FM Modulation: Solving Problems with 400KHz and 40 Amplitude

[mohlam12]

Hello,

So I was studying for my exam and came across this exercice we did in class and which I really don't know how we got the answer.

It says that if we have a FM with a carrier frequency of 4MHz, and the bandwidth is 400KHz, what is then the maximum deviation.. The answer is 200KHz.

So how did they figure it out? I know that BW = 2 ( Freq. Dev. + Signal Freq.)

And, the second question states: if the maximum amplitude of the source signal is 40, what would the modulation index be? The answer is 5.

Anyone can tell me how they solved it ? Thanks.

 

[fss]

It says that if we have a FM with a carrier frequency of 4MHz, and the bandwidth is 400KHz, what is then the maximum deviation.. The answer is 200KHz.

So how did they figure it out? I know that BW = 2 ( Freq. Dev. + Signal Freq.)

You can just think about this conceptually. If you have a signal 400 kHz wide centered on 4 MHz, you can only deviate ±200 kHz in either direction around the center frequency.

And, the second question states: if the maximum amplitude of the source signal is 40, what would the modulation index be? The answer is 5.

Anyone can tell me how they solved it ? Thanks.

This question seems unclear to me. Amplitude only matters in AM as far as the modulation index.

 

[skeptic2]

And, the second question states: if the maximum amplitude of the source signal is 40, what would the modulation index be? The answer is 5.

Anyone can tell me how they solved it ? Thanks.

The modulation index is the maximum frequency deviation divided by the maximum modulating frequency. We already know the maximum deviation is 200 kHz and 200 kHz divided by 5 = 40 kHz.

I suspect the problem was misstated. Instead of maximum amplitude it should have said maximum frequency and instead of 40 it should have been 40 kHz.

 

[mohlam12]

Thank you. I think the problem was misstated.

 

[DeeNos]

Hello,

It seems like you are studying FM modulation and are having trouble understanding how to solve these types of problems. Let me break down the steps for you:

1. In FM modulation, the bandwidth is equal to the sum of the frequency deviation and the signal frequency. So, in this case, the bandwidth is 400KHz, which means it is equal to the frequency deviation + 4MHz (carrier frequency).

2. We can rearrange this equation to solve for the frequency deviation, which is what we are looking for. So, 400KHz = frequency deviation + 4MHz. Subtract 4MHz from both sides, and we get the frequency deviation = 400KHz - 4MHz = -3.6MHz.

3. However, we know that frequency deviation can't be negative, so we take the absolute value of -3.6MHz, which is 3.6MHz. This is the maximum frequency deviation.

4. Since frequency deviation is equal to the modulation index (m) multiplied by the maximum amplitude of the source signal, we can rearrange this equation to solve for the modulation index. So, m = frequency deviation / maximum amplitude = 3.6MHz / 40 = 0.09.

5. However, the modulation index is usually expressed as a ratio or percentage, so we multiply 0.09 by 100 to get 9% or we can also express it as 1/11.

I hope this helps you understand how to solve these types of problems. Let me know if you have any further questions. Best of luck on your exam!