Transfer Function Ideas

[opacheco]

Hi to everyone,

I am trying to anlyze a classic and vintage audio active equalizer using vacumm tubes inder, this units use severals filters with feedbacks loops in order to get a specific frequency response proposed for the manufacturer. My idea is to get the transfer function vo/vi of the all filters in order to modify to my needed and see the importance and performace of each circuits elements. I have done some work already using the classical network equations (Kirchoff and Network Theorems...) but the works is very hard to do solving systems of equations and mathematics simpllifications and many hours of hand and pen work with a lot of concentration. I would like to get some advises in order to know if does exist any theorical method more easier for get the transfer functions in these kind of electrical/electronical networks using various feedbacks loops in the same net??

I have attached one active filter drawing of the severals in cascaded found in the unit.

I appreciate any advise or help
Thanks anticipated
opacheco.

 

[rjenkinsgb]

That looks a lot like a second order low-pass Butterworth filter?

eg. This is a common opamp implementation:

Some info on the design of these:

https://www.electronics-tutorials.ws/filter/filter_8.html

 

[Tony Stewart]

Except the Ron must be biased to be much lower than the R's and the max gain will be < 1 as a source follower depending on Ron/(Ron+R/2) (?). So the poles may not be equal.

 

[danadak]

Signal Flow Graph to get at T(s).

https://feng.stafpu.bu.edu.eg/Electrical%20Engineering/3127/crs-13461/Files/Lecture%20(5)_4-11-2015.pdf

https://github.com/hanspi42/signalflowgrapher/releases Utilities

Or attached.


Regards, Dana.

 

[The Electrician]

Hi to everyone,

I am trying to anlyze a classic and vintage audio active equalizer using vacumm tubes inder, this units use severals filters with feedbacks loops in order to get a specific frequency response proposed for the manufacturer. My idea is to get the transfer function vo/vi of the all filters in order to modify to my needed and see the importance and performace of each circuits elements. I have done some work already using the classical network equations (Kirchoff and Network Theorems...) but the works is very hard to do solving systems of equations and mathematics simpllifications and many hours of hand and pen work with a lot of concentration. I would like to get some advises in order to know if does exist any theorical method more easier for get the transfer functions in these kind of electrical/electronical networks using various feedbacks loops in the same net??

I have attached one active filter drawing of the severals in cascaded found in the unit.

I appreciate any advise or help
Thanks anticipated
opacheco.

The source shown in your image shows what is apparently a VCVS (voltage controlled voltage source). This is not typically how a vacuum tube is modeled. One resistor is labeled "Rd", typically how a "drain resistor" would be labeled. Also, there is a voltage labeled "Vs" which is what a person would label a voltage in the source of a FET, not the voltage at the cathode of a vacuum tube. Is your active device a vacuum tube or a FET?

Could you please clarify these issues.

 

[MrAl]

Hi to everyone,

I am trying to anlyze a classic and vintage audio active equalizer using vacumm tubes inder, this units use severals filters with feedbacks loops in order to get a specific frequency response proposed for the manufacturer. My idea is to get the transfer function vo/vi of the all filters in order to modify to my needed and see the importance and performace of each circuits elements. I have done some work already using the classical network equations (Kirchoff and Network Theorems...) but the works is very hard to do solving systems of equations and mathematics simpllifications and many hours of hand and pen work with a lot of concentration. I would like to get some advises in order to know if does exist any theorical method more easier for get the transfer functions in these kind of electrical/electronical networks using various feedbacks loops in the same net??

I have attached one active filter drawing of the severals in cascaded found in the unit.

I appreciate any advise or help
Thanks anticipated
opacheco.

Hi,

There circuits are not that hard to analyze even if they might look so at first glance.
The idea is to use Nodal Analysis combined with complex numbers. This leads to the transfer function which can then be plotted using math software. There is very little hand work involved, and you don't even have to understand complex numbers that well in order to analyze this you just have to know how to use math software like Maxima (free).

If all of the channels are the same, you basically have it made. You only have to analyze one channel then just change values in your final transfer function.

For this you can also make use of Superposition. You treat the circuit as having two sources where the output of the amplifying device is considered just another source. That makes writing the equations even faster. I could show you how to use this in the equivalent op amp circuit.

BTW that looks a lot like a Sallen Key filter or similar.

 

[aliarifat794]

SPICE-based simulators like LTspice or PSpice can model and analyze circuits, providing insights into transfer functions without extensive manual calculations. You can also use MATLAB : https://www.theengineeringprojects.com/2022/10/step-response-of-an-lti-system-in-matlab.html

 

[danadak]

Transfer function of second-order Butterworth filter

I'm trying to understand the second order Butterworth filter and build a transfer function of it for analysing in the frequency plane. I have my second order Butterworth filter. Then I specify the

electronics.stackexchange.com

Additional info.

 

[MrAl]

Here's a brief outline of how to use superposition to analyze the circuit when using an op amp.