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…d ‰ X:q^g3ZthH]‡_kŽa/Œ X7_ [ {ƒ sGZ d [t[ sug X*… v*X7qˆwZtVuZ Zt]`[y#a e eauz n„ _ke,‰l… ZmX X:{ q_k… q^XW| sY{ _q^„Š_k|‘[tsYvWX%ZtZtZtVY]‡yk|‹aY|~_ X7{Ta@‚~[ ƒ ’_#]‡Zta~]`aY[tX'su„X e,‚…“•”X=Zrq^| X7–Yekq^Œ X:X:ZtZ X7a@e [ ae [tvW]‡_kwaG—„ ˜ e,df™m… g3X š h —k› dœ™mgš [ hŸž X7–MX e [
]df{ ƒ=g3[^hHsYX ŽŒ ƒ7Xe [ qtƒ q^s/]`X:„qr„e,… e,X … { X’_kq^]o|±ZQZ W{ ¡^_k¢q £¤ e da/¥§vW¦w²¡ ™©Zm¨«]‡ykªMa ¬ue­\zlg3e š au„n±sY|X:qtX'd [ –Yg su]oZ ]Te ®¯‰Y–Y]‡a ]œ°e  q^h³Gn e [ e „ e,… X { _#qt| ¨ b ¨ b ¨ b “ b “ b ¨ b “ bQ„]´[^s
‰YX e#]`[*ƒ s npVYƒ:qe e Zt[^X ]`h _#a¶µ hu” _~[tsu]‡Z { _#q ‚ np]´·>X7q^X7a@[ …ez VYX=Z_ {Ÿ¸#¹ºH»uh ¼Yš b h »Yš  h »uh v z Zm_±Z Œ X[ ƒ s/[^sYXPZt]`y#a ez½ƒ _kauZm[tX z`zoe [^]`_#a]‡a
¾§dfe@¿lg3ÀJh Á§µÆÂ=sYÃfX¿MÄjv*Å wÇZt]`y#a ez Z d [ g ]`a¶[tsuX e Z^Zm]‡ykaY|~X:a#[*B]oZÆqtX:„qt]`[m[^X7asYX7q^X { _kq ƒ _ka … X:aY]`X:a ƒ X
dbg
¤ df™mg ®ÉÈ dœ™mg ¢£¤ d ¥§¦¡ ™mg ® ’¡:Ê`b ¨-¸#¹,ËÌdœ™mg•Í ¢7£¤ d ¥§¦¡ ™mg
„sYX:qtX ËÌdœ™mg ®Š *Β¢£¤ d ¥§¦Î ™mghrirz X e q z ³ š©d b gƃ _kV z n‰lXq^X7„q^]´[t[tX:a e Z
d g
¤ dœ™mg ®Š W¡^¢£¤ d ¥§¦¡ ™mg©¨ W¡ ¸#¹ Î ¢£¤ d ¥§¦ Î ™mg ¢£¤ d ¥§¦k¡ ™mg
vQaln¶Zt]‡a ƒ X
¢7£¤ d ¥§¦Î ™mg ¢7£¤ d ¥§¦ ¡ ™mg ® b d ¢7£¤ d ¥ d ¦ ¡ ¨ ¦Î g•™mg§¨ ¢£¤ d ¥ d ¦ ¡HÏ ¦Î g\™mgmg
d  g ƒ _kV z n¶‰MX { _kq^|PV z ]`Ð:X:n e Z
df‚@g
¤ df™mg ®É ’¡t¢7£¤ d ¥§¦¡ ™mg§¨ b ’¡ ¸@¹ Î d ¢£¤ d ¥ d ¦¡ ¨ ¦ Î g•™mg§¨ ¢£¤ d ¥ d ¦¡ Ï ¦ Î g\™mgmg
Ѹ@¹ ]`y#® VYq^»YX%Õ ÖYb*š _#¦a±¡ – ®×e y#b X’»#¸pØ«ZtsYÙl_š „Q¦ ÎZ ek®Úz`z>ƒ b _@¸pZmØ«]‡aYÙlXWšp„ e aue,… n¶X:Z We ¡ au®Én± sY_Î „$®Ú[tsubÛX’Zt„VYsY|ÒX:a _ { ƒ [^qtsYX eX7[^|Ò]`aYÓuy a Ñ e]`z‡y#z ³ VYq^{ XG_kq^b |±h ZH[^sYXWvWw²„ e,… X hԀ X’VuZtX
