Lecture 20: Amplitude modulationDANIEL WELLER

THURSDAY, APRIL 4, 2019

AgendaModulating signals for transmission

Amplitude modulation

Envelope detection-based demodulation

Synchronous demodulation

Amplitude shift keying

Don’t move that dial! We’ll be right back after these messages…

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Review of modulationRecall: Multiplying two sinusoids together shifted the frequencies. Multiplying a signal by a sinusoid is called modulation.

To see why multiplying two sinusoids shifts the frequencies, let’s review a trigonometric identity:

Substituting a = 2π(3520)t and b = 2π(2093)t, we get a+b = 2π(5613)t and a-b = 2π(1427)t.

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3520 Hz 2093 Hz Combined

Review of modulationVisually:

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Full spectrum

Full spectrum of signal multiplied by cos(2𝜋𝑓1𝑡)

𝑓1−𝑓1

× 𝑠 𝑡 = cos 2𝜋𝑓1𝑡

Modulation in communicationThis is just one type of modulation. More generally, modulation is the act of fitting a signal into a channel.

Why modulation? ◦ Commonly, the signal frequency spectrum does not line up with the carrier frequency (pass)band

◦ For instance, consider the spectrum of an audio signal generated by recording a mandolin:

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Modulation in communicationZooming in, this signal appears to have a 20 kHz bandwidth. We have two options:

1. We could transmit that signal as is (baseband transmission).

2. Transform the information so that it is transmitted in a different frequency range (modulated transmission).

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Baseband versus modulationBaseband transmission has many disadvantages:

◦ Disregards the characteristics of the channel at those frequencies. Other frequency ranges may have better signal-to-noise ratio or less attenuation (signal loss).

◦ Prevents others from reusing that bandwidth without some kind of orthogonal coding.

◦ Does not make use of the full available spectrum.

These are overcome by modulation:◦ Transmitted frequency range can fit the channel characteristics for optimal gain, SNR.

◦ Other transmissions can use different frequency ranges, avoiding congestion or interference.

◦ Make use of all available spectrum by spreading different signals throughout.

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Amplitude modulationTo begin, consider modulating a data signal by multiplying it by a carrier signal xc(t) (a sinusoid with amplitude AC and frequency fC).

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xC(t) = AC cos(2fCt)

Carrier Wave

Amplitude modulationAssume the data signal xm(t) has a range (amplitude) between -1 and 1:

Then, let the amplitude modulated (AM) signal xAM(t) = xc(t) [1 + m xm(t)], with the modulation index m fixed, and 0 < m ≤ 1. Note: Why add one? What is the purpose of m?

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-1 xm(t) 1

Modulation Signal

Amplitude modulation exampleObserve:

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AM Signal

xAM(t) = xC(t)[1+mxm(t)]

m = 1

ExampleObserve the shape of the original data (modulation) signal on top of the sinusoid:

We’ll use this observation later to recover xm(t) from the AM signal.

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xAM(t) = xC(t)[1+mxm(t)]

1+mxm(t)

Varying the modulation indexWhat happens as m increases from 0 to 1?

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xAM(t) = xC(t)[1+mxm(t)]

m = 0.3

m = 0.9

m = 0.6

m = 1.0

Varying the modulation indexObserve a value of m > 1 distorts the shape of the blue curve:

Moral of the story: we’ll want to keep m ≤ 1 for easy recovery of xm(t).

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xAM(t) = xC(t)[1+mxm(t)]

m = 1.5

Envelope [1+mxm(t)] when m > 1

Tone Modulation

xm(t) = cos(2fmt)

Another example: tone modulationTo understand what’s happening in the frequency domain, it’s useful to imagine modulating a simple tone:

𝑥𝑚 𝑡 = cos 2𝜋𝑓𝑚𝑡

Then, we can use trigonometry to find the sinusoidal components of xAM(t).

