Hi Erwin,
With the relatively low current of 20mA on the secondary, the TPS54620 should support this no problem. The key specification when looking at using a buck converter as a fly-buck is the negative current limit. The equation below from the TPS55010 datasheet can be used to estimate the negative peak current. Iout in this equation is the second side Iout. The TPS55010 apps section considers only a secondary side load.
With the very low current on the secondary in this application, we can specify the inductance of the primary side like a normal inductor ignoring the secondary output. The transformer should also be rated for the current needed in the application. Again we can specify this based on the buck portion of the circuit only since the secondary current is so low in this application.
Lastly the turns ratio should be set to get the right output on the secondary side. When calculating the turns ratio, make sure to account for the voltage drop across the diode on the secondary side. Assuming a 0.7V drop across the diode, target a 4.0V output before the diode giving a primary to secondary turns ratio of 1:4.0/1.8 = 1:2.2. For this calculation it would be best to look at the forward voltage of the diode they plan to use. I suspect it will have a lower forward voltage drop than 0.7V and they may be able to use a 1:2 turns ratio as a result.
Anthony
