Adam,
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You may be chasing a red herring.? In many older or even current inexpensive digital oscilloscopes, if you view the waveform at a much lower rate than its true value, you can see all sorts of sub-sampling effects and aliasing, showing what appear to be real signals, but are not really present.? This is because the scope firmware decimates the sampling rate it uses for low frequencies, causing aliasing if the signal is really at a higher rate. ?My new inexpensive digital scope does the same thing.
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If your 25MHz clock was truly fully modulated by that low frequency 'signal' you are seeing, you would also see traces of varying amplitudes when viewed on the scope at 25MHz - but the 25MHz waveform is clean, no trace of varying amplitudes due to sinusoidal modulation, which would definitely be captured by the full rate sampling.? I think what you are demonstrating may be the effects of digital sampling in your oscilloscope, rather than a true modulating signal.
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To verify, find someone with an analog scope and check with it.
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Stan KC7XE