Talk:Foster's reactance theorem

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A fact from Foster's reactance theorem appeared on Wikipedia's Main Page in the Did you know column on 10 June 2010 (check views). The text of the entry was as follows:

Did you know... that Foster's reactance theorem ensures that plots on a Smith chart of an electrical network impedance function always travel around the chart in a clockwise direction with increasing frequency?

A record of the entry may be seen at Wikipedia:Recent additions/2010/June.

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Monotonically increasing?

Odd that for the formulator of this theorem, a function such as x/(1-x^2) is considered to be increasing (for the range x>0). Won't this lead to difficulties in the application of the theorem to situations where values are being compared? 84.227.254.143 (talk) 10:02, 30 March 2014 (UTC)[reply]

I don't think you can use Foster's theorem in that way (comparing two discrete measurements) to determine if the network is a Foster network or not. Clearly, it will fail if there is a pole between the two measurements. One must have knowledge of the sign of the slope of the function across the whole frequency range. Spinning Spark 13:24, 30 March 2014 (UTC)[reply]

There might be another way to formulate it that won't lead to initial confusion. There's a hint of this in the reference to going clockwise in a Smith diagram -- the monotonicity is really a kind of "around the clock" phase monotonicity, like for tan(x). Not being familiar with the field, I wonder if there is a formulation that draws on the specialist literature, but would also satisfy literalists. Perhaps simply "except when crossing poles"? 84.227.254.143 (talk) 15:54, 30 March 2014 (UTC)[reply]