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Tone modulation

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Trigonometric Identity:

xAM(t) = xC(t) [1+m xm(t)]

cos × cos × cos( + cos(

= AC cos(2fCt) [1 + m cos(2fmt)]

= AC cos(2fCt) mAC cos(2fCt) cos(2fmt)]

= AC cos(2fCt) mAC [cos(2fC + fm)t) + cos(2fC - fm)t)]

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Significance: the information in xm(t) has been shifted in frequency from fm to fC+fm and fC-fm.

Tone modulation: spectrumSo, given a suitable carrier frequency (fC > fm), the positive spectrum of xAM(t) looks like this:

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xAM(t) = AC cos(2fCt) [1 + m cos(2fmt)]

fC fC + fmfC - fm

AM radioOlder radio stations frequently used amplitude modulation to transmit audio on high frequency carriers licensed to them for broadcasting by the FCC. Many of these AM radio stations still use such modulation (although many broadcast digital (HD) versions on top of it).

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540 WDMV POCOMOKE CITY MD religious gospel

550 WSVA HARRISONBURG VA talk/news

560 WFRB FROSTBURG MD nostalgia/talk

570 WWRC BETHESDA MD business news/talk

580 WHP HARRISBURG PA talk/news

600 WCAO BALTIMORE MD religious gospel

610 WNTW WINCHESTER VA religious

630 WMAL WASHINGTON DC talk/news

680 WCBM BALTIMORE MD talk/sports

700 WWTL WALKERSVILLE MD ethnic/Arabic

730 WKDL ALEXANDRIA VA Spanish music/talk

750 WBMD BALTIMORE MD religious

780 WABS ARLINGTON VA religious

810 WYRE ANNAPOLIS MD country/oldies

820 WXTR FREDERICK MD news

860 WBGR BALTIMORE MD religious/gospel

900 WILC LAUREL MD Spanish contemporary

920 WPTX LEXINGTON PARK MD off-the-air

930 WFMD FREDERICK MD talk/news

950 WCTN POTOMAC-CABIN JOHN MD religious

970 WAMD ABERDEEN MD oldies/adult contemporary

980 WTEM WASHINGTON DC sports talk

1010 WOLB BALTIMORE MD urban talk

1030 WWGB INDIAN HEAD MD religious

1050 WPLC SILVER SPRING MD Spanish adult contemporary

1090 WBAL BALTIMORE MD talk/news

1120 WUST WASHINGTON DC ethnic/multi-lingual

1150 WMET GAITHERSBURG MD business news/talk

1190 WBIS ANNAPOLIS MD business news

1200 WAGE LEESBURG VA talk

1220 WFAX FALLS CHURCH VA religious

1230 WITH BALTIMORE MD religious/talk

1230 WFVA FREDERICKSBURG VA adult contemporary/nostalgia/talk

1240 WJEJ HAGERSTOWN MD adult contemporary/easy listening

1250 WPRZ WARRENTON VA talk/religious

1260 WGAY WASHINGTON DC nostalgia/easy listening

1280 WHVR HANOVER PA adult contempoary

1300 WJFK BALTIMORE MD talk

1310 WDCT FAIRFAX VA Korean

1330 WJSS HAVRE DE GRACE MD religious/gospel

1340 WYCB WASHINGTON DC religious

1350 WYSK FREDERICKSBURG VA adult contemporary

1360 WWLG BALTIMORE MD oldies/nostalgia/talk

1370 WGMU FAIRFAX VA progressive/college sports

1390 WZHF ARLINGTON VA ethnic/Spanish/Chinese

1400 WWIN BALTIMORE MD religious gospel

1400 WINC WINCHESTER VA talk

1420 WKCW WARRENTON VA country

1430 WNAV ANNAPOLIS MD adult contemporary/talk/news/sports

1450 WOL WASHINGTON DC urban talk

1450 WFTR FRONT ROYAL VA talk

1450 WTHU THURMONT MD big band/sports/country

1460 WKDV MANASSAS VA ethnic/Asian/country

1470 WTTR WESTMINSTER MD oldies

1480 WPWC DUMFRIES VA off-the-air

1500 WTOP WASHINGTON DC news,sports

1520 WTRI BRUNSWICK MD off-the-air

1540 WACA WHEATON MD Spanish contemporary/talk

1550 WMRE CHARLES TOWN WV nostalgia

1550 WSER ELKTON MD news/talk/sports

1560 WKIK LA PLATA MD classic contemporary

1570 WNST TOWSON MD sports talk

1580 WPGC MORNINGSIDE MD religious/gospel

1590 WJRO GLEN BURNIE MD religious

1600 WKDM ROCKVILLE MD Spanish music/talk

