# Passive RC network with voltage gain greater than unity?

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.

• 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? – Alfred Centauri Jun 26 '16 at 2:19
• 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. – hedgepig Jun 26 '16 at 3:12
• 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. – Massimo Ortolano Jun 26 '16 at 9:29