Multiple Gain Feedback Active Filter Help

[let it be]

Hello people,

These days I've been struggling with an homework that I attached to the post. It is about a multiple gain feedback active filter. Is there anyone who is able to help me?

Homework:

Thanks!

[Marco]

It's way too long ago for me, I'd need time to even remember how to get my computer to give me all the answers ... but I think you will get better help if you tell people how far you got.

Did you manage to do the inverse Laplace transform of the transfer function? (Of course you could just google it as well, but that won't work during an exam so I wouldn't advise it.)

[f5r5e5d]

yes hope they don't expect anyone in 2015 to the algebra by hand

I've used symbolic math solvers for this for the past 1/4 century

do you have any of Maple, Mathcad, Mathematica?

otherwise you could try one of the free CAS such as the XCAS or wxMaxima, Sage Math project...

but you do need to know how to setup the nodal system equations and most CAS will require hand manipulation to get the form of the equation expected


a different circuit question example: http://www.diyaudio.com/forums/solid-state/259470-your-opinions-sought-audio-power-amplifier-design-6th-edition-douglas-self-36.html#post4017165

[let it be]

I managed to find the transfer function H(jw) and H(s) using google, since it is not an exam I hope it'll work

I attached the transfer functions I found. However, I don't know how to go further with step 2 of the question also how to depict those graphs and so on. It is just a weird homework that I will never use in my engineering life since I'm not interested with this topic.

Btw, thanks for your replies!

[f5r5e5d]

oddly enough people paying you may expect you to do things that don't interest you to get the work done - particularly if you have the Degree, were hired on the basis of being able to use the course material expected of someone with the credential

however as an experienced analog designer I'm not familiar with the use of "critical point" in that filter context - bandpass filters have center frequency, Q/bandwidths

[let it be]

Any other help regarding the critical point, depicting H(jw) and bode diagrams?

[Marco]

The questions just seem intentionally confusing AFAICS.

The critical point I assume is simply referring to the simple calculus definition of the point where the derivative is zero, which is simply w0 again.

The bode diagrams in question 4 are simply the |H(jw)| and angle(H(jw)) graphs you already drew in question 3, except that bode diagrams are generally given as a function of frequency in Hz rather than radians.

PS. I'd really advise you to go back to your textbooks until you can derive laplace representations manually for an arbitrary opamp filter and you understand everything well enough to at least get a math program to solve everything for you and to draw the plots you're after. Question 1 is by far the most important here, the rest is only difficult by misdirection.

[let it be]

I found some other documents to depict the graphs but now I have another problem with determining the resistor and capacitor values. According to the document I uploaded it says determine them comparing with the transfer function of the circuit and the transfer functions I obtained using center frequencies. However some confusing equations came up when I try to do so.

[f5r5e5d]

time constants need a choice of impedance to be realized as real component values - usually chosen for a variety of reasons from noise, op amp circuit drive capability, available values of component (mostly for Caps of the desired size, quality, tolerance, price...)

when in doubt in typical op amp active filters pick a R, set it to 1 kOhm and see what values fall out for the rest

[LvW]

I found some other documents to depict the graphs but now I have another problem with determining the resistor and capacitor values. According to the document I uploaded it says determine them comparing with the transfer function of the circuit and the transfer functions I obtained using center frequencies. However some confusing equations came up when I try to do so.

The classical procedure for determining the time constants (element values) for such a circuit is to compare the relevant circuits transfer function with the theoretical (general) second order bandpass transfer function. Therefore my question: What is the transfer function of the shown circuit? Show us the "confusing equations" you have obtained. On the other hand, you can of course search for (and apply) the known formulas for finding the various element values. It is a simple procedure.

[LvW]

By the way - I forgot to mention that the name of the circuit topology as shown is NOT "Multiple gain..." but "Multiple Feedback" structure (MFB).

[let it be]

Thank you all for your helps. In the end, I set the capacitor values to 100 nF and then calculated the resistor values. I guess that was the only way, otherwise I'd have 3 equations with 4 unknows which was not possible to solve.

[LvW]

BTW, for such a high order system, it could be better if you use state matrix to represent it, and convert it back to transfunc.

...high order ? It is a classical second-order circuit which can be designed with a known set of formulas.