Question about correlated shocks

Hello, I have a question about setting up correlation between shocks.

Based on the posts that I found so far, I know that there are two ways of setting up correlation between shocks. The first way is to include the commands in .mod as below,

var eps_1; stderr STD_1;
var eps_2; stderr STD_2;
var eps_1, eps_2 = CORR_12STD_1STD_2;

The second way is to imposing a common factor representation of the shocks in the model block. Based on
Correlation between shocks, I can set,

u1 = eps_corr + eps_1;
u2 = CORR_12*eps_corr + eps_2

where u1 and u2 are endo. variables and eps_corr, eps_1 and eps_2 are exogenous variable.

However, I just want to know how to set up the correlation using the second way such that I have “equivalent” setup as using the first way to set up. In this case, how should I set standard deviation of eps_1, eps_2 and eps_corr?

Thanks for your kind attention…