Calculating Bandwidth of FM Signal: Angle Modulation Q1

In summary: So in summary, the question asked for the bandwidth of an output signal from a device with a transfer function of y(t) = x(t), given an input FM signal with frequency deviation of 90 Khz and modulating frequency of 5 Khz. The modulating index was calculated to be 18 and using the Carson rule, the bandwidth was determined to be 190 Khz. However, a discrepancy arose when the source provided the answer of 380 Khz. After further discussion, it was determined that the question may have been misprinted and the correct answer would have been 380 Khz if the transfer function was y(t) = x^2(t).
  • #1
lazyaditya
176
7
Q1. A device with input x(t) and output y(t) is characterized by y(t) = x(t). If a FM signal with frequency deviation 90 Khz and modulating frequency 5 Khz is applied to the input terminals of the device then what will be the bandwidth of the output signal received ?



What i did was calculated the modulating index i.e by dividing frequency deviation by the modulating frequency and got the value equal to 18. Then by using carson rule calculated the bandwidth of the FM signal to be B.W = 2(18 + 1)(5) = 190 Khz.

But answer is not this , how should i do the question then ?
 
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  • #2
Decades since I did this but isn't the modulation index the other way up eg

5/90 = very low

so only one pair of side bands?

B.W = 2(v.small + 1)(5) = 10 Khz
 
  • #3
I got the same answer you did: 2(90 + 5) the way I did it.

Maybe your source wasn't satisfied with 98% of the energy contained within the Carson bandwidth. After all, the real answer is infinity! The Bessel function expansion of the modulated carrier extends without limit ...
 
  • #4
The answer given to me was 380 Khz that is 2 * 190 and i dnt know why , do it have to do something with the transfer function but h(t) = 1 since y(t)=x(t) , the FM signal is having bandwidth equal to 190 Khz at the time of input but how and why will it double when passed through the device having relationship y(t) = x(t), please help ?
 
  • #5
rude man said:
I got the same answer you did: 2(90 + 5) the way I did it.

Maybe your source wasn't satisfied with 98% of the energy contained within the Carson bandwidth. After all, the real answer is infinity! The Bessel function expansion of the modulated carrier extends without limit ...

why is the real answer infinity ?
 
  • #6
CWatters said:
Decades since I did this but isn't the modulation index the other way up eg

5/90 = very low

so only one pair of side bands?

B.W = 2(v.small + 1)(5) = 10 Khz

Modulation index is 90/5 , i gave frequency deviation to be 90 and modulating frequency to be 5
 
  • #7
lazyaditya said:
why is the real answer infinity ?

Because if you expand the modulated signal in a series, that series has an infinite number of harmonics. In this case it's a Bessel series. You get Bessel series whenever you get functions like sin(a + bsin(x)) etc. This should be available somewhere in Wikipedia, if your textbook doesn't cover the subject rigorously.

E.g. http://en.wikipedia.org/wiki/Frequency_modulation
 
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  • #8
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  • #9
rude man said:
Because if you expand the modulated signal in a series, that series has an infinite number of harmonics. In this case it's a Bessel series. You get Bessel series whenever you get functions like sin(a + bsin(x)) etc. This should be available somewhere in Wikipedia, if your textbook doesn't cover the subject rigorously.

E.g. http://en.wikipedia.org/wiki/Frequency_modulation

Ya total bandwidth is infinity but we don't consider the low powered components right? so they are neglected. But what about 380 Khz ?
 
  • #10
lazyaditya said:
Modulation index is 90/5 , i gave frequency deviation to be 90 and modulating frequency to be 5
With a modulation index of 18 it would be considered broadband FM, I think. But I can't see how bandwidth can be much different from 2*(18+1)*5 kHz.
 
  • #11
lazyaditya said:
Ya total bandwidth is infinity but we don't consider the low powered components right? so they are neglected. But what about 380 Khz ?

Right on the first part.

As for the second: I have no idea where the 380KHz comes from. It's obviously twice the answer we're getting. Are you sure you wrote the question down right? Seems funny they gave you y(t) = x(t). That's just a straight feedtru from input to output! If they had given you y(t) = x2(t) then you would have generated the 2nd harmonic of 190 KHz = 380 KHz at the output.
 
  • #12
rude man said:
If they had given you y(t) = x2(t) then you would have generated the 2nd harmonic of 190 KHz = 380 KHz at the output.
Ding! I believe we have the winner.
 
  • #13
rude man said:
Right on the first part.

As for the second: I have no idea where the 380KHz comes from. It's obviously twice the answer we're getting. Are you sure you wrote the question down right? Seems funny they gave you y(t) = x(t). That's just a straight feedtru from input to output! If they had given you y(t) = x2(t) then you would have generated the 2nd harmonic of 190 KHz = 380 KHz at the output.

Thanks for this , i think then the question in book would have been wrong and answer would have been this "380 Khz" when y(t)= x^2(t)
 

FAQ: Calculating Bandwidth of FM Signal: Angle Modulation Q1

1. What is the formula for calculating the bandwidth of an FM signal?

The formula for calculating the bandwidth of an FM signal is B=2*(Δf+fm), where B is the bandwidth, Δf is the peak frequency deviation, and fm is the maximum modulating frequency.

2. How does varying the modulation index affect the bandwidth of an FM signal?

The bandwidth of an FM signal is directly proportional to the modulation index. This means that as the modulation index increases, the bandwidth of the signal also increases. Conversely, as the modulation index decreases, the bandwidth decreases.

3. Can you explain the difference between narrowband and wideband FM signals?

Narrowband FM signals have a smaller bandwidth and therefore carry less information compared to wideband FM signals. Narrowband FM signals are commonly used for voice communication, while wideband FM signals are used for high-fidelity music transmission.

4. How does the maximum modulating frequency affect the bandwidth of an FM signal?

The maximum modulating frequency has a direct impact on the bandwidth of an FM signal. The higher the maximum modulating frequency, the wider the bandwidth of the signal will be. This means that higher frequencies can carry more information, but also require more bandwidth.

5. Can the bandwidth of an FM signal be reduced without affecting the quality of the signal?

No, the bandwidth of an FM signal is directly related to the amount of information it can carry. Reducing the bandwidth will result in a loss of information and a decrease in signal quality. However, techniques such as pre-emphasis and de-emphasis can be used to selectively reduce certain frequencies and improve the overall quality of the signal.

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