# Low Entropy derivation of Transfer Functions with OP AMPS

I was recently low entropy equations of passive filters, and came across the Extra Element Theorem and all of its uses.

I was wondering if the there is something similar for OP AMP circuits/ Active Filter Circuits?

• What do you find from googling? Commented Jun 27, 2018 at 14:04
• Look for Middlebrooks General Feedback Theorem
– HKOB
Commented Jun 27, 2018 at 14:23
• Why do you think, the EEE could be limited to passive filters only? This theorem can be applied to linear active and passive circuits.
– LvW
Commented Jun 27, 2018 at 14:53
• I haven't gone through the EEE formally, I have gone through a tutorial which explains its use for passive circuits. Commented Jun 28, 2018 at 17:18

Yes, active filters are simply passive filters where you can ignore impedance losses and you don't have to worry about load or source impedance.

Here is an example of turning a transfer function into a "low entropy" state for an active filter

$$W(s) = \frac{R_2}{-R_1+(-R_2-R_3)C_1R_1s-C_2C_1R_3R_2R_1s^2}$$

to

$$H(s) = -\frac{R_2}{R_1}\frac{1}{1+(R_2+R_3)*C_1s+C_2C_1R_3R_2s^2}$$

• Besides the question if "active filters are simply passive filters" I like to mention that for the majority of active filters we must NOT ignore source impedances.
– LvW
Commented Jun 28, 2018 at 6:33