I am trying to figure what kind of antenna model (gain, impedance, radiation, bandwidth) would it be if you parallel a uhf loop and a vhf dipole ? like a typical rabbit ear antenna with a uhf loop.

The reason I am asking is that I happened to notice that when I just use a uhf loop I get all the uhfs pretty good but the vhf-hi is weak. And when I use the rabbit ear (converted to a dipole for Ch11) I get strong vhf-hi, and I also get other uhf channels with reasonable strength, except for the weakest one. I understand these results are as expected with each type of antenna. I am using a 75ohm coax in both cases (and not a 300ohm twin lead with a matching transformer).

However, what I am trying to understand is why do all channels - vhf and uhf - become weak when I connect both the loop and dipole in parallel (in hopes of getting the best of both the worlds). All channels loose some signal strength. None of them come in as strong as they would with each antenna seperately. So what could be going on here ? Does the impedance of the combined antenna change dramatically ? In that case is it higher or lower ? Does the overall gain drop ?

How are joining the VHF and UHF antennas?

Yes, the impedance of the parallel antennas is different than the impedance of either antenna alone, and not always in obvious ways. You can use an antenna modeling program (such as NEC2) to determine the impedance of the combined system at various frequencies, but if this is a practical problem, you just need a uhf-vhf combiner (often sold as a "UVSJ").

If you're currently combining them with a regular splitter (rather than literally connecting them in parallel), the problem is not impedance but a combination of loss due to the splitter, and possibly destructive interference from getting signals from both antennas which are out of phase with each other. The solution is the same, though -- use a UVSJ instead of a splitter.

I am not using a splitter or a combiner. I have them literally hot wired in parallel. The feedpoints of the loop and dipole are in direct contact.

Use this:
http://www.solidsignal.com/prod_display.asp?PROD=UVSJ

And a pair of these:
http://www.solidsignal.com/prod_display.asp?prod=WMXFMRPT

Or... buy a "real" VHF/UHF combo antenna. :)

I think the 'real' vhf/uhf indoor antennas (comparing apples to apples) also suffer from the same effect. I tried 3 such antennas and none of them even came close to the loop or dipole by itself in its own band. They were worse. So I guess what I am trying to do is just understand what is the cause of this degradation in such combo antennas. Just a learning exercise than anything else.

So what exactly does this splitter/combiner/joiner do under the hood ? What is its theory of operation so to speak ?

I have EZNEC demo, but am still climbing the learning curve and I dont think it has a circular loop or not. but if someone's willing to model this that would be great!

So what exactly does this splitter/combiner/joiner do under the hood ? What is its theory of operation so to speak ?
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Basically it's a set of filters, one high-pass for UHF and one low pass for VHF. So UHF signals get one path, VHF signals get the other, and you get neither destructive interference nor impedance mismatch.

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I have EZNEC demo, but am still climbing the learning curve and I dont think it has a circular loop or not. but if someone's willing to model this that would be great!

Model it as a square loop and you should be able to see the effect.