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Re: Integrator transfer function and arbitrary continuous input signals

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"Edward Rawde" <invalid@invalid.invalid> wrote in message news:107dc33$fcb$1@nnrp.usenet.blueworldhosting.com...
> "Christopher Howard" <christopher@librehacker.com> wrote in message news:877bz9zt1m.fsf@librehacker.com...
>> Hi, I'm trying to work slowly through the great Op Amp book by Roberge et al
>> that was recommended earlier. I downloaded the 2nd edition v. 1.8.1. I'm
>> finding it enlightening to slowly process the paragraphs and take notes
>> on the diagrams and equations.
>>
>> Something I'm getting hung up on though is they dive early on into
>> transfer functions, and that hasn't been covered yet in my introductory
>> DE book. I've been trying to cram in some quick Internet research on
>> laplace transforms and such but it has been a bumpy ride.
>>
>> In chapter one (equation 1.21) they gave the transfer function of an
>> integrator, i.e., an op amp with resistor and capacitor feedback
>> network, as -1/(RCs). I found that if I replaced s with 2 pi f, I could
>> predict the gain from a steady sinusoidal signal of matching frequency,
>> and when I tried this out with my real integrators, I got matching
>> results.
>>
>> My questions:
>>
>> (1) so, if I replace s with a complex number, one that has both a real
>> and an imaginary part, what does that mean?
>
> It means that instead of just individual numbers, variables consist of pairs of numbers.
> This is so that both magnitude (length) and phase (angle) can be accommodated.
> For example (1, 0) is equivalent to the real number 1 and it has a length of 1 unit.
> It can be written 1 + j0 or just 1
> The number (0, 1) also has a length of one unit but it's not on the real number line, it's been rotated 90 degrees 
> counterclockwise.
> It can be written 0 + j1 or just j
> The following may be worth watching. It's not specifically about electronics.
https://www.youtube.com/watch?v=cUzklzVXJwo
> If you don't want to watch it all, just watch the part at 19:10
> Note also that outside electronics j usually becomes i.
> Except in some of my old handed down textbooks where "operator j" is used and the complex plane is called the Argand diagram.
> https://en.wikipedia.org/wiki/Jean-Robert_Argand
> I think it remained j in electronics because i is used for current.
>
>> Is that the same as
>> calculating the gain for a sinusoidal input of a particular amplitude
>> and frequency?
>>
>> (2) How do I use/apply this transfer function if I've got some
>> nonsinusoidal continuous input, like say a steady voltage, or a linear
>> ramping voltage?
>>
>> -- 
>> Christopher Howard
>
> 

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Integrator transfer function and arbitrary continuous input signals Christopher Howard <christopher@librehacker.com> - 2025-08-11 09:07 -0800
  Re: Integrator transfer function and arbitrary continuous input signals Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-08-11 17:34 +0000
  Re: Integrator transfer function and arbitrary continuous input signals "Edward Rawde" <invalid@invalid.invalid> - 2025-08-11 14:17 -0400
    Re: Integrator transfer function and arbitrary continuous input signals "Edward Rawde" <invalid@invalid.invalid> - 2025-08-11 14:19 -0400
    Re: Integrator transfer function and arbitrary continuous input signals Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-08-11 19:43 +0000
  Re: Integrator transfer function and arbitrary continuous input signals "Edward Rawde" <invalid@invalid.invalid> - 2025-08-11 16:56 -0400
  Re: Integrator transfer function and arbitrary continuous input signals JM <sunaecoNoChoppedPork@gmail.com> - 2025-08-15 23:14 +0100
    Re: Integrator transfer function and arbitrary continuous input signals Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-08-16 00:34 +0000

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