The 'formula' is really the transfer function sometime denoted by "T(s)". It's really just an AC network analysis.Hi,
My first question is that the 2-pole second order passive RLC low pass filter is a 4th order filter?, as shown below. And also, what is the formula for Attenuation and how to calculate the Attenuation of this filtered signal (which is appear at the output of L2) ?.
View attachment 251239
Locate R2 properly by placing it in parallel with C2. In your schematic the low frequency response will be down much further than you expect because there is no DC path to ground.Hi,
My first question is that the 2-pole second order passive RLC low pass filter is a 4th order filter?, as shown below. And also, what is the formula for Attenuation and how to calculate the Attenuation of this filtered signal (which is appear at the output of L2) ?.
View attachment 251239
You have cascaded two 2nd order filters which makes a 4th order filter. You should be able to work out the two different 2nd order responses. The combined response is the product of the two. There is a problem however and that problem is the mismatch between the output impedance of the 1st filter does not match the input impedance of the 2nd filter so there are additional losses.Hi MrAl,
My first question is that the 2-pole second order passive RLC low pass filter is a 4th order filter?, as shown above.
Is this { T(s)=1/(s*C*R+1) } transfer function of 4th order RLC filter?. If not, please can you post me the formula for 4th order RLC filter?
What is the units of these R=2 and C=3 values?. How you chosen these values?.
Hi Papabravo,You have cascaded two 2nd order filters which makes a 4th order filter. You should be able to work out the two different 2nd order responses. The combined response is the product of the two. There is a problem however and that problem is the mismatch between the output impedance of the 1st filter does not match the input impedance of the 2nd filter so there are additional losses.
No T(s)=1/(sRC+1) is the transfer function for a 1st order (one reactive element) filter. An example of a fourth order filter with the two 2nd order factors shown would be something like:Hi Papabravo,
The problems will see later, first I would like to know how to do the calculations the attenuation of filtered signals at each stage. So please could you answer the questions which are listed below:
Is this { T(s)=1/(s*C*R+1) } transfer function of 4th order RLC filter?. If not, please can you post me the formula for 4th order RLC filter?
What is the units of these R=2 and C=3 values?. How you chosen these values?.
Hi Papa,\[ T(s)\;=\;\frac{105}{s^4+10s^3+45s+105s+105}\;=\;\frac{105}{(s^2+5.74292s+9.14013)(s^2+4.20758s+11..4878)} \]
They come from the condition that describes the transfer function for a Bessel Filter. The condition is that the phase be linear with a negative slope, the magnitude will be constant, and then the group delay will be constant.Hi Papa,
Where those values come from which are in the above question?.
I need help from you that, I want have a 2nd order and 4th order equations, and also the attenuation value to be calculated from the above simulation circuit (from the post 1). Please don't make me complex. I'm also expecting from you that the calculations would be more readable and understandable.
Thank you for your help in advance.
I've simulated both of the circuits from your original post separately to guide you in how to derive their individual transfer functions. I've show you how you can derive the 2nd order transfer function for each circuit. To find the 4th order transfer function you need multiply the two 2nd order transfer functions together. The algebra does require some care. You need to make some effort here.Hi Again,
I was totally confused. Why do you simulated the different circuit?. Just provide me the formula to calculate the attenuation of 2nd order series RLC filter?. If possible, please also do the calculation in order to find the attenuation value at the end of the each 2nd order filter which is shown in the first post.
Hi again,I've simulated both of the circuits from your original post separately to guide you in how to derive their individual transfer functions. I've show you how you can derive the 2nd order transfer function for each circuit. To find the 4th order transfer function you need multiply the two 2nd order transfer functions together. The algebra does require some care. You need to make some effort here.
R1, L1, C1, RL1 form the 2nd order lowpass filter. It's response is the green trace. Notice how flat the response is up to about 100 kHz.
R2, L2, C2, and RL2 form the 2nd order highpass filter. It's response is the blue trace. Notice that the response of this filter is NOT very flat above 100 kHz.
Refer back to the response in post #7 and look at that response. It is the sum of the responses in post #9
This is why it is hardly worth the effort to analyze. You can grind it out if you wish, but I'll take a pass.
Hi,pinkyponky, is this homework? If it's not, why have you posted it in the homework forum?
This is the homework forum. You can't just post your "requirements" and expect somebody to do the work for you.Hi again,
There is no high pass filter in my circuit (posted in #1), I don't want simulations, I want to know the value of the attenuation by doing the mathematical calculation. Just I want to have a value of attenuation after 2nd order filter and 4th order filter. And also I want to have fully mathematical calculation with formula, how the attenuation value is calculated?. That's it. I hope you understand my requirement.
Fine. It blocks DC, like a highpass section does, has a narrow passband, and has a high frequency rolloff. On one of the simulations, I gave you a number of hints on what to do. You could have done the work and used the simulation results to check your answer. Instead you continue to whine. It is getting tiresome. Show us some work.Hi again,
There is no high pass filter in my circuit (posted in #1), I don't want simulations, I want to know the value of the attenuation by doing the mathematical calculation. Just I want to have a value of attenuation after 2nd order filter and 4th order filter. And also I want to have fully mathematical calculation with formula, how the attenuation value is calculated?. That's it. I hope you understand my requirement.
Hi MrAl,7.0361928e-8-j*2.6525822e-4 to 8 significant figures in units of peak voltage,
so the real part is 7.0361928e-8 and the imaginary part is -j*2.6525822e-4.
We can then calculate the AC peak amplitude by finding the norm of that, and get:
2.65258e-4 volts peak (amplitude)
and the phase angle:
-1.57053 radians (phase angle)
So the output in this case is small and phase angle nearly -90 degrees. Other frequencies will produce different amplitudes and phase angles.
Hi again,But more to the point, this calculation is not going to help you. As Papabravo said in post #9:
" When you solve the two simpler problems, you multiply the two transfer functions together. This gives you a 4th order transfer function, which assumes that the second section does not present an appreciable load to the first section. It does do that so you have to work a bit harder to get the result you are looking for. "
Because your circuit in post #1 has the second RLC low pass loading the first one, you must derive the transfer function for the whole thing at once. For the work shown in this post, you started out with a expression for H(s) without showing how you derived it. For the next showing of your work, namely the working out of the transfer function for the entire circuit, show how you derive the transfer function expression in terms of the "s" variable. You could treat the circuit as a cascade of two voltage dividers, or you could use mesh or nodal analysis.
by Aaron Carman
by Jake Hertz
by Duane Benson