I'm a EE student who recently purchased the classic Art of Electronics (new 3e). I was reading the first few chapters when I was referred to appendix J in the book depicting a SPICE tutorial but also with a circuit containing only resistors and capacitors (no inductors!) claiming to have a voltage transfer function greater than unity.


simulate this circuit – Schematic created using CircuitLab

Could someone kindly explain to me how this circuit operates such that V_out is greater than V_in? If it is a common circuit, what name does it have? The peak, according to the textbook, is at 1.096kHz with a voltage gain of 1.142. All the simulators I have tried agree with this result, and at least according to the textbook an actual circuit probed with an oscilloscope had the same behavior.

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    \$\begingroup\$ A passive circuit cannot have power gain but, as is the case here, a 2nd order circuit can certainly have voltage gain (\$Q \gt 1)\$. Have you tried solving for the transfer function for this circuit? \$\endgroup\$ Jun 26, 2016 at 2:19
  • \$\begingroup\$ I have not yet; I apologize for posting so early; I was a bit shocked that a second order filter without an inductor could do so as a quick Google search did not yield that information... I will solve for the transfer function and edit my post accordingly. \$\endgroup\$
    – hedgepig
    Jun 26, 2016 at 3:12
  • \$\begingroup\$ Have a look at the comments to this question, I've put a bit of references. Unfortunately, I'm too in hurry to write here a proper answer. \$\endgroup\$ Jun 26, 2016 at 9:29

1 Answer 1


To put in the simple term, the phase shift created by R1, C1/C2 and the phase shift created by R2, C2 are as such that the phases of voltages across C1 and C2 are aiding each other (although not perfectly in the same vector direction), their combined value is greater than the supplied voltage.

This is not so extraordinary as there are some op amp circuits especially notch filters which uses resistors and capacitors to stimulate the behaviour of inductors.


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