Carrier spacing related to period to go in phase

[Natalie Johnson]

Hi,

I start at 100 MHz have 10 carrier frequencies all starting in phase at t=0 and the carrier frequencies have 25 kHz spacing. So my frequency range is 100-100.25 MHz, with 10 single frequencies equally spaced in this range. They are therefore all different frequencies, spaced 25khz apart.

Ive found on a graphing tool that they come in phase every 4x10^-5 seconds. The equation Frequency = 1 / Time_period works for this... with frequency being the frequency of the carrier spacing. Even though they are all different frequencies with different time periods they are all in phase every 4x10^-5 seconds.

The time period between all carriers coming back in phase (after going out of phase at t=0 or at any time after they realign) is directly related to the spacing of the carrier frequencies using this equation. I am struggling to see how this is related but it works. Perhaps I am looking for an elegant explanation of this

Please can someone advise

 

[BvU]

Work out $\ \sin (2\pi f t) = \sin (2\pi (f+\Delta f) t)$ and $\ \cos (2\pi f t) = \cos (2\pi (f+\Delta f) t)$ (for the derivative) and you see it.

 

[Natalie Johnson]

Work out $\ \sin (2\pi f t) = \sin (2\pi (f+\Delta f) t)$ and $\ \cos (2\pi f t) = \cos (2\pi (f+\Delta f) t)$ (for the derivative) and you see it.

Hi,
Interesting but can you explain a bit more with what you mean

 

[BvU]

You know that $\ \sin (x) = \sin (x+2\pi) \$, I hope ?

 

[Natalie Johnson]

You know that $\ \sin (x) = \sin (x+2\pi) \$, I hope ?

Hi,
Yes but I'm not sure what you are trying to show and how it relates

 

[BvU]

That you are back to the situation at $\ t=0\$ after a time span of $\ 1/\Delta f\$ which I consider an explanation as asked for

 

[Natalie Johnson]

That you are back to the situation at $\ t=0\$ after a time span of $\ 1/\Delta f\$ which I consider an explanation as asked for

Hmm I already have this on my script and it's shows they are back in phase, but I was looking for a bit of an explanation of why a frequency of frequencies has this time period and the time period they all come back in phase is the same regardless of how many single frequencies you have .

I mean I can have 200 or 1000 frequencies all starting at time zero in phase, because the frequencies have the same spacing between them then they always come back in phase at a later time with time interval t= 1/spacing_frequency

 

[BvU]

What more can I say ? Do you understand it ?
Are you familiar with trigonometric functions for beats and sum/differences ?

regardless of how many single frequencies

as long as they all have the same frequency difference (or multiples of that), things will repeat after $\ 1/\Delta f\$...

 

[skeptic2]

I ran into this situation at a previous job. We had 10 transmitters spaced 600 kHz apart with all their frequencies derived from the same frequency reference. When all their phases aligned every 1/600kHz sec, all the transmit waveforms would be at max power (or min power) at the same time. This resulted in a 600 kHz modulation of the power supply which in turn caused a 600 kHz intermod spur around each carrier. If a carrier went off, there was still the intermod spur on that frequency from the adjacent channels.

 

[jim hardy]

Ive found on a graphing tool that they come in phase every 4x10^-5 seconds.

Graphing is the best way to visualize it.

Or perhaps think of square waves as in digital logic with flip-flop frequency dividers. Every forty microseconds they align because of common term in the denominator. ...

 

[Baluncore]

So my frequency range is 100-100.25 MHz, with 10 single frequencies equally spaced in this range. They are therefore all different frequencies, spaced 25khz apart.

Take out a common factor of 25k from all 10 channels and you get frequencies separated by exactly 1Hz. They will obviously all repeat in phase every 1 second = 1/ 1Hz. Put the factor of 25k back into get phase repetition of 40 μsec = 1/ 25kHz.