Relation between output transfer characteristic and step input response

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):

______ / / / /

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?

Reply to
Michael Robinson
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Look at AC, not DC parameters for clues. The DC transfer function can be any crazy thing and still oscillate -- or not.

Tim

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Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms
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Reply to
Tim Williams

One usually thinks about ringing as the result of some linear-ish circuit that is underdamped.

What you're describing is presumably a nonlinear effect, which can be practically anything depending on the circuit, e.g. the input and output impedances of your current source are probably drastically different in the two regions. Why not post the schematics?

Cheers

Phil Hobbs

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Reply to
Phil Hobbs

Sorry, I'm a bit confused... is the vertical axis output current, and the horizontal input 'voltage'?

Ringing only for big input steps? or do little steps (within the linear region) also ring?

George H.

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Reply to
George Herold

I have modified the pulse sources in PSpice such that rising and falling edges are the TANH function, smooth like most real sources. ...Jim Thompson

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| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
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Reply to
Jim Thompson

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=A0 =A0 ...Jim Thompson

=A0 =A0| =A0 =A0mens =A0 =A0 |

=A0 | =A0 =A0 et =A0 =A0 =A0|

=A0|

=A0 =A0 =A0 |

Great idea! By using the exponential function you make certain that ALL derivatives exist!. And there's nothing like a missing derivative to make math blow up. - reference Prof Ron Bracewell's book on Fourier Transforms

Reply to
Robert Macy

[snip]

Yep. I've gone a bit "TANH-crazy" with _virtually_all_ of the behavioral models I've created. Bye, bye convergence problems. ...Jim Thompson

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| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
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Reply to
Jim Thompson

characteristic

looks=20

input, it=20

rise=20

input.

is=20

about=20

characteristic=20

(differentiable)=20

Personally, i would keep the option for trapezoidal pulse sources as = well.

?-)

Reply to
josephkk

[snip]

Looks like my smooth pulse source is SIN-based rather than TANH:

Newsgroups: alt.binaries.schematics.electronic Subject: Relation between output transfer characteristic and step input response (SED) - RealPulse.pdf Date: Sun, 11 Mar 2012 09:16:58 -0700 Message-ID:

Robert, As I recall, you have no access to A.B.S.E, so I've E-mailed you a separate copy. ...Jim Thompson

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| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
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Reply to
Jim Thompson

"Jim Thompson" wrote in message news: snipped-for-privacy@4ax.com...

Strange. I've written TANH transfer curves before (basically to simulate logic elements) and fairly often had them produce bizarre errors, namely, singular matrix and divide by zero.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms
Reply to
Tim Williams

I quickly found out why I used SIN-based... TANH won't fit a nice

10-90% definition without a discontinuity. ...Jim Thompson
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| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
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Reply to
Jim Thompson

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