You can use your VCR as an analog TV tuner.
In most cases you would want to use the RCA composite connectors to connect the VCR's outputs to the DVR's input but depending on what inputs and outputs the DVR & TV have. You might do it in other ways.
The main limitation is that your DVR probably doesn't have any way to control the tuner on the VCR. If you don't need to program channel changes that won't be a problem.
You can try programming channel changes on the VCR and times on on the DVR (make sure that their clocks match!). You will have to check and make sure the VCR automaticly outputs video when doing a timer recording and you may need to have a tape in the VCR to have it do programmed channel changes.
If you want to use RCA composite (yellow- red- white) cables for both the DVR & TV inputs, you can buy short cables that split the RCA cables.
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If you use an antenna:
After 2/17/09 you will need a digital tuner (aka "converter box") to receive over the air TV broadcasts. All of the converters that you can use the government coupon with have composite & RF outputs so you can hook it up just like a VCR.
The models that are out so far all have to have their channels set manually, but around July 08 a model (Echostar TR-40) is supposed to come out that has a "VCR timer". Just what this "VCR timer" does hasn't been explained yet.