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Timebase Corrector is actually a 'sync doctor' (from Video Demystified Glossary), most of the time when the video source is from VCR, sync pulses get screwed up and you should use some heuristics to correct them. There is no standard way to do that, it's up to you to design an ad-hoc TBC.
Timebase correctors are used to stabilise and correct the fluctuations in sync pulse signals when a video signal is distorted . The most common use is for video tape syncrinisation. Video signals tend to very duo to tape strech and deack mechanics. They are quite difficulte to build as I have tryed and My advice would be to look for a tried and tested circuit on the net.
There are simple TBCs like that one used in Panasonic AG4700 and similar devices. This TBC corrects 3 consecutive transmitted lines so they are precisely in time. When the first line has left the memory the fourth line is stored into it so always 3 lines are corrected.
This helps reducing jitter which appears at the h-sync. It helps when the picture is basically in sync but the line beginnings are unstable.
If the pictures (frames) are not in sync to each other (from two asynchronous sources) you will have to use a full-frame TBC. This one stores a complete frame and is more difficult to build. For a simple 3-line TBC look at the schematic of the VTR mentioned above.