Need 28 VDC UPS for a phone PBX Control Box

How long a power outage do you want to plan for?
Here is one suggestion:
Three 14.4 volt Nicad power packs meant for portable electrical tools, plus a charger. "Generic" packs can be bought for ~16GBP in the UK so I guess they are cheap in the US?
Put a rectifier in series with the output from the existing supply (probably not needed but better to be safe than sorry). Put five rectifiers in series with two of the power packs and connect that supply in parallel with the existing supply (plus its new rectifier).
Fully charge all the packs. Temporarily hook up a multimeter, on the amps range, in series with the battery packs. It should read zero. If it doesn't read zero, add more rectifiers. Now short out one of the five rectifiers. Repeat until the meter starts reading current, no matter how small. Then unshort the last rectifier. The meter should read zero. Turn down the multimeter to a lower amps range and check that it still reads zero. If not, unshort rectifiers until it does. Repeat until you reach the mA range of the meter.
The third battery is so that you can periodically have a recharge session, putting the two in use packs through the charger whilst the spare is in their place. Don't forget to have a recharge session after each outage.
Here is another suggestion:
Buy 3 12 volt sealed lead-acid batteries (sized to suit the reserve time you want), together with 3 suitable float chargers. Wire the batteries in series. Buy a 24 volt 3 terminal regulator IC, a suitable heatsink, a couple of resistors and capacitors and a couple of rectifiers (I can give you the details if this solution appeals - there is some electronics-style soldering involved). The resistors offset the reference voltage of the regulator, so it produces approx. 28 volts. (This will be adjusted, monitoring the current, so that the load is met by the main supply under normal conditions.)
Stick one rectifier in series with each supply and parallel their outputs.
Note that as the float chargers are connected to the mains and also to the phone system, via this arrangement, this may not be a legal solution - as the chargers probably wouldn't be certified for such use. Laws vary according to where you live. Most phone companies are (quite rightly) paranoid about the possibility of mains being shoved back up their phone lines.. no matter how unlikely the possibility.
Hence the first suggestion - where the charging is done "off-line". No need for certified mains chargers.
HTH Sue

Actually two 12 volt batteries is only 24 volts under no load, when fully charged.
On the other hand, if they are being trickle charged the voltage will bu just over 26 volts. And if being equalized, 28 volts.
And when being discharged the battery should have a low voltage cutoff at about 21 volts.
Which suggests that your PBX may or may not run off a pair a 12 volt batteries... and only by looking at the specs will you know for sure.
It will almost certainly be least expensive to buy a UPS that puts out 120VAC and plug your existing 28VDC 1 AMP supply into it. Such an UPS is a commodity item these days, while a 24 volt system is still a relatively special item not used by consumers.
But one point is also certain: it is a *lot* less complex to figure out the right 120VAC unit!

Very much agree - you could have added that it is quite possibly going to be the only solution that keeps the phone company happy!
The "very large" existing power brick is very large probably because it is type-approved for use with the phone system and has the necessary fault protection. Any mains-connected system in parallel with it would need to be similarly certified.
A UPS before the power brick would not need that certification.

Thanks to all for the suggestions. I live in the US and am a bit confused over the term "certification". I assume it is something similar to a UL (Underwriters Labs) listing meaning that it has passed certain safety standards. The PBX control unit I have must have some DC to AC invertors because it does generate ring voltage (about 90 VAC) for the phone extensions.
The Office Max and Office Depots stores are selling these super cheap $20 UPS units with a very limited VA rating (I think it was 150 VA or so). I bought one of these when they a bit more expensive about two years ago and was very disappointed with its performance. Just recently, this UPS spontaneously failed and the battery would no longer hold a charge. The worst part was that the failure mode resulted in a dead output to the protected circuit, even after the main AC power came back on. I would expect it to keep supplying power, but set off the warning beeper or something. In this case, this particular UPS caused more trouble than it was worth.
Beachcomber

Simplest is to buy a UPS and plug the wall wart into it.
The idea below requires a little work: The PBX probably would run fine from 24 volts. If it will run reliably from 24 volts, the solution is simple enough:
--------- D1 D2 ----- |Existing |+28--->|--->|---+--------------| PBX | |Wall | | | | |Wart | ----- | | | | | 24V | | | | | | Batt| | | | | ----- | | | | | | | | |----------------+--------------| | --------- -----
D1,D2 = 1N5400; Batt = 2 12V Gel Cells
The two diodes drop the voltage to protect the batteries from overcharge, and also prevent them from pushing current through the wall wart when mains power drops. The wall wart and diodes will keep the batteries charged. You would have to measure the wall wart output to verify that it produces 28 volts. If it is unregulated, it could produce significantly more, which would overcharge the batteries. However, if it supplies well over 28 volts, that could open up the possibility of using an additional 6 volt battery for a total of 30 volts.
Ed

It isn't high voltages appearing on extensions that worry phone companies, it is high voltage appearing on *their* lines (it may have an engineer connected to them or someone from BAT..). But I haven't a clue what is mandatory in the US, in that respect.
I use UPS and inverters all the time ( I live in the middle of a National Park and also play with boats). You get what you pay for. I would rather buy a second hand good quality one from ebay (and budget on replacing the batteries, if fitted) than a cheap new one from Staples (a poor copy of your Office Depot.. doesn't sell *any* guns).

its possible this UPS sacrificed its life to save your expensive phone system :)
one consideration in rigging up a direct battery back up is it will void any warranty. a service tech making a call will go what the heck is this?
an additional problem that could crop up is hum in the audio if you are charging the battery from an unregulated supply.
one possibility, if warranty is not an issue, is to add a large capacitor to the 28 VDC point. this might, depending on capacitor size and load, be enough to unplug the unit briefly while swapping UPS units without losing your programming.
you might want to check into the phone system to see if it has an internal memory battery that has failed or is missing or something.

The proper float voltage for a '12-volt' lead acid battery is about 13.5 to 13.8 volts depending on the exact chemistry of the battery. I suggest using only 1 diode. Bill Kaszeta Photovoltaic Resources Int'l Tempe Arizona USA snipped-for-privacy@pvri-removethis.biz

Again thanks to all contributers. I wound up doing the Office Depot route today and bought an APC 200 watt UPS. It seemed like the easiest and least expensive solution after considering the discussion here.
It cost $39.95 which I think is a pretty good price. In the past two years it seems that the commodity UPS technology has advanced. This unit appears to have more sensing capacity for the condition of the battery, a "soft" on-off switch and more status lights to display if the battery is low (or needs to be replaced).
One reader suggested checking for an internal battery on my phone system. Actually, It had a small 6 volt lead-acid battery that is supposed to keep the memory alive during power outages. I replaced this battery several times but it doesn't seem to hold a charge. I tried it with and without a diode Open circuit (charging) voltage on the load side is 5 V. I have no schematics to attempt troubleshooting, but as long as I keep the main wall-wart power supplied with voltage, the system stays happy.
For those interested in the phone system, this is a Voice Pro 412 PBX phone controller that works with plain old telephones and makes it sound to your callers like you have a $15000 voice mail system. As far as I know, the company is out of business, but sometimes you can buy refurbished Voice Pro units on eBay for $450-$500. Except for the power issue... It works flawlessly and is a good system for a small business.
Beachcomber

it is easy to make guesses from far away but what if the measured 5 volts is what the memory is looking for to stay alive and the battery charge supply is just dead?
a 6.3 volt battery will need a bit more then that (voltage) to keep charged up.
installation manual here