[tÓud ‰suy#Xg3VYh qtÑ vWX=]‡ZykwÞVue qtq^ZmXBX*]‡yk[^a sYeekXauz |~n „X:Ñ]´Z^[^Z]‡sàyke VYykáß q^X'¥X Zm‚]‡ƒ7yke a– qtekz q^_z ]`Z[WX:qB„[tsY–u]`[tX s s¶e‚#[tZt” suXâX'q^ZmX7sYZ –ue ] {qt|~[ X=š ZmX X:q^{a#X:q^[ZtX:e–lä@[^X VY]`ƒ_#X7[^aa ] … ƒ _ X³{ z ³ ¦ [^hãÎsYXBh†HvWµÆz X wÜsYe XZtX¶Ztƒ7]`eaYy#qta_q^[^e]‡XX7z q „[t„s ]`[te ] sÝz‡[Gz aYaY[^sY__kX[ƃ7‰Me ƒ qtX%_@q^Zm]‡np]‡X7aYX:qX–Y–Y] ƒ„ s [tee,X=…Zmn/XBX:]‡ZBZma¶sY]‡a$[t] {sY[ X‰Me _‚#au[^” sn
q^X7–Yq^X:ZtX7a@[ e [t]‡_ka h µÆsY]oZ ƒ _#V z n¶‰MXÆå\VuZm[t]`ÓuX:n¶]‡a[^sYX { _ z‡z _„]`aYy~npX=npV ƒ [^]`_#a º
b
:XµÆä@sYV X'e [t|~]‡_kXa [^sY_pn { _#qÆ_k‰p[ e ]‡aY]`auyB[^sYX— ˜¤ dœdœ™m™mgÆg e ®Éaln/— ˜ — dœ™m› g dœ¢7™m£g ¤ ]‡dZ[t¥§_ ¦ ¡ ƒ ™m_#g |GÏ – —e ›q^X*df™m[^g ¤sY­çXæHZ d d[ ¥§g ¦ ]‡¡ a ™mg d b g „]`[ts¶[tsYXy#X7aYX:q ekz |G_pnpV z‡e [t]‡_ka
€€ ]`]`[t[tss–Y–YsYsY]œ]œ®®¶»Yè š š „ „ X X ƒ ƒ _k_kV V z znn/ÓuÓuauaunn[^[ts s e e [Q[Q— —˜ ˜ dœdœ™m™mg g ®Š® »G¡ e d aub n¶¨-—k¸ › ¹ df˙mg df®É™mgmgÆ ’e ¡ aud bn/¨é— › ¸@dœ¹,™mgËÌ® dœ™mgt»Yg3h h
irz X e q z ³ š aYX7]`á[tsuX7qQ—˜ dœ™mg aY_#q—k› df™mgƃ _ka@[ e ]‡auZr[tsYX ƒ:e q^qt]‡X7q h
Figure 1. How the sum of 3 cosine waves makes an AM wave
2
s(t)
Ac*cos(2pi*fc*t)
1/2*(Ac*ka*Am)*cos(2pi*(fc+fm)*t)
1/2*(Ac*ka*Am)*cos(2pi*(fc−fm)*t)
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1
t(msec)
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Figure 2. 3−D representation of the AM signal without carrier shift
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vq(t)
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vi(t)
1
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t(msec)
Figure 3. 3−D representation of the AM signal with pi/2 carrier phase shift
1.8
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vq(t)
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vi(t)
−1
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t(msec)
