Trajectory of the tip of a phasor of an AM modulation for a single tone:

Dr. H.M. de Oliveira, FEDERAL UNIVERSITY OF PERNAMBUCO-UFPE  (UFPE)

control parameters are {m, fm/fc }, respectively, the AM modulation index and the frequency ratio of the tone for carrier frequency.

m=0,2

m_0v2_fmDIVfc_0v1.PNGm_0v2_fmDIVfc_0v3.PNGm_0v2_fmDIVfc_0v7.PNG

fm/fc=                   0,1                                                                        0,3                                                                                        0,5                                                                        0,7 

m=0,5

m_0v5_fmDIVfc_0v1.PNGm_0v5_fmDIVfc_0v3.PNGm_0v5_fmDIVfc_0v5.PNGm_0v5_fmDIVfc_0v7.PNG

fm/fc=                   0,1                                                                        0,3                                                                                        0,5                                                                        0,7 

 

m=0,8

m_0v8_fmDIVfc_0v1.PNG m_0v8_fmDIVfc_0v3.PNG m_0v8_fmDIVfc_0v5.PNG m_0v8_fmDIVfc_0v7.PNG

fm/fc=                   0,1                                                                        0,3                                                                                        0,5                                                                        0,7 

 

m=1,0

m_1_fmDIVfc_0v1.PNGm_1_fmDIVfc_0v3.PNGm_1_fmDIVfc_0v5.PNGm_1_fmDIVfc_0v7.PNG

fm/fc=                   0,1                                                                        0,3                                                                                        0,5                                                                        0,7 

 

CASES in which the carrier is slower than the signal (not usual in AM modulation for transmission

m=0,2

m_0v2_fmDIVfc_2.PNGm_0v2_fmDIVfc_3.PNGm_0v2_fmDIVfc_5.PNG

fm/fc=                                   2                                                                                            3                                                                              5

m_0v2_fmDIVfc_7.PNGm_0v2_fmDIVfc_10.PNGm_0v2_fmDIVfc_25.PNG

fm/fc=                                   7                                                                                            10                                                                            25

m=0,5

m_0v5_fmDIVfc_2.PNGm_0v5_fmDIVfc_3.PNGm_0v5_fmDIVfc_5.PNG

fm/fc=                                   2                                                                                                           3                                                                                               5

   m_0v5_fmDIVfc_7.PNGm_0v5_fmDIVfc_10.PNGm_0v5_fmDIVfc_25.PNG

fm/fc=                                   7                                                                                            10                                                                                           25

m=0,8

m_0v8_fmDIVfc_2.PNGm_0v8_fmDIVfc_3.PNGm_0v8_fmDIVfc_5.PNG

fm/fc=                                                   2                                                                                            3                                                                                              5

m_0v8_fmDIVfc_7.PNGm_0v8_fmDIVfc_10.PNGm_0v8_fmDIVfc_25.PNG

fm/fc=                                      7                                                                                           10                                                                                                       25

m=1,0  m = 1.0 LIMIT CASES WITHOUT OVERMODULATION — modulator signal faster than carrier

m_1_fmDIVfc_2.PNGm_1_fmDIVfc_3.PNGm_1_fmDIVfc_5.PNG

fm/fc=                                                   2                                                                                            3                                                                                              5

m_1_fmDIVfc_7.PNGm_1_fmDIVfc_10.PNGm_1_fmDIVfc_25.PNG

fm/fc=                                      7                                                                                            10                                                                                                       25

BITONAL CASE (example)   fm1/fc=5  fm2/fc=0,1

m1_0v3_m2_0v1fmDIVfc_5_0v1.PNGm1_0v3_m2_0v3fmDIVfc_5_0v1.PNGm1_0v3_m2_0v5fmDIVfc_5_0v1.PNGm1_0v3_m2_0v8fmDIVfc_5_0v1.PNG

m1=0,3 m2=0,1                                                 m1=0,3 m2=0,3                                                 m1=0,3 m2=0,5                                                m1=0,3 m2=0,8

 

BITONAL CASE (example)   m1=0,5  m2=0,2

fm2_fm0v1.GIFfm3_fm0v1.GIFfm5_fm0v1.GIFfm7_fm0v1.GIF

 

fm1 & fm2=                 2 & 0,1                                                             3 &0,1                                                                    5 & 0,1                                                              7 & 0,1

 

Relationships have some similarities with

EYE DIAGRAMS, and with some NYQUIST DIAGRAMS, geometric figures (folio, lemniscatas, cardioides ...), FIGURES OF LISSAJOURS ...

 

Some animations showing the evolution of the figures by gradually increasing the modulation depth m are shown:

 

Transition0v3.gif 

 

Transition3.gifTransition5.gif