Effect of amplitude magnification in passive RC network

Hi,

I'll be very thankful if somebody can bring me an explanation or send me a link to some papers describing the following effect in passive RC network. If we have a plurality of RC sections (see attached schematic PNG and LTSPice models in ZIP) and each of it has the same RC constant for some particular frequency on some specific place of the network I witness increase of the input voltage. For me it sounds crazy but in the simulations I can clearly see magnification of the amplitude up to 1.27x (if the driving voltage is 1.0V on some place of the network for some particular frequency I can measure 1.27V).

I made also an experiment with real parts and I found that the effect is existing not only in the simulations but in the reality as well. A real prototype of generator was built by using this principle and it works well with amplification equal to 1.0. The RC network was placed in appropriate way in the feedback of JFET transistor and the RC network was used to make the total amplification in the feedback bigger than 1.

In LC group an effect of amplitude magnification is well known (Q factor) but I never heart about a similar effect in RC networks. My explanation is that the network works as a non effective charge pump - you can see how the voltages on each of the resistors is slightly shifted by phase (see attached image Differential voltages.png)

I attached LTSpice models so you can easy prove what I said. LTSpice is excellent free simulator from https://www.linear.com/designtools/software/#LTspice which I hotly recommend to everyone.

Thank you.

Kind regards
Luben

Head on over to the library (or use IEEExplore) and look up this paper:

"Synthesis of Passive RC Networks with Gains Greater than Unity", Herman Epstein, Proceedings of the IRE, July 1951, page 833.

Gives examples and theory.

Brilliant!

I din't expect to get so quickly the response.

Thank you!