Can an arbitrary RLC-circuit network have non-minimum phase zeros? I am working with certain input-output maps that can be thought of as large RLC-networks.  I thought maybe this might be a place to get some thoughts/ideas/answers.
My basic question is, given some large connected RLC network (all linear and ideal elements) and two ports in the network, say 'a' and 'b', can the transfer-function between the ports have non-minimum phase zeros?
More generally, is it true that every transfer function representing an RLC-circuit network is minimum phase?
I suspect the answer is true, but I am having a hard time proving it.
Thanks!
 A: 
More generally, is it true that every transfer function representing
  an RLC-circuit network is minimum phase?
I suspect the answer is true, but I am having a hard time proving it.

It's not true because you can have an RLC all-pass filter. To see a more specific example, let's analyse a lattice phase equaliser topology:

Writing the node equations:
$$(V_A - 1)Z^{-1} + (V_A - 0)Z'^{-1} = 0\quad{\rm (node\ A)}$$
$$(V_B - 1)Z'^{-1} + (V_B - 0)Z^{-1} = 0\quad{\rm (node\ B)}$$
Reordering:
$$V_A(Z^{-1} + Z'^{-1}) - Z^{-1} = 0\quad{\rm (node\ A)}$$
$$V_B(Z^{-1} + Z'^{-1}) - Z'^{-1} = 0\quad{\rm (node\ B)}$$
Subtracting the equations and reordering:
$$(V_A - V_B)(Z^{-1} + Z'^{-1}) - (Z^{-1} - Z'^{-1}) = 0$$
$$(V_A - V_B)(Z^{-1} + Z'^{-1}) = Z^{-1} - Z'^{-1}$$
$$V_A - V_B = \frac{Z^{-1} - Z'^{-1}}{Z^{-1} + Z'^{-1}}$$
By linearity and definition of transfer function:
$$ H(s) = \frac{Z(s)^{-1} - Z'(s)^{-1}}{Z(s)^{-1} + Z'(s)^{-1}}$$
If we use an inductor $L$ as impedance $Z$ and a capacitor as impedance $Z'$ we get:
$$Z(s) = sL$$
$$Z'(s) = (sC)^{-1}$$
$$H(s) = \frac{\frac{1}{sL} - sC}{\frac{1}{sL} + sC}$$
$$H(s) = \frac{\frac{1 - s^2LC}{sL}}{\frac{1 + s^2LC}{sL}}$$
$$H(s) = \frac{1 - s^2LC}{1 + s^2LC}$$
$H(s)$ has zeroes at $s = \pm(LC)^{-\frac{1}{2}}$, so it cannot be minimum phase.
[Added 10/15]
Zeroes in the right half-plane can be obtained even when limited to RC circuits. To see that, consider the transfer function of this filter:

We can get the node voltages directly, because both branches are generalized voltage dividers:
$$\displaystyle V_A = \frac{(sC)^{-1}}{R + (sC)^{-1}}$$
$$\displaystyle V_B = \frac{R}{R + (sC)^{-1}}$$
$$\displaystyle H(s) = V_A - V_B = \frac{(sC)^{-1} - R}{R + (sC)^{-1}} = \frac{1 - sRC}{sRC + 1} = -\frac{s - (RC)^{-1}}{s + (RC)^{-1}}$$
The general restrictions in RC (and RL) transfer functions are:


*

*All  poles  are  simple  and  on  the  negative  real  axis.

*All  residues  are  real  but  can  be  positive  or  negative.

*Zeros  can  be  anywhere  in  the  s-plane,  but  complex  zeros  must  be  in  conjugate  pairs.

*Zero  and  infinite  frequency  cannot  be  poles.


(Extracted from p. 5 of The synthesis of voltage transfer functions, the best online reference I've been able to find.)