Ñíçdf{ƒ=]`g3y#„rh VYXq^Ñ X’Zt]‡Xykê [QVuš Wqt„rXB¡ X šê¶e[^npsYZtZtX:X VY–Yƒ7|~] eƒ [^X’qtZq^[t]`X:svWq e wë[e |~[tZtsY–]‡Xykz a]´‰Y[^ekVu]`z[*npZWXnp„šVY]´[tq [^_e sc[^b]`‰u_#š ]`a¶„a eµŠX'qts³â]‡Z%e,]‡… aYb7X |±–Yº VYZm[^X Z ƒh e alnÝnp]`·MX:qtX:a@['|~_pnpV zoe [^]`_#a ƒ _@X7ì ƒ X7a@[ˆZ h%í a ƒ q^X e [t]‡aYy
Ñ _#q ¸#¹ ® »YÕî¼pš [tsYX%Zt]‡yka ekz©ƒ _kalZ\[^X z‡z‡e [t]‡_ka¶]‡Z dœï>š ³ g ® d b hî¼pšY»Yhî¼kgh
‚
ÑÑ _#_#qq ¸¸ ¹¹ ®Ú®b ÕÕ »Y»Yšš [t[tsYsYX%X%ZtZt]‡]‡ykykaa ekekz©z©ƒƒ _k_kalalZ\Z\[^[^XX z‡z‡z‡z‡ee [t[t]‡]‡_k_ka¶a¶]‡]‡ZZ dœdœï>ï>šš ³³ gg ®® ddJ‚Y šušp“»@b g3gh h
µÆZt_ sYz VpX±[tZt]‡_k]`y#a a h ezHƒ _kauZm[tX z`zoe [^]`_#auZ e ‰M_ … X e q^XGX e Zt³[t_– z _[%]‡aÌð “òñ – z‡e aYX h µÆsYX:qtX { _kq^X š [^sYX7³ e q^XB_#|G]`[m[^X:n { q^_k|[^sY]‡Z
Figure 4. Amplitude Modulation with Binary inputs
2
ka=0.5
s(t)
1
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ka=1.0
s(t)
1
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ka=2.0
s(t)
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t(mesc)
4
5
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7
UWi _kVYalX=Z\Zm[^]onp]`_#X7aq e |~X:Z^Z e ykXZt]`y#a ez>ËÌdœ™mg ®Š » ¢7£¤ d ¥ ™mgr… _ z [ˆZƄ]´[^s¶[tsYX ƒ:e q^qt]‡X7qƄ e,… X'¢ dœ™mg ® ¼» ¢£¤ d b »#» ¥ ™mgj… _ z [ˆZ h
dfd ‰e@g3g3hHh †jÑ z]`_kal[ n/[^[^sYsYX%Xv*–Mw_„r„X:qQe,…npX'X … Z X d z [ _kgr–M{ X:_#n qWekó ƒ¼ q^_#–lZ^X:Z q ƒ e~X7a@z _ [e |~n__ nY{ V b,z‡ô e [th ]‡_ka h
†ö X7]‡a@q ƒ[ X:º a@ [ e Î y#X*®Š|~ _p»YnpšuV ¸@zo¹ e [^® ]`_#»YaÕ »k]oZ‚ ó b ¼Y»#š »#Zt¸@_G¹ [ts Î e [ ®ÚËb õ »#»® ˶¸#õÔ¹ hÔ í a¶Î y#® X7aY»YX:Õ q ó ek¼Gz e ¤ ZÎ Ztdœ–l™mg X ƒ ®É]`Óu ’X:n ¡:hÊ`b ¨-¸#¹ Î ¢7£¤ d ¥§¦ Î ™mgçÍ ¢£¤ d ¥§¦¡ ™mg
¾§dfe@¿lg3ÀJh Á§µÆÂ=ÃfsY¿MXÄjvWÅ wZt]‡yka ekz „]´[^s«ó ¼ –lX:q ƒ X7a@[|G_pnpV z‡e [t]‡_ka ƒ _#V z n‰MX–YqtX=ZmX:a@[tX:n e Z
¤ dœ™mg ® ¡ d b ¨é¸ ¹ ËÌdœ™mgmg ¢£¤ d ¥§¦ ¡ ™mg ® ¼k»ud b ¨  »@¸ ¹ ¢£¤ d ¥ ™mgmg ¢£¤ d b »k» ¥ ™mg ® ¼»ld b ¨é»YÕ ó ¼ ¢7£¤ d ¥ ™mgtg ¢£¤ d b »k» ¥ ™mg
