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Is a simple pi network causal?

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padpan

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+As known a simple pi-network is fully passive and stable. The simplest representation would be as attached figure1.jpg. But is this netwrok causal?

I applied a simple step response in the input (0 to 1V from 1ns to 1.01ns, i.e. rise time = 10ps). figure2.jpg is displaying the signal at the input (colored blue) and the signal at the output (colored red). Black curve is the ideal stimulus of the signal generator.

It seems that the output at t=0+ follows the input, which i believe is in contrast with causality theory; as if the line inductance that the pi-network represents brings no delay.





So it all comes to the question: can any lumped element based network have a causal behavior? Also, how severe would the impact of such a non-causality be?

thanks,
--pap
 

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FvM

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The question sounds strange, because passive networks can't be but causal. Your circuit has however undelayed and first order low-pass pathes between input and output, so the observed waveform isn't surprizing.
 

albbg

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Passive networks must be causal (from conservation of energy). The reason of the curves you post is not very clear to me. Could you, please, post the complete circuit with components values as well as how the generator (and its impedance) is connected to the circuit ?
 

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