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# [Moved]: how to find transfer function for block diagram like that

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#### MahmoudHassan

##### Full Member level 6
Hello
I am struggling in calculating transfer functions from blocks like that ( I can calculate it using small signal models) but I found papers and projects also calculate transfer functions from block diagram like that
How can I calculate it ?
Best Regards

Re: how to find transfer function for block diagram like that

Each transconductor (g_m) is a voltage controlled current source, so using nodal analysis You are able to achieve a transfer function for it in easy way.

MahmoudHassan

### MahmoudHassan

Points: 2
Re: how to find transfer function for block diagram like that

As an alternative, you simply can apply Blacks formula for the closed-loop gain Acl of feedback systems:

Acl=Af/(1-LG)

with Af=total forward gain (without feedback); LG=Loop gain (negative gain of the whole feedback loop)

MahmoudHassan

### MahmoudHassan

Points: 2
Re: how to find transfer function for block diagram like that

Each transconductor (g_m) is a voltage controlled current source, so using nodal analysis You are able to achieve a transfer function for it in easy way.
Thanks a lot for your help , really appreciated

Aha great , where is the controller voltage for the input gm1 , I know it is the input voltage but for gmc (in feedback network) where is the controller voltage for this dependent current source ?

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As an alternative, you simply can apply Blacks formula for the closed-loop gain Acl of feedback systems:

Acl=Af/(1-LG)

with Af=total forward gain (without feedback); LG=Loop gain (negative gain of the whole feedback loop)

I will try it mathematically ,
Thanks a lot for your time
really appreciated

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