Integrator

Integrators are the essential building blocks of analog computers. They perform 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 program.

Electronic 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.
• The time constant of the 1 inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a -1 signal to the 1 input, the output will ramp from 0 to 1 machine unit in 1ms. The time constant of the 10 inputs is 100μs (100kOhm * 1nF = 100μs).

Extended Usage of an Integrator

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

To extend the number of inputs, connect the SJ panel of the integrator to the SJ panel of a XIR element. Now the other panels of the corresponding XIR element function as inputs of the connected integrator. See also XIR.

Mathematics and Electronics about analog integration

On an electronical level, Integrators work quite similar to Summers (and Inverters, respectively), given the closed-loop operational amplifier setup. However, they feature a capacitor in the feedback channel which holds the current integration level. This makes an integrator stateful in contrast to the stateless Summers.

In the THAT circuits, you find the integrators on page File:Anathing_v1.0_base_3.pdf. As you can see there, they are implemented with ICs called TL074H. See [1] for the datasheet of this chip.

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