I use matlab function tf2sos to convert digital filter transfer function data to second-order sections form:

[sos,g] = tf2sos(b,a)

Taken from the help menu of the matlab:

G is a scalar which accounts for the overall gain of the system

My question is: Because G is the overall gain if i draw the block diagram is going to be something like below (i use office visio for the pictures, if you press view picture the resolution is good but in this thumbnails they look awfull, sorry about that) :

enter image description here

But if i want yo design my system like: enter image description here

how can i find the gain between every node(b1,b2...etc)?

enter image description here


If I understand your question correctly, you want to split the total gain between two or more stages. In this case you just have to satisfy $G=g_1g_2g_3$, where $G$ is the total gain returned by tf2sos() and the $g_i$ are the individual gains per stage.

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