac [1+ kam(t)]cos(2πfct)
In this case, we define µ = k a A m : modulation factor or modulation index. Find the power efficiency of the AM modulated signal in terms of μ.
23 Efficiency of Single Tone Modulation (cont.)
µ 2 Power Efficiency = 2 + µ 2
µ ∞: Eff 1 (leads to DSB, studied later) In order to use envelope detector, we need µ < 1: Maximal power efficiency of AM?
0.35
0.3
0.25
0.2
Efficiency 0.15
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 24 Modulation Index Modulation factor µ Summary of AM
s(t) = Ac [1+ kam(t)]cos(2πfct) Advantage: Simple demodulation Envelope detector Disadvantages: Low power efficiency: Carrier power is wasted Waste of bandwidth: Bandwidth is twice of the BW of the message. USB and LSB have the same information Measurement of modulation factor Concepts: Percentage Modulation Modulation factor (index): for single tone messages only. µ = ka Am 25