why do you find it harder to sleep when you're on a diet?

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i observed recently that when im on a low caeb diet i have trouble sleeping, and when i do get to sleep, i'll doze off for about 3 hours then i'll wake ip and won't be ablo to go back to sleep/ sometimes i would be laying there for hours till its time to get out of bed. and i've been told by my friends and brother that they experience the same thing when they're dieting. what's that all about? can't it be possible to diet and enjoy a good night's sleep?