Consider a current source circuit with an output transfer characteristic that has a spot where it has an angle or kink, like this (view with non-proportional font):
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I was looking at a current source circuit with an output curve that looks just like that. When you turn it on, in other words when you subject it to a step input, it rings like mad. I found a way to modify the circuit so it doesn't have a kink in the transfer characteristic; the new circuit's curve looks like a transistor output. The current rise looks parabolic and it merges smoothly into the part where it levels off. I simulated the new circuit; it doesn't ring when subjected to a step input. I can understand that the circuit with the smooth output characteristic is more stable, and the simulation demonstrated that. Now this has got me wondering about the mathematical connection between a circuit's output transfer characteristic and the input step response. It seems that when the output characteristic isn't smooth (differentiable) the circuit has a stability problem. But how to go about justifying it analytically?