Integrator

An Integrator is an elementary building block of an analog computer which carries out an Integration in time, as in c = integral_0^t integrand(t') dt'. The Analog Thing features five integrators. This allows computing five integrals in a circuit.

Analog computers typically perform integration by charging and discharging capacitors. The key difference between an integrator and a summer is the capacity in the feedback channel instead of a simple resistance. Accordingly, all integrators are also summing their inputs. For more details, please refer to Analog computing literature.

Basic Usage of an Integrator on The Analog Thing

A single integrator

• Circles represent inputs, triangles represent outputs
• Analog integrators sum their inputs. That is, if you have a sum under your integral, you can save a single summer before the integrator. Otherwise, just put your integrand into the upper left input labeled with 1.
• There are two output slots. Just use one of them as you like.
• The IC slot stands for initial conditions. It is an input where you have to provide suitable initial conditions. As shorthands, -1 and +1 are right to the hand. If this slot is left empty, 0 is taken as initial condition.
• Beginners may ignore the slots SJ and SLOW.

Attention: Make sure the sum of your inputs does not exceed the machine unit (±10V), otherwise an overload will occur (indicated by the OL LED) . See Logic levels for details.

Extended Usage of an Integrator

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Changing the integration speed

Internal wiring and effect of slowing down integrator.

You can change the integration time scale factor k0 of a particular integrator by connecting SLOW to OUT. This effectively decreases the k0 by factor 100. The circuit on the right was taken from File:Anathing v1.0 base 3.pdf.

Making use of the Summing junction

See also XIR.

Mathematics about analog integration

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