Integrator

Integrators are the essential building blocks of analog computers. They perform integration in time, as in F(t) = F(0) - ʃ_0^t f(t')/k0 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, i.e. specify what value F(0) should take. 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 integrator's constant k0 is defined as k0 = 1/(R*C), which means the unit of k0 is [1/s] (Source: "Analogrechnen" by Giloi and Lauber, on the page before page 1). For THAT's integrators the constant is k0 = 1000 s^-1 in normal mode, or k0 = 10 s^-1 in SLOW mode.
• The integration time scale factor of the 1 inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a -1 signal to a 1 input, the output will ramp from 0 to 1 machine unit in 1ms. The 10 inputs have a integration time scale factor of 100μs (100kOhm * 1nF = 100μs), meaning in the aforementioned scenario the signal rises ten times faster from 0 to 1 when using a 10 input instead of a 1 input. In SLOW mode the integration time scale factors are 100ms for 1 inputs or 10ms for 10 inputs.

Extended Usage of an Integrator

Changing the integration speed

Internal wiring and effect of slowing down integrator. Source: File:Anathing v1.0 base 3.pdf.

You can change the integration time scale factors k0 of a particular integrator by connecting SLOW to OUT. This increases the time scale factors of the respective integrator by a factor of approximately 100. For the constant integration scenario described above, this means the output takes 100 times longer to transition from 0 to 1 than for the same inputs with SLOW disconnected.

You can also increase the time scale factor by 10, if you connect an external 10nF capacitor between SLOW and OUT.

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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