What is the transfer function and voltage gain equation for this filter?

 

What is the transfer function and voltage gain equation for this filter?

See the following design aid:

Sallen-Key High-pass Filter Design Tool (okawa-denshi.jp)

 

There is a link for RLC BSF on the bottom of the link you sent.

I put in my values but it seems to be out. Could you just confirm. My components are 300 ohms 100mH 100uF what is the center frequency?

 

There is a link for RLC BSF on the bottom of the link you sent.

I put in my values but it seems to be out. Could you just confirm. My components are 300 ohms 100mH 100uF what is the center frequency?

Cancel my last message I made a mistake

 

My components are 300 ohms 100mH 100uF

A Sallen-Key filter is an active configuration with only resistors and capacitors, no inductors.

 

Do you have a good link for the a pole Zero diagram simulator?

 

Here is what I get for fc=50Hz and Q=0.707 with 1% resistor values

 

Does this mean I have 4 poles and 4 zeros?

 

No. Look carefully at the notation. You are getting the actual value and the magnitude. The vertical bars which are also used for "absolute value" also mean "magnitude" when applied to complex numbers. Fun fact: real numbers on the negative real axis have positive magnitudes. Fun fact #2 is that imaginary numbers have positive real magnitudes.

 

No. Look carefully at the notation. You are getting the actual value and the magnitude. The vertical bars which are also used for "absolute value" also mean "magnitude" when applied to complex numbers. Fun fact: real numbers on the negative real axis have positive magnitudes. Fun fact #2 is that imaginary numbers have positive real magnitudes.

I'm still confused at what the data is showing me in terms of Poles and Zeros. Would it be possible to see a graphical representation please?

Is my filter stable?

 

Would this not give my poles and zeros?

 

I'm still confused at what the data is showing me in terms of Poles and Zeros. Would it be possible to see a graphical representation please?

Is my filter stable?

The data is showing you the coordinates of the poles and zeros in the complex plane. Complex numbers consist of a real part and an imaginary part. We often represent them by writing the two parts as the sum of the real part and the imaginary part. The letter j or i is attached to the imaginary part to help distinguish it from the real part. The magnitude of a complex number is computed as:


\( \sqrt{{Re^2}+{Im^2}} \)

The pole zero plot you can make from the values on the Okawa-Denshi start with a set of perpendicular axes. The horizontal axis is the real axis. the vertical axis is the imaginary axis. Using a compass with the point at the origin you draw a circle with a radius of 50 units. Label the intersection of the circle and the positive real axis with the number +50. Label the intersection of the circle with the negative real axis with the number -50. Label the intersections of the circle with the imaginary axis as +j50 and -j50. This circle represents all of the points in the complex plan with a magnitude of 50, which is the corner frequency of your network. The poles form a complex conjugate pair in the left half plane and the zeros are located on the imaginary axis. You know this because they have a real part of 0.

So far nothing here shows any inclination to wander into the right half plane. All realizable second order systems have their roots in the left half plane and are stable. Instabilities arise in higher order system with variable gain which can cause the members of a complex conjugate pair to move into the right half plane. This is evident from a root locus diagram.

ETA: On the Okawa-Denshi site you will get a pole zero plot for a 3rd order filter. I'm guessing they don't do it for the 2nd order filter because the case is trivial and never unstable.

 

Would this not give my poles and zeros?

It seems that it will, and the results should agree with the results from the Okawa-Denshi site. Once it does that can you plot them?

 

It seems that it will, and the results should agree with the results from the Okawa-Denshi site. Once it does that can you plot them?

Hello your explanation is spot on it has all clicked in place now.

My poles and zeros match with the simulation.

Only think I am unsure about now is how to put them onto a diagram. Is there any way of doing this online?

Thanks for the help, sorry I'm such a novice!

 

Any mathematics program that allows graphing should work. If you are familiar with Python, you can write a short Python script to make a nice-looking plot of poles and zeros.

 

Any mathematics program that allows graphing should work. If you are familiar with Python, you can write a short Python script to make a nice-looking plot of poles and zeros.

Do you think this would work on Excel?

 

Do you think this would work on Excel?

It should

 

https://emea01.safelinks.protection...Eq6yM1ncGHpspY4uXhzEJgOaM8zxvPN3o=&reserved=0

For anyone using this thread. The link about shows a MatLab simulator that draw pole zero diagrams.

 

https://emea01.safelinks.protection.outlook.com/?url=https://uk.mathworks.com/help/control/ref/dynamicsystem.pzplot.html&data=05|02||fcb45bd077de4a4d6b0c08dcc1eb9be8|84df9e7fe9f640afb435aaaaaaaaaaaa|1|0|638598464896028834|Unknown|TWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0=|0|||&sdata=rL2dNVZRUNEq6yM1ncGHpspY4uXhzEJgOaM8zxvPN3o=&reserved=0

For anyone using this thread. The link about shows a MatLab simulator that draw pole zero diagrams.

That's funny, the link seems to be for the commercial version of Matlab. Once upon a time I sprung for the student version, but who wants to pay full price for Matlab? I suppose you could also use Scilab or Maxima since both of those are free.

 

That's funny, the link seems to be for the commercial version of Matlab. Once upon a time I sprung for the student version, but who wants to pay full price for Matlab? I suppose you could also use Scilab or Maxima since both of those are free.

I used the test function build into he site and managed to simulate my pole zero diagram. Thanks for all your help PapaBravo.