## RC Circuit vs Op amp integrator

I'm still learning about this, but it seems that an RC circuit performs the same function as an op amp integrator (http://www.electronics-tutorials.ws/opamp/opamp_6.html). In other words, they both can be used as integrators/low pass filters.

If this is true, why would anyone bother with an op amp integrator?

The only difference that I can see is that an RC circuit would be more sensitive to drawn current than an Op amp integrator would be. Am I missing something?
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 For one, op-amp integrator can hold virtual ground at the integrator input, this is very important in certain cases where you need the input to have constant potential. Also op-amp integrator can be faster. If you have a high speed current pulse, you can see the op-amp step up much faster and settle faster. Also, op-amp integrator can be design to hold the output level much better by having a very high impedance discharging path. Where as the RC LP filter get discharged by the R. It is not unusual to have op-amp integrator that can react to nS pulses and hold for mS.
 Have you learned about input and output impedance? It is true that an unloaded RC circuit has an integral transfer characteristic. It is also true that it can be at least as fast as an op amp, it just depends upon realising suitable circuit values. But connect suitable circuit values for integrting the frequencies of interest to an input and an output and what happens?

## RC Circuit vs Op amp integrator

You can easily design and build a single pole filter (a single resistor and single capacitor). If you need to design a filter with better selectivity, higher order filter, using only passive components you will need a multistage passive circuit. Each stage of this filter will load previous stage reducing, dividing, incoming signal. After second or third stages of a passive filter you will end up with no signal at all. Using active circuit (OPAMP) you can easily design multistage filters.
Filters are fun.

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 If this is true, why would anyone bother with an op amp integrator?

Operational Amplifiers are used to perform math operations like sum, difference, multiply, differentiate, integrate, find logaritrhm, etc...

there are times you need a true integration not the approximate one you get from a simple RC circuit .
An example would be a process controller with integral term.

Sometimes an approximate integral is close enough for what you're trying to measure and that's where you might get away with the simple RC.

For example if you need the integral of a sinewave a simple RC can get you pretty close.

But if you need the integral of a step function, whhich would be a straight line of constant slope, observe that the RC only approximates that for a fraction of a time constant.

It'd be a 'Judgement Call" by the fellow doing the work..
 Use of integrators as basic building blocks of filters was a significant advance in analog integrated circuit technology because these "state variable filters" can be made very insensitive to component tolerances. Discrete high order filters required precise component values, often requiring manual calibration. Components inside of integrated circuits are much poorer in quality than what can be achieved with discrete components, so implementing anything other than a very basic low order filter was out of the question. Use of integrator based state variable filters allowed precise, high order, filters to be implemented in silicon thanks to the insensitivity to component tolerance inherent in this topology. These used to be called KHN filters back in the day. Kerwin, Huelsman & Newcomb developed this specifically for the analog IC use. I have a copy of their original paper somewhere. If I find it I will post it for those interested.
 Like said above, an op amp can give you gain. Like when you turn up the volume on your stereo. This gain translates into + dB. An even better example would be an equalizer on your stereo. When you adjust the different frequencies, you will either have a rise in dB or a fall in dB at that specific frequency. This can not be done with an RC circuit...but can certainly be done with an op amp on each frequency. Set your break frequency for that amp and then put a variable resistor (knob or adjustable button on EQ) in the feedback loop. An RC circuit will only give a gain of 1 or 0 dB.
 Here is a nice interactive rc integrator webpage to play with. Try different values in the scope app. http://www.st-andrews.ac.uk/~jcgl/Sc...integ/int.html
 Thank you all very much for the fast and thorough replies. This helps immensely. I'm sorry I'm not the best at quoting. Some follow up questions: yungman: I could be off base here, but doesn't the value of R*C determine how fast integration takes place? I.e. if the value of RC determines the 3db cutoff frequency that is passed in the low pass filter, why would a op amp be 'faster' than a simple RC circuit? Also: I have a rudimentary understanding of impedance, but I'm not sure how the RC Low Pass filter 'would get discharged by the R.' jim hardy: Along the same lines, if both circuits integrate, then I'm confused why one would integrate 'faster' than the other - they both would integrate the step function in the same way, and thus would only be correct for a part of the signal, right?
 Hello, Dude, did you read my posts ? Consider an RC integrator. The governing equations are $$\begin{array}{l} {V_{in}} = IR + \frac{1}{C}\int {Idt} \\ {V_{out}} = \frac{1}{C}\int {Idt} \\ \end{array}$$ Now we can only make this an integrator of input voltage if we make the time constant RC very long compared to the period of the input wave, resulting in a small voltage across the capacitor. Under those circumstances we can write $$\begin{array}{l} {V_{in}} \approx IR \\ hence \\ I = \frac{{{V_{in}}}}{R} \\ hence \\ {V_{out}} = \frac{1}{{RC}}\int {{V_{in}}dt} \\ \end{array}$$ Which is the equation of the integrator we seek. But the condition on RC places severe practical constraints on the values and frequencies we can adopt. Further, as I have already mentioned, the input and output are also affected by the impedances of the preceding and following circuit blocks.

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Studiot gave the math very nicely.

Her's the "words" to go with it.

If you build both an RC and an opamp integrator and hand them a step input,
their outputs will both start to change with same slope because initial current flow into both capacitors is the same.

After a short while the RC integrator's slope will decrease -
that's because current into the RC's capacitor = (Vin - Vcapacitor)/R

but the current into opamp's capacitor = Vin/R

so the RC briefly approximates integration but the opamp does it exactly.
That's what Studiot was telling you when he said
 Now we can only make this an integrator of input voltage if we make the time constant RC very long compared to the period of the input wave, resulting in a small voltage across the capacitor.
and that's the significance of Yungman's comment
 For one, op-amp integrator can hold virtual ground at the integrator input,
opamp holds one end of resistor at zero so current into cap = Vin/R not (Vin-Vcap)/R. With the latter, as Vcap goes up the slope gets smaller - less current into cap.

So the latter gives you an exponential approach to Vin not the straight line you get from true integration.

Further the RC integrator won't "hold" when input voltage returns to zero, the cap discharges back into signal source through input resistor.
I once built an opamp analog integrator that'd hold last value within 0.1% overnight.

hope you have enough offerings here topiece together a mental model that works. When it agrees with Studiot's math then it's probably right.

old jim
 Thank you both! I understand much more clearly now. I promise I read each response several times...

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