µÆsYX { _ z‡z _„]`aYyGÓuy#VYq^X'nYX7–Y] ƒ [ˆZ [tsYX e ‰l_ … X'vWwÇZm]‡yka ekzJh
ê
AM signal with 75 percent modulation
100
80
60
40
s(t)
20
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t(sec)
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2
Zsd ‰ d e,[ g3… gjhîX Ž ƒ ]`_#a V ƒ zXn÷„ ‰lX X ƒ ƒ7_ke#V ƒ zV n¶zoe „[^X:q^n~]´[^X%‰³±Z d Zm[ VYgÆ|~e Z|~[t]‡sYaYX%y%Zt[^VYsY|àXW–M_ _{5„ ‚±X7qrƒ _#nYZtX ]`… auX X’z _#„ –le,X=… n~X=Z‰š ³G[^sYX ekXƒ –ls _ƒ „ _#X7ZtqQ]`aunYXQX „… X e,z … _#X –lX=ekn ƒ qtek_@ƒZtq^ZŸ_#[tZ^sYZ X’eGZ e z _ |Ge Xnz _ _ { e n b=ôŠhT€ ‰@³ X
¤ dœ™mg ® ¼» ¢£¤ d b »k» ¥ ™mg½¨ b df‚ ó Õî¼ ¢£¤ d b » ¥ ™mg½¨‚ ó Õî¼ ¢£¤ dfø#Ö ¥ ™mgtg
Ž ]‡a ƒ X’[^sYX–l_„ X7q †5š nYX … X z _#–lX=n e#ƒ q^_#Z^Z eBz _ e n/_ { b,ô‰³ e~ƒ _@Zm]‡aYXZt]`y#a ez W¢£¤ d ¥§¦ ™mgš ]oZ
ù ® á
Ž _G[tsuX–l_„ X7qnpX … X z _k–MX:n‰³Z d [ g3š npX:aY_[^X:n¶‰³ ù5ú š ]‡Z
dê g
ù5ú ® ¼» á:û  ¨Šdf‚ ó Õî¼ û  g á:û Bü%® ¼» á:û  ¨ Gü ‚ ó Õî¼ á:û Ö ®Úb:ý » b Õ ¼ ý# ¼#þ
UWi _kVYalX=Z\Zm[^]onp]`_#X7a q e‚ Zm³pZm[tX:|]`a„sY] ƒ s e |~X:Z^Z e ykXGZm]‡yka ekz ]‡Z'|BV z [^]`– z ]‡X:nc‰³ e Z^ä@V e q^XG„ e,… XP„]`[ts|G]‡aY]‡|PVY| … _ z [ e ykX »
eZtsYal_n±„Š| sYe_ï „¯]`|BVuVYZt| ]‡aYy±… _ | z [ e e [tyksuXPX7| b ee [^al] n±ƒ Z –le X:alqt]‡n _pn«e b ‰ û z _¦ƒˆ¡ ŒhHi npe] e a±ykq[tesu| ]‡ZÆhjZt³íç{ Zm[t³#X:_k|ÒV‰lVuX’ZtX VueZtX:Ón±z [t[^X:_Pq y#š X7ZmaY–MX:X q ƒ e ] { [t³¶X ]´e [ˆa/Z v*ƒ X7wxa@[tX:„ q e,{ … qtXX={ä@_kVYq^X7|÷a ÿ ƒ ³ íç{ e Zmau_ n š
‰¾§e ¿lauÀJÁ§np„Â=Ãf]o¿MnÄj[ts Å h
eŽ Z]‡a ƒ XQ[tsYX’Ztä@V e qtX„ e,… X š npX7au_[tX=n~‰³GZ^ä@V e q^X d [ g3š ]oZH–MX7q^]`_pnp] ƒš „rX ƒ _kV z n~„q^]´[^XQ]`[^Z Ñ _kVuqt]‡X7qjZtX7q^]‡X:ZHnpX ƒ _#|G–M_#Zt]`[t]‡_ka
dJ¼#g
¤ õ È dœ™mg ® d È ¢£¤ d ¥ ¸ ¦¡ ™mg§¨ ¤ ­çæHd ¥ ¸ ¦¡ ™mgtg
¼