1690 WPTX LEXINGTON PARK MD talk/nostalgia

AM radioThe FCC has allocated ~10 kHz to each AM radio station, which permits stations to broadcast without interfering with each other.

A broadcast signal is first recorded and filtered at a frequency < 5 kHz (why?), then modulated to the assigned carrier frequency, and amplified and transmitted.

The AM tuner or receiver in a radio then receives and (if necessary) amplifies the modulated signal. The signal must then be demodulated, or converted to the baseband version for playback. It turns out AM demodulation is easy, hence its prevalence in the early days of radio.

◦ What would the modulated signal sound like if we did not demodulate?

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Demodulation = envelope detectionRecall:

Approach: find peaks of AM signal, interpolate between them, and subtract offset and rescale.

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xAM(t) = xC(t)[1+mxm(t)]

1+mxm(t)

Example

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Envelope Detection

Find Peak Values

Envelope Detection

Interpolate Peak Values

Example

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Envelope Detection

Subtract DC offset

Optional: rescale by 1/m to account for modulation index.

Alternative: synchronous demodulationThe envelope detection method requires a robust means to find the peaks and perform interpolation.

Another way would use modulation to shift the frequencies of the AM signal backwards, thus moving the signal to the original frequency band.

◦ How? Multiply by the cosine carrier xc(t) again.

◦ Recall cosine function has negative frequency peak as well as positive one.

◦ Then, we can filter out everything above the baseband signal bandwidth.

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Example

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xAM(t) = AC cos(2fCt) [1 + m cos(2fmt)]

fC fC + fmfC - fm

cos(2fCt) xAM(t)

2fC 2fC + fm2fC - fmfm

DemodulationSince there are two copies of the message spectrum in the AM signal, we’ll get one copy on the left side of 0-frequency (DC) and one copy on the right side.

◦ These are called the lower side band (LSB) and upper side band (USB)

◦ All the signal information is in both the LSB and USB.

◦ Why not just transmit and receive one of these, saving half the bandwidth? (assumes real-valued signal)◦ Answer: You can, it’s called single side band (SSB) transmission (used in shortwave, TV, etc.) But, you’ll need a more sophisticated

receiver to demodulate.

Another observation: the frequency component at the carrier frequency itself is not information-bearing. Why not just transmit the LSB and the USB, not the carrier, and save power?

◦ Answer: We can, and it’s called AM – SC: Suppressed carrier

◦ AM-SC can be demodulated by the synchronous detection approach (multiplying by the carrier cosine).

◦ AM-SC cannot be demodulated by envelope detection.

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Digital amplitude modulationWhen transmitting digital signals (binary), the demodulated signal can only be two values. Thus, a simpler model can be used to modulate or transmit: just multiply the carrier by 0/1.

◦ This is called amplitude shift keying (ASK). Note how it compares to AM of a binary signal:

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xAM(t) = AC cos(2fCt) [1 + m xm(t)]xASK (t) = AC cos(2fCt) xm(t)

Amplitude Shift Keying

AnnouncementsNext class: Other modulation schemes (e.g., frequency modulation)

I’ll be away next week.

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