To my knowledge, a conventional transformer is a balun – you simply connect a single-ended signal at the primary side, you get the balanced signal at the secondary side – magnetic coupling doesn't care where the ground is. It also automatically offers DC isolation.
But I see broadband RF mixers and amplifiers have a center-tap at the balanced side as well, for example Mini-Circuit offers a lot of baluns with center-tap. I often see the tap is grounded (or sometimes AC-coupled to ground), and seems to serve no purpose (*).
I found an application note from Mini-Circuit, AN-20-002: Application Note on Transformers, it says,
For Balun applications, choose a balun with center tap on balanced side as it provides excellent amplitude and phase balance.
In other words, a balun with an unconnected center-tap (or without one), has worse amplitude and phase balance than a center-tapped balun? Why? So a connection to ground can force the center to be at common ground potential, thus making the balanced side to have better balance?
(*) I know in double balanced diode mixers, a center-tap is needed to extract IF signal. I also read that a grounded center-tap can remove excessive common-mode voltage at the balanced side, that may degrade the performance of a differential amplifier. But I'm asking about the balun device, not its applications.
Best Answer
For RF transformers/baluns, the inter-winding capacitance can play a big part in reducing common-mode signals between unbalanced input and balanced output. A 1 pF inter-winding capacitance may not seem that much but, at 1 GHz, it's an impedance of 159 ohms.
So, if you don't ground the centre-tap your balun won't be working as effectively as it can do because the balanced output will be strongly capacitively coupled to the unbalanced input. For most circuits this won't matter, but if you are relying on very low common-mode coupling then you need to ground the centre-tap.