The phasing method generates a single sideband signal, given
mathematically as
cos(( )t) , where
the + (-) sign gives the upper (lower) sideband, and
= 2f_{c} where f_{c} is the carrier frequency.
Similarly,
= 2f_{a} where f_{a} is the audio modulating frequency.
The cosine can be written as

cos(( )t) = cos(t)cos(t) sin(t)sin(t),

(1)

the basic equation of the phasing method.
The multiplications on the right-hand side are accomplished using
balanced modulators, and the two audio frequencies (as well as
the two radio frequencies) must be 90^{ o } out of phase and
of equal amplitude.
I will assume that the radio frequencies are exactly 90^{ o }
out of phase, and of equal amplitude.
Using the usual
complex notation with
V_{A}e^{ jt} to be one audio
signal, and
V_{B}e^{ jt} to be the other, the result
of using a nonideal phasing network will be