Hi,
I don´t see this "earthed one side of an antenna problem"
An offline SMPS is powered from mains. Mains usually is earthed.
Then follows a rectifier. Is the output of the rectifier still earthed or not? I´d say: partly.
Then capacitor, switcher. The switcher causes the HF problems, because the DC (capacitor) will be turned into a PWM.
And due to capacitive coupling this HF will be pushed to the secondary side.
This common mode voltage noise initially will be in the same magnitude as the PWM voltage at the switcher. more than 300V-pp.
Primary side switcher --> capacitive coupling in transformer --> secondary
Stray impedances (series, parallel) may reduce this a little.
But if you connect a capacitor from primary to secondary... it´s job is to reduce this voltage.
Let´s say the coupling capacitance is 100pF (ignoring other stray impedances) and the pri-sec-capacitor is 1nF, then idealy the common mode voltage noise can be reduced to 1/11.
Mind: this does not reduce the short circuit noise current.
An additional inductive common mode filter increases series impedcance, thus it reduces short circuit noise current and further reduces common mode voltage.
Mind: voltage always needs a reference. And current needs a loop.
A sketch that shows these "reference" and "loop" will help to understand.
Klaus