t[„™ susY]‡Z%X:qtÊ »ZtX~_ zÈ Vpß [^]`®g_#š a Ztáß ä@{ š_#V q%È e qtnpX X® d [ [ e g »/] ®Bz Z{ bG_k_#q „ac¸sYsu] z _‘X~„ÚZt»ä@[tV_e eauƒ:qtn ekX ƒ d [V g z‡®e ® [t»±X±»u{ È _#š q ™e au® n Ê ß ß gè ©h÷ß ßí a ghP{ƒ _#_k€ q |~¸]`–Y[tscVYÚ[t[t]‡aYsY»Ìy«X~d –sYÈ zX X z e–e ZmauX~_ n {Wq^X dò{¼kX7gš q’š „ [^„r_X X [^e ƒ sYZ^_#XZmV Vuez |Gn«–YXG–Mq^X7X7[^–Yals q^npe X:][ ïZtX7{ _#a@_ q[{
[tsuXqtX=ZmV á z [_ { |PV z [t]‡– z ³@]‡aYy±| d [ g „]`[ts e Ztä@V e qtX’„ e,… X e Z á
dý g
¤ df™mg ® Ëdf™mg ¤ õ È dœ™mg ® ËÌdœ™mg ¤ ­çæHd ¥ ¸ ¦¡ ™mg§¨ È Ëdf™mg
ß
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dó g
¤ dœ™mg ® ß Ëdf™mg ¤ ­çæHd ¥übü¦¡ ™mg ® ¥  Ëdf™mg ¤ ­çæHd ¥§¦¡ ™mg
Ñir]`z y#X VYe qq^zX ³ š¼Y[^h sYXP_#Vp[t–uVp[W_ { [tsYXPÓ z [^X7qW]‡Z e÷”'Ž r“•Žui vWwÜZt]`y#a ezòh µÆsYXBnY] e ykq e |à_ { [tsYX e ‰M_ … X%Z ƒ sYX7|~X%]oZWyk] … X7a]‡a
"!
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&%$')(+*,'(
.-
m(t)
Soutput(t)
-fc
+fc
square(t)
Figure 5. The diagram illustrating how to
make AM waves with square wave as the carrier
UWi _kVYalX=Z\Zm[^]onp]`_#X7aq e ê aPvWw}Zm³pZm[tX:|„]`[ts …e q^] e ‰ z X ƒ:e q^qt]‡X7q e |~– z ]´[^VunpX eYš ZmV ƒ s'[ts e [Ÿ¤ dœ™mg ®Š ¡ d È ¨B¸ ¹ ËÌdœ™mgtg ¢£¤ d ¥§¦ ¡ ™mg©e aun
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Figure 6: AM signals with variable carrier amplitudes and their FFTs
s(t)
2
50
0
10
20
30
t(msec)
s(t)
5
50
1000
2000
3000
frequency(Hz)
4000
5000
a=1,ka=2
50
0
10
20
30
t(msec)
40
50
0
0
1000
2000
3000
frequency(Hz)
60
a=0.5,ka=1
4000
5000
a=0.5,ka=1
40
20
0
10
20
30
t(msec)
1
40
50
0
0
1000
2000
3000
frequency(Hz)
60
a=0,ka=1
4000
5000
a=0,ka=1
40
0
−1
0
100
0
−2
0
150
a=1,ka=2
2
s(t)
40
0
−5
a=1,ka=1
100
0
−2
s(t)
150
a=1,ka=1
20
0
10
20
30
t(msec)
40
50
0
0
1000
2000
3000
frequency(Hz)
4000
5000
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