If we consider two complex Higgs doublets with $SU(3)_{c} ⊗ SU(2)_L ⊗ U(1)_Y$ quantum numbers $\phi_{A,B}$ ∼ (1,2,1), such that

$\phi_A =
\begin{pmatrix} 
\phi_{A}^{\dagger}\\
\dfrac{1}{\sqrt2} (Re \phi_{A}^{0} + iIm \phi_{A}^{0})
\end{pmatrix}$   &  $\phi_A =
\begin{pmatrix} 
\phi_{B}^{\dagger}\\
\dfrac{1}{\sqrt2} (Re \phi_{B}^{0} + iIm \phi_{B}^{0})
\end{pmatrix}$

If we assume that they acquire the vacuum expectation values (vevs):

$<\phi_A> =
\begin{pmatrix} 
0\\
\dfrac{v_A}{\sqrt2} 
\end{pmatrix}$   & $<\phi_B> =
\begin{pmatrix} 
0\\
\dfrac{v_B}{\sqrt2} 
\end{pmatrix}$

I know that we can change the basis from {$\phi_A,\phi_B$} to a {$\phi_1,\phi_2$} basis, bearing in mind that only one doublet gains a non zero vev as follows:

$<\phi_1> =
\begin{pmatrix} 
0\\
\dfrac{v}{\sqrt2} 
\end{pmatrix}$   & $<\phi_2> =
\begin{pmatrix} 
0\\
0 
\end{pmatrix}$

My issue is that which particular transformation can I use to be able to do this transformation and how do I proceed from there. Basically asking for how can I express {$\phi_A,\phi_B$} in terms of {$\phi_1,\phi_2$} and relate the $v_A, v_B $ and $v$ altogether

Please someone help me out.

Thanks!