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How is this transfer function algebraically deduced ?

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STOIKOV

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H(s) oscillatory system

how is this transfer function algebraically deduced ?

Thks.
 

v_c

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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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