M
Michael Robinson
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?
that has a spot where it has an angle or kink, like this (view with
non-proportional font):
______
/
/
/
/
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?