Groups | Search | Server Info | Login | Register

Groups > sci.electronics.design > #734886

Re: Integrator transfer function and arbitrary continuous input signals

Show all headers | View raw

"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? 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?

These days you just use LTSpice and you see that your ramps become parabolas as expected.
Also look at what happens without R2.

Version 4.1
SHEET 1 880 680
WIRE 208 -96 160 -96
WIRE 352 -96 288 -96
WIRE 160 32 160 -96
WIRE 224 32 160 32
WIRE 352 32 352 -96
WIRE 352 32 288 32
WIRE -304 128 -304 80
WIRE -256 128 -304 128
WIRE -256 144 -256 128
WIRE -64 144 -96 144
WIRE 32 144 -64 144
WIRE 160 144 160 32
WIRE 160 144 112 144
WIRE 240 144 160 144
WIRE 352 160 352 32
WIRE 352 160 304 160
WIRE 400 160 352 160
WIRE 240 176 192 176
WIRE -304 192 -304 128
WIRE 192 224 192 176
WIRE -96 256 -96 144
WIRE -96 384 -96 336
FLAG -256 144 0
FLAG -304 0 +15
FLAG -304 272 -15
FLAG 272 128 +15
FLAG 272 192 -15
FLAG 400 160 Parabola
FLAG -64 144 Ramp
FLAG 192 224 0
FLAG -96 384 0
SYMBOL OpAmps\\UniversalOpAmp 272 160 R0
SYMATTR InstName U1
SYMATTR Value2 Avol=100k GBW=8Meg Vos=0
SYMBOL voltage -304 -16 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V1
SYMATTR Value 15V
SYMBOL voltage -304 176 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V2
SYMATTR Value 15V
SYMBOL voltage -96 240 R0
WINDOW 123 24 124 Left 2
WINDOW 39 0 0 Left 0
WINDOW 3 76 51 Left 2
SYMATTR Value2 AC 1
SYMATTR Value PULSE(0 1 0 1ms 0ms 0 0 10)
SYMATTR InstName V3
SYMBOL res 128 128 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R1
SYMATTR Value 10k
SYMBOL cap 288 16 R90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName C1
SYMATTR Value 10nF
SYMBOL res 304 -112 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R2
SYMATTR Value 100k
TEXT -464 416 Left 2 !.tran 10ms

Back to sci.electronics.design | Previous | Next — Previous in thread | Next in thread | Find similar

Thread

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

csiph-web