Re: [Repeater-Builder] Occupied Bandwidth.

[scomind]

Hi Bob,     >I didn't want to confuse a highly technical topic with the FM/PM thing again.  Personally, I > find it easier to think of angle modulation in terms of frequency as opposed to phase.     Sure, me too - - maybe most of us on the list. That's probably because we're used to thinking in terms of sine waves. You draw a sine wave, and then you move the zero-crossing point left or right to show how you can change the phase.   The problem is that you can also move the zero-crossing point left or right to show how you can change the frequency. That's what got me. So how do you show the difference between phase and frequency?   The sine wave isn't the right tool to talk about phase, a rotating phasor diagram is. But that's okay. We can do this with sine waves if we look at a string of them.   If you shift the phase by 10 degrees and then leave it that way for a number of cycles, the frequency would change only momentarily. It would change during the time the phase was actually changing, not before or after.   So, a "step" in phase angle resulted in a spike in frequency. Since frequency results from a change in phase, if you differentiate phase, you get frequency. This is just like differentiating velocity to get acceleration.   The reverse works as well. If you change the frequency, the phase must continuously change to accomplish that. And that's the whole difference between PM and FM.     > I didn't want to complicate the discussion of Carson's Rule & TX bandwidth by having to > explain how the numbers add up if using a phase modulated TX.  For example, how do we > determine the modulation index from phase deviation for use in calculating the sideband > amplitudes from the Bessel function?     I forwarded your message to Virgil and this is his response:   The text book general case for the Carson rule does not state highest modulating frequency because the formulae is good for any modulating frequency.  In the case below, they simply have used the bandwidth requirement to condition the formulae for finding the highest modulating frequency. The Carson rule works whether or not the modulating frequency is the highest modulating frequency. My issue is the math statement that implies that BW is found by using the highest modulating frequency. The definition below used the term CBR (bandwith requirement) which is the correct math form for defining the fm as the highest modulating frequency.   Modulation Index for PM is >  MIp = k*Vm  ( k = some constant as detemined by phase modulator )                       For an frequency modulation >Delta f  =  k*Vm ( k = some constant as determined by frequency modulator)    Modulation Index for FM is > MIf = Delta f  /  modulation frequency   Modulation Index for PM is equal to Modulation Index for FM >  MIp = Mif   Carson's Rule for:    FM is >    BW = 2 times ( Delta f   +  modulating frequency )                                                         By using the relationship between PM and FM modulation index.                                      ( Delta f = modulation index times modulating frequency )                                PM is >  BW = 2 times (modulating frequency) times ( modulation index plus one )                                                 The Bessel function x axis is the modulation index - whether the modulation index is from PM or FM.     73, Bob Yahoo! Groups Links To visit your group on the web, go to: http://groups.yahoo.com/group/Repeater-Builder/   To unsubscribe from this group, send an email to: [EMAIL PROTECTED]   Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.