![\"](\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/angle-modulation.jpg\")
<\/p>\nThere is another method of modulating a sinusoidal carrier wave, namely, angle modulation in which either the phase or frequency of the carrier wave is varied according to the message signal. In this method of modulation the amplitude of the carrier wave is maintained constant.<\/p>\n
We begin our study of angle modulation by writing the modulated wave in the general form<\/p>\n
x(t) = Acos[\u03b8(t)]<\/p>\n
Where the carrier amplitude A, is maintained constant, and the angular argument \u03b8(t) is varied by a message signal m(t). In any event, a complete oscillation occurs whenever \u03b8(t) changes by 2\u03c0 radians. If \u03b8(t) increases monotonically with time, the average frequency in hertz, over an interval from t to t +\u2206t, is given by\u00a0![\"](\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/angle-modulation-1.jpg\")
<\/p>\n
Phase modulation (PM) is that form of angle modulation in which the angular argument \u03c6(t) is varied linearly with the message signal m(t), as shown by<\/p>\n
Here \u03c6(t) \u221d m(t) where, kp is the phase modulation constant with generally the unit of the radian\/volts or radian\/Ampere. \u03b8(t)=2\u03c0fc<\/sub>t + kp<\/sub>m(t) Note: The instantaneous frequency in PM case:<\/p>\n \u03c9i<\/sub>(t) = d0i<\/sub>(t)\/dt = \u03c9c<\/sub> + kp<\/sub>\u00a0dm(t)\/dt<\/p>\n fi<\/sub>(t) = \u03c9c<\/sub> \/2\u03c0 + kp<\/sub>\u00a0\/2\u03c0 d\/dt m(t)<\/p>\n Frequency modulation (FM) is that form of angle modulation in which the instantaneous frequency fi<\/sub>(t) is varied linearly with the message signal m(t), as shown by<\/p>\n fi<\/sub>(t) \u221d m(t) where, kf <\/sub>is the frequency sensitivity of the modulator with generally the unit of the rad\/sec\/volt or Hz\/volt. \u03c9i<\/sub> = \u03c9c<\/sub>\u00a0+ kf<\/sub>m(t) fi<\/sub> = fc<\/sub> + kf<\/sub>m(t)<\/p>\n Consider a sinusoidal modulating wave defined by<\/p>\n m(t) = Am<\/sub>cos (2\u03c0fm<\/sub>t)<\/p>\n The instantaneous frequency of the resulting FM wave equals<\/p>\n fi<\/sub>(t) = fc<\/sub>+ kf<\/sub>\u00a0Am <\/sub>cos(2\u03c0fm<\/sub>t)<\/p>\n = fc<\/sub> + \u2206f cos(2\u03c0fm<\/sub>t)<\/p>\n where \u2206f = kf<\/sub>Am<\/sub><\/p>\n The quantity \u2206f is called the frequency deviation, representing the maximum departure of the instantaneous frequency of the FM wave from the carrier frequency fc<\/sub> . A fundamental characteristic of an FM wave is that the\u00a0 frequency deviation frequency deviation \u2206f is proportional to the amplitude of the modulating wave and is independent of the modulation fr modulation frequency.<\/p>\n Using the above equation the regular argument \u03b8(t) of the FM wave is obtained as Consider a sinusoidal modulating wave defined by<\/p>\n m(t) = Am<\/sub>cos(2\u03c0fm<\/sub>t)<\/p>\n The instantaneous phase of the resulting PM wave equals<\/p>\n The quantity \u03b2 is the modulation index, representing the maximum departure of the instantaneous phase of the PM wave from the carrier phase \u03c6(t) = 2\u03c0fc<\/sub> t. A fundamental characteristic of an PM wave is that the modulation index modulation index \u03b2 is proportional to the amplitude of the modulating wave and is independent of the modulation fr modulation frequency.<\/p>\n The instantaneous frequency of the phase modulated wave can be obtained as << Previous<\/a> | Next >><\/a> There is another method of modulating a sinusoidal carrier wave, namely, angle modulation in which either the phase or frequency<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[758,6],"tags":[784,783,782,785],"class_list":["post-2841","post","type-post","status-publish","format-standard","hentry","category-communication-systems","category-ec","tag-fm-modulation","tag-frequency-modulation","tag-phase-modulation","tag-pm-modulation"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/2841","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=2841"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/2841\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=2841"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=2841"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=2841"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\ntherefore, \u03c6(t) = kp<\/sub>m(t)<\/p>\n
\nNow, combining the result with the carrier phase we get,<\/p>\n
\nx(t) = Ac<\/sub>cos [2\u03c0fc<\/sub>t + kp<\/sub>m(t)]<\/p>\n
\n<\/strong><\/p>\nFrequency Modulation<\/h3>\n
\nfi<\/sub>(t) = kf <\/sub>m(t)<\/p>\n
\nNow, combining the result with the carrier frequency we get,![\"](\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/frequency-modulation.jpg\")
<\/p>\n\n
\nfi<\/sub> = fc<\/sub> + kf<\/sub>\/2\u03c0 m(t)<\/p>\n\n
Single-Tone Frequency Modulation<\/h3>\n
FM Modulation<\/h4>\n
![\"FM](\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/fm-modulation.jpg\")
<\/p>\nPM Modulation<\/h4>\n
![\"PM](\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/pm-modulation-1.jpg\")
<\/p>\n![\"](\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/pm-modulation-2.jpg\")
<\/p>\n
\n Must Read: <\/strong> What is Communication?<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"