Your options for a signal connection are a physical cable (phone to amp), Bluetooth or WiFi.
Physical is easy to understand, but obviously ties the phone to the stereo system while plying music. You're using Bluetooth right now, so you've already got a handle on the distance limits and understand that the phone is using your mobile data allowance for 3G/4G if it cn't reach the house Wi-Fi for an internet connection. Wi-Fi is a bit like Bluetooth except the range you can move with the phone in your pocket is much greater, and the music is streamed via your house broadband connection.
Related to this then is which of the features are supported (and how) by any amps you might look at.
Again, physical is easy. Most amps have a Line Input of some description. Bluetooth could be built in to an amp, or available as an add-on adapter that connects to a Line Input on an older/non-Bluetooth (BT) amp. BT is a low cost technology. It's possible to pick up a BT plug-in adapter for under £25. You'd then be able to choose any amp you wish.
Wi-Fi is more expensive but more flexible too. Audio devices that support Wi-Fi generally have the ability to stream audio directly from the net.
Matching the amp to your speakers
Your B&O speakers are a nominal 4 Ohm load (impedance). They're also fairly large and fitted with a 12" bass driver. The consequences of the impedance and the bass driver size is that they'll need an amp capable to delivering some real wattage. What this means is that the cheap Chinese Class-T and Class-D amps might not be up to the task despite what the spec sheets and sales blurb claims.
You see, the adverts make some claims about power that look really enticing for the price, and unless you happen to be a bit of an electronics buff then it's very hard for you to verify or disprove those claims. Fortunately, some of us here have been there, done it and bought the tee-shirt, so if you want, you can learn from our experience rather than waste your own money.
Prompted by your enquiry, I've just been looking at Ebay and the sales page for a "600W" amp with BT and USB and FM, all for £25 delivered from China. 600W!?!.... my left buttock.
The spec is almost non-existent, so a quick look at the pictures reveals the power rating for the DC input. It shows 12V/5A, and since Wattage = V x A, and 12 x 5 = 60, then our '600W' amp can draw at most 60W. What we're looking at then is the first lie. The amp can't generate extra power. That would break the laws of physics. All it can work with as continuous power is what it draws from the mains. In this case it's 10% of the claimed power output. However, that's not the end of the story.
60W is the total maximum power consumption with all the features running. The tuner takes a bit of power, and so does the USB socket and the vacuum fluorescent display and the pre-amp and not to mention a bit of energy lost as heat too, so there's an overhead to running the product. Let's be generous and say that it's only 10%. This leaves us 54W maximum.
It's also well-known in electrical circles that the sort of digital amps found in these products are, at best, 70% efficient. The very best digital amps achieve 90%, but they cost hundreds and thousands of Pounds, not £25 delivered. That means at least 30% of the power is lost in the amplifier stage, so we have, at best, 38W in total.
The final nail in the coffin is distortion.
The maximum power available is with the amp running flat out, and that means a lot of distortion in the signal too. Distortion is bad for speakers. More tweeters are killed because of distortion than are killed because an amp is too powerful. With these small digital amps, they go in to distortion quite early. You might get to half or 2/3rds of the available power before distortion becomes noticeable, at which point the amp is already throwing out 10% distortion. Let's be generous and say it's 2/3rds the power. Our 38W then drops to 25W, and you have to divide that by two because you have two speakers. A whopping 13W per channel then of useable power, and even then it's at the sort of distortion levels that no self-respecting Japanese or European amp manufacturer would consider acceptable in a music product.
When I started looking at amps on Ebay for this reply, I came across a second-hand Yamaha AX300. It's on a Buy-it-Now at £39 delivered. It looks tidy. The only negatives are that it would need a BT adapter, and that the mains cable is short.
Specs for this type of product are widely available. I can see that the maximum power consumption is 180W, and yet Yamaha rate the amp at just 30W/ch. That's because they rate the power output very conservatively. The distortion figure is 0.05%, and measured with both channels driven continuously and using a real music signal (20Hz-20kHz). They've taken an RMS value for power which is another conservative step because it's 70% of what would be available as peak power. The bottom line is that this older Yamaha has a lot more real world power than any of the Chinese Class-T/Class-D amps under £150.
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