# EC05032Notes-31.pdf

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www.jntuworld.com www.jwjobs.net ANALOG COMMUNICATIONS LECTURE NOTES-31 UNIT-IV UNIT-IV ANGLE MODULATION Notes-31 Generation of FM Waves: There are two methods of generating frequency modulating wave namely indirect FM and Direct FM. Indirect FM :  In this first consider the generation of a narrow-band FM Wave.  Consider the expression for FM Wave S1 (t ) = A1 cos[2πf 1t + φ1 (t )] Where f1 is the carrier frequency and A1 is the carrier amplitude.  Now the argument φ1(t) is given by t φ1
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ANALOG COMMUNICATIONS UNIT-IV LECTURE NOTES-31 D.TIRUMALA RAO ECE GMRIT Page 1 of 3 Ref: Analog & Digital Communications Simon Haykins UNIT-IV ANGLE MODULATION Notes-31 Generation of FM Waves: There are two methods of generating frequency modulating wave namely indirect FM and Direct FM. Indirect FM :    In this first consider the generation of a narrow-band FM Wave.    Consider the expression for FM Wave [ ] )(2cos)( 1111  t t  f  At S   φ π   +=  Where f  1  is the carrier frequency and A 1  is the carrier amplitude.    Now the argument φ 1 (t) is given by )2()(2)( 011  −= ∫ t  dt t mK t  φ   Where K 1  is the frequency sensitivity of the modulator And φ 1 (t) is assumed to small for all t. [ ][ ] )4()()(sin )3(1)(cos 111 −≈−≈ t t and t  φ φ φ       The FM wave equation (1) becomes )5()(2sin22cos )(2sin2cos)( 01111 111111 −−=−= ∫  dt t mt  f  At  f  A t t  f  At  f  At S  t  π π π φ π π       The above narrow band FM wave can be generated as shown in figure below.       The above expression shows difference with standard form in two ways: i. the envelope contains a residual amplitude modulation which varies with time and www.jntuworld.com www.jntuworld.com www.jwjobs.net   ANALOG COMMUNICATIONS UNIT-IV LECTURE NOTES-31 D.TIRUMALA RAO ECE GMRIT Page 2 of 3 Ref: Analog & Digital Communications Simon Haykins ii. for a sinusoidal modulating wave, the phase of the FM wave contains harmonic distortion in the form of 3 rd  & higher order harmonics of modulation frequency f  m .    The above two can be reduced by maintaining the modulation index β   ≤  0.3.    Now the narrow band fm wave can be made wideband fm by passing through a frequency multiplier.    The frequency multiplier consists of a non-linear device and a bandpass filter as shown in fig. below.    In this the memory less non-linear device has input-output relation )6()(............)()()( 1212112  −+++=  t S at S at S at S   nn  Where a 1 , a 2  ……… a n  are constant coefficients.    Substituting (5) in (6), the expression S 2 (t) has a dc component and in frequency modulated waves with carrier frequencies f  1 , 2f  2 ……nf, and frequency deviations ∆ f  1 , 2 ∆ f  2 ……n ∆ f  1  respectively.    Here ∆ f  1  can be determined by frequency sensitivity K 1  of narrow-band frequency modulator and maximum amplitude of the modulating wave m(t)    The band-pass filter is used in 2 respects. i. to pass the fm wave centered at the carrier frequency nf1 with frequency deviation n ∆ f  1  ii. to suppress all other FM spectra.    Now the narrow-band frequency modulator and frequency multiplier are connected to produce a wideband frequency modulated wave S(t) with carrier frequency nf1 and frequency deviation ∆ f= n ∆ f  1  as shown in fig. below.    Now the frequency sensitivity of wideband modulator Kf is n times that of a narrow-band modulator.    Crystal oscillator is used for more stability at high frequencies. www.jntuworld.com www.jntuworld.com www.jwjobs.net   ANALOG COMMUNICATIONS UNIT-IV LECTURE NOTES-31 D.TIRUMALA RAO ECE GMRIT Page 3 of 3 Ref: Analog & Digital Communications Simon Haykins www.jntuworld.com www.jntuworld.com www.jwjobs.net

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