Integrator - Revision history

MKoch: /* Basic Usage of an Integrator on The Analog Thing */

2024-06-12T07:59:34Z

Basic Usage of an Integrator on The Analog Thing

← Older revision		Revision as of 07:59, 12 June 2024
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	* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.		* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.
	* 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 <code>SLOW</code> mode.		* 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 <code>SLOW</code> mode.
	* The integration time scale factor of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input.		* The integration time scale factor of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input. In <code>SLOW</code> mode the integration time scale factors are 100ms for <code>1</code> inputs or 10ms for <code>10</code> inputs.

	== Extended Usage of an Integrator ==		== Extended Usage of an Integrator ==

MKoch: /* Basic Usage of an Integrator on The Analog Thing */

2024-06-12T07:56:09Z

Basic Usage of an Integrator on The Analog Thing

← Older revision		Revision as of 07:56, 12 June 2024
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	* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.		* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.
	* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.		* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.
	* 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 <code>SLOW</code> mode.		* 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 <code>SLOW</code> mode.
	* The integration time scale factor of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input.		* The integration time scale factor of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input.

MKoch: /* Basic Usage of an Integrator on The Analog Thing */

2024-06-12T07:55:32Z

Basic Usage of an Integrator on The Analog Thing

← Older revision		Revision as of 07:55, 12 June 2024
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	* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.		* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.
	* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.		* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.
	* 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)		* 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 <code>SLOW</code> mode.
	~~That means for~~ THAT's integrators k0 = 1000 s^-1 ~~innormal~~ mode, or k0 = 10 s^-1 in <code>SLOW</code> mode.
	* The integration time scale factor of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input.		* The integration time scale factor of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input.

MKoch: /* Basic Usage of an Integrator on The Analog Thing */

2024-06-12T07:53:52Z

Basic Usage of an Integrator on The Analog Thing

← Older revision		Revision as of 07:53, 12 June 2024
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	* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.		* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.
	* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.		* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.
	* 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)		* 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)
			That means for THAT's integrators k0 = 1000 s^-1 innormal mode, or k0 = 10 s^-1 in <code>SLOW</code> mode.
	* The integration time scale factor of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input.		* The integration time scale factor of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input.

MKoch at 07:48, 12 June 2024

2024-06-12T07:48:26Z

← Older revision		Revision as of 07:48, 12 June 2024
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	* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.		* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.
	* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.		* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.
	* The integration time scale factor ~~<code>k0</code>~~ of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input.		* 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)
			* The integration time scale factor of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input.

	== Extended Usage of an Integrator ==		== Extended Usage of an Integrator ==

MKoch: /* Changing the integration speed */

2023-07-07T09:57:22Z

Changing the integration speed

← Older revision		Revision as of 09:57, 7 July 2023
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	You can change the integration time scale factors <code>k0</code> of a particular integrator by connecting <code>SLOW</code> to <code>OUT</code>. 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 <code>SLOW</code> disconnected.		You can change the integration time scale factors <code>k0</code> of a particular integrator by connecting <code>SLOW</code> to <code>OUT</code>. 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 <code>SLOW</code> disconnected.

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

MKoch: /* Changing the integration speed */

2023-07-07T09:56:50Z

Changing the integration speed

← Older revision		Revision as of 09:56, 7 July 2023
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	You can change the integration time scale factors <code>k0</code> of a particular integrator by connecting <code>SLOW</code> to <code>OUT</code>. 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 <code>SLOW</code> disconnected.		You can change the integration time scale factors <code>k0</code> of a particular integrator by connecting <code>SLOW</code> to <code>OUT</code>. 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 <code>SLOW</code> disconnected.
			You can also increase the time scale factor by 10, if you connect an external 10nF capacitor between <code>SLOW</code> and <code>OUT</code>.

	=== Making use of the Summing junction ===		=== Making use of the Summing junction ===

Lukas.platz at 00:45, 2 March 2022

2022-03-02T00:45:59Z

← Older revision		Revision as of 00:45, 2 March 2022
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	* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.		* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.
	* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.		* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.
	* The integration time scale factor <code>k0</code> of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to ~~the~~ <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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.		* The integration time scale factor <code>k0</code> of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to a <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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 <code>10</code> input instead of a <code>1</code> input.

	== Extended Usage of an Integrator ==		== Extended Usage of an Integrator ==

Lukas.platz: correct formula and clarify integration time scales of different inputs and configurations

2022-03-02T00:43:36Z

correct formula and clarify integration time scales of different inputs and configurations

Lukas.platz: /* Basic Usage of an Integrator on The Analog Thing */

2022-03-01T23:45:57Z

Basic Usage of an Integrator on The Analog Thing

← Older revision		Revision as of 23:45, 1 March 2022
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	* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.		* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.
	* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.		* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.
	* The time constant is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to the <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms.		* The time constant of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to the <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The time constant of the <code>10</code> inputs is 100μs (100kOhm * 1nF = 100μs).

	== Extended Usage of an Integrator ==		== Extended Usage of an Integrator ==

← Older revision		Revision as of 00:43, 2 March 2022
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	'''Integrators''' are the essential building blocks of analog computers. They perform '''integration in time''', as in <code>c = ~~integral_0~~^t ~~integrand~~(t') dt'</code>. [[The Analog Thing]] features five integrators. This allows computing five integrals in a program.		'''Integrators''' are the essential building blocks of analog computers. They perform '''integration in time''', as in <code>F(t) = F(0) - ʃ_0^t f(t')/k0 dt'</code>. [[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 [[Literature\|Analog computing literature]].		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 [[Literature\|Analog computing literature]].
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	* 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 <code>1</code>.		* 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 <code>1</code>.
	* There are two output slots. Just use one of them as you like.		* There are two output slots. Just use one of them as you like.
	* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.		* The <code>IC</code> slot stands for ''initial conditions''. It is an input where you have to provide suitable initial conditions, i.e. specify what value <code>F(0)</code> should take. As shorthands, <code>-1</code> and <code>+1</code> are right to the hand. If this slot is left empty, <code>0</code> is taken as initial condition.
	* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.		* Beginners may ignore the slots <code>SJ</code> and <code>SLOW</code>.
	* The time ~~constant~~ of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to the <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The ~~time constant of the~~ <code>10</code> inputs is 100μs (100kOhm * 1nF = 100μs).		* The integration time scale factor <code>k0</code> of the <code>1</code> inputs is 1ms (1MOhm * 1nF = 1ms). That means if you connect a <code>-1</code> signal to the <code>1</code> input, the output will ramp from 0 to 1 machine unit in 1ms. The <code>10</code> 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.

	== Extended Usage of an Integrator ==		== Extended Usage of an Integrator ==
	=== Changing the integration speed ===		=== Changing the integration speed ===
	[[File:Slow-integrator.png\|thumb\|Internal wiring and effect of slowing down integrator.]]		[[File:Slow-integrator.png\|thumb\|Internal wiring and effect of slowing down integrator. Source: [[:File:Anathing v1.0 base 3.pdf]].]]

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

	=== Making use of the Summing junction ===		=== Making use of the Summing junction ===
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	{{todo\|write more}}		{{todo\|write more}}


	[[Category:Components of The Analog Thing]]		[[Category:Components of The Analog Thing]]