At least, I'm sure it'll be simple to some of the folks on here.
I am looking at pole-zero diagrams: I am in particular looking
at the pole-zero diagram for a first order low pass RC filter.

It's open loop, unloaded, so obtaining the transfer function is trivial,

T.F. = (1/CR)/ ((1/CR) +S)

Nothing controversial there. I understand S is the complex variable,

S = (sigma + jw)

which is all to do with Laplace and stuff. We plot the T.F. on the complex s-plane and obtain a single pole at sigma = -(1/CR): the zero is at infinity.

My problem is what physical interpretation can we put on this pole? I understand that the T.F. along the jw axis is a back-to-back Bode plot, i.e. response versus frequency, and I understand that the sigma (real) axis is an indicator of exponential growth or decay, i.e exp-(sigma*t).

I cannot for the life of me though figure out how the transfer function ( Vout/Vin ) of an RC low-pass filter develops an infinite gain ( pole ) at what is zero-frequency on the -sigma axis ( for jw=0 ). Not even negative resistances explains the shape of the graph to me. Anyone have a physical interpretation as to the meaning of this pole at sigma = -(1/CR)?????

Apologies if this is not the sort of stuff to post here, I am unfamiliar with this group,

Andy.

It's open loop, unloaded, so obtaining the transfer function is trivial,

T.F. = (1/CR)/ ((1/CR) +S)

Nothing controversial there. I understand S is the complex variable,

S = (sigma + jw)

which is all to do with Laplace and stuff. We plot the T.F. on the complex s-plane and obtain a single pole at sigma = -(1/CR): the zero is at infinity.

My problem is what physical interpretation can we put on this pole? I understand that the T.F. along the jw axis is a back-to-back Bode plot, i.e. response versus frequency, and I understand that the sigma (real) axis is an indicator of exponential growth or decay, i.e exp-(sigma*t).

I cannot for the life of me though figure out how the transfer function ( Vout/Vin ) of an RC low-pass filter develops an infinite gain ( pole ) at what is zero-frequency on the -sigma axis ( for jw=0 ). Not even negative resistances explains the shape of the graph to me. Anyone have a physical interpretation as to the meaning of this pole at sigma = -(1/CR)?????

Apologies if this is not the sort of stuff to post here, I am unfamiliar with this group,

Andy.