Finding the times when one cycle occurs for FM wave

In summary, the conversation discusses the search for the times when one cycle occurs for a FM wave, and the attempt to find an exact solution by plotting the wave argument in n-t "space". The approximate solution of t_{2} ≈1/f_{c} + t_{1} is found, but an exact solution has not been determined. A correction is made to the equation for y(t).
  • #1
Rick66
6
0
Hello everyone,

I'm trying to find the times when one cycle occurs for a FM wave. For instance, given

y(t) = sin(2∏f[itex]_{c}[/itex]*t[itex]_{1}[/itex] + sin(2∏f[itex]_{m}[/itex]*t[itex]_{1}[/itex]))

at an arbitrary time t[itex]_{1}[/itex], I wish to find the time t[itex]_{2}[/itex] such that

(f[itex]_{c}[/itex]* t[itex]_{2}[/itex] + sin(2∏f[itex]_{m}[/itex]* t[itex]_{2}[/itex]) – (f[itex]_{c}[/itex]*t[itex]_{1}[/itex] + sin(2∏f[itex]_{m}[/itex]*t[itex]_{1}[/itex]) = 1 (cycle).

Now I've tried plotting the wave argument in n-t "space" (i.e. n is cycles),

n = f[itex]_{c}[/itex]*t + sin(2∏f[itex]_{m}[/itex]*t)

to see if some solution presents itself. For instance, we can see that it gives oscillations about the regularly increasing line n = f[itex]_{c}[/itex]*t so that t[itex]_{2}[/itex] ≈1/f[itex]_{c}[/itex] + t[itex]_{1}[/itex] gives an approximate solution. But as to an exact solution, I've hit a brick wall. So if somebody could point me in the right direction it would be greatly appreciated.
Thank you
Rick66
 
Last edited:
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  • #2
Rick66 said:
Hello everyone,

I'm trying to find the times when one cycle occurs for a FM wave. For instance, given

y(t) = sin(2∏f[itex]_{c}[/itex]*t[itex]_{1}[/itex] + (1/∏)sin(2∏f[itex]_{m}[/itex]*t[itex]_{1}[/itex]))

at an arbitrary time t[itex]_{1}[/itex], I wish to find the time t[itex]_{2}[/itex] such that

(f[itex]_{c}[/itex]* t[itex]_{2}[/itex] + sin(2∏f[itex]_{m}[/itex]* t[itex]_{2}[/itex]) – (f[itex]_{c}[/itex]*t[itex]_{1}[/itex] + sin(2∏f[itex]_{m}[/itex]*t[itex]_{1}[/itex]) = 1 (cycle).

Now I've tried plotting the wave argument in n-t "space" (i.e. n is cycles),

n = f[itex]_{c}[/itex]*t + sin(2∏f[itex]_{m}[/itex]*t)

to see if some solution presents itself. For instance, we can see that it gives oscillations about the regularly increasing line n = f[itex]_{c}[/itex]*t so that t[itex]_{2}[/itex] ≈1/f[itex]_{c}[/itex] + t[itex]_{1}[/itex] gives an approximate solution. But as to an exact solution, I've hit a brick wall. So if somebody could point me in the right direction it would be greatly appreciated.
Thank you
Rick66

PS: I have made the correction to y(t) above.
 

1. How do you determine the frequency of an FM wave?

The frequency of an FM wave can be determined by finding the number of cycles that occur in one second. This can be done by measuring the time it takes for one complete cycle to occur and then dividing that time by one second.

2. What is the formula for finding the frequency of an FM wave?

The formula for finding the frequency of an FM wave is f = 1/T, where f is the frequency and T is the period, or the time it takes for one complete cycle to occur.

3. How do you find the period of an FM wave?

The period of an FM wave can be found by measuring the time it takes for one complete cycle to occur. This can be done using a stopwatch or other timing device.

4. Can you find the frequency of an FM wave by counting the number of cycles in a given time period?

Yes, you can find the frequency of an FM wave by counting the number of cycles that occur in a given time period and then dividing that number by the total time. This will give you the frequency in cycles per second, or Hertz (Hz).

5. How do you use an oscilloscope to find the times when one cycle occurs for an FM wave?

To find the times when one cycle occurs for an FM wave using an oscilloscope, you can use the horizontal scale to measure the time it takes for one complete cycle to occur. You can then divide this time by one second to find the frequency of the wave.

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