• If I have the spectrum of a FM modulation, does the frequency of the carrier disappear when the modulation index is too big?
  • Does the amplitude of any side band depend from the modulation index?
  • And does the total number of side bands depend on the modulation index?
  • $\begingroup$ This sounds like homework. Did you try to answer these questions? What have you thought so far? $\endgroup$ – Tendero Apr 5 '17 at 1:46
  • $\begingroup$ These are three questions in one. Reduce to one question, show what you've tried so far, and discuss where you encountered problems. If you don't do that: smells like homework you're trying to offload unto us, like Tendero said. $\endgroup$ – Marcus Müller Apr 5 '17 at 6:41

Assuming an FM modulation of a sine wave of frequency $f_m$. Theoretically, the modulated signal is an infinite sum of cosines at the frequencies $f_c + nf_m$ ($n\in \mathbb{Z}$) which the amplitudes depend on the coefficients $J_n(\beta)$ (of course in addition to the amplitude of the carrier wave), where $\beta$ is the modulation index and $f_c$ is the carrier frequency. At this stage, the answer to the question Q.2. is yes. For the other items:

  • Q.1. The PSD of the modulated signal in $f_c$ is determined for $n=0$, then the PSD at that frequency depends on the coefficient $J_0(\beta)$. Knowing that $J_n(\beta)$ trends to zero as $\beta$ trends to infinity, so the PSD of the modulated signal in $f_c$ trends to zero as the modulation index trends to infinity.

  • Q. 3. Theoretically the bandwidth of an FM modulated signal is infinite. But when considering Carson bandwidth rule ($B_C$), the answer to your question is yes since this rule considers the modulation index. $B_C=2(1+\beta)W$ where $W$ is the baseband bandwidth of the modulating signal (assuming a sine wave, $W=f_m$).

  • $\begingroup$ you might want to add the quantitative expression of the Carson rule. $\endgroup$ – robert bristow-johnson Apr 6 '17 at 2:41
  • $\begingroup$ @robertbristow-johnson Updated. Thanks. $\endgroup$ – Sofiane Apr 6 '17 at 5:09

Its IES or Gate question having last option which you didn't mention here as "carrier frequency can not disappear." . Here correct answer among these 4 option is b i.e. the amplitude of any sideband depends on modulation index . . 2.Frequency spectrum of FM is analysed using Bessel's function .FM spectrum theoretically has infinite number of sidebands . Each sideband has an amplitude , a function of J(β) i.e. β dependent . . 1. Although , as β increases , J(β) decreases , and hence carrier frequency component decreases significantly , true , but won't disappear . Carrier in FM disappears VIRTUALLY , what it means is , as the modulation index vary , sideband amplitudes varies and hence power contents in each side band , which is also a function of β , varies at the cost of power content in carrier component . Being total power constant and equal to carrier power without modulation, At some specific values of β ( not necessarily to be high) , whole of the FM power is distributed in sidebands and hence carrier power becomes zero , or we say carrier disappeared. So option 4 , carrier can't disappear is wrong , as it can disappear and option 1 is wrong as β need not to be high. . Option 3 , total number of sidebands are dependent on β ? Wrong . Total number of sidebands are always infinite , what Carson rule tells is , number of significant sidebands holding most of power ( ~90%) are equal to β+1 sidebands on either side , keeping in mind , channel is of finite bandwidth , we use those significant bands in calculation , that doesn't mean total number of sidebands are β dependent .


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.