# How is this transfer function algebraically deduced ?

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#### STOIKOV

##### Full Member level 4
H(s) oscillatory system

how is this transfer function algebraically deduced ?

Thks.

#### v_c

Re: H(s) oscillatory system

The input to the gain block is
$X=V_{in}-V_{out}$
the output of the gain block is
$V_{out}=H(s) X=H(s) (V_{in} - V_{out}) = H(s) V_{in} - H(s) V_{out}$
rewriting this with $V_{out}$ on the left and $V_{in}$ on the right we get
$(1 + H(s)) V_{out}= H(s) V_{in}$
rearranging by cross multiplying gives
$\frac{V_{out}}{V_{in}} = \frac{H(s)}{1+H(s)}$

I hope this helps you out.

Best regards,
v_c

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### STOIKOV

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