Hi again,

I have added the two real parts together (which are in the left and right sides of the imaginary part, in the above calculation) and also keep separate the imaginary part. I didn't understand what is the wrong with that.

Imagine you had this fraction:

\(\frac{1}{3+2 j}\)

You can't just split the denominator and get this:

\(\frac{1}{3}+\frac{1}{2 j}\)

You have to rationalize the denominator.

View this video for the procedure:

This transfer function just I have taken from the video tutorial which is shown in post #15.

I haven't found any transfer function of 4th order RLC circuit. So, please could you provide me the transfer function of 4th order, so that I will do the mathematical calculation for the attenuation of filtered circuit.

Part of your problem is that you must derive the transfer function of your circuit in post #1 yourself. Once you have the transfer function you can then calculate the attenuation. Do you know how to analyze circuits that contain inductors and capacitors?

If the circuit you gave in post #1 were composed of 6 resistors (no capacitors, no inductors) would you be able to calculate the voltage at the right end of it all with a voltage of V1 volts applied by the source at the left end?

If you can do that, please do it and show your work. For this let L1 = 2 ohms, C1 = 3 ohms, L2 = 4 ohms and C2 = 5 ohms.

 

Imagine you had this fraction:

\(\frac{1}{3+2 j}\)

You can't just split the denominator and get this:

\(\frac{1}{3}+\frac{1}{2 j}\)

You have to rationalize the denominator.

View this video for the procedure:

Part of your problem is that you must derive the transfer function of your circuit in post #1 yourself. Once you have the transfer function you can then calculate the attenuation. Do you know how to analyze circuits that contain inductors and capacitors?

If the circuit you gave in post #1 were composed of 6 resistors (no capacitors, no inductors) would you be able to calculate the voltage at the right end of it all with a voltage of V1 volts applied by the source at the left end?

If you can do that, please do it and show your work. For this let L1 = 2 ohms, C1 = 3 ohms, L2 = 4 ohms and C2 = 5 ohms.

Thank you for the info.. But, I don't know how to derive the transfer function, please can you help with this, so that I will do the mathematical calculations.

 

Thank you for the info.. But, I don't know how to derive the transfer function, please can you help with this, so that I will do the mathematical calculations.

You didn't answer the question I asked in my previous post:

"If the circuit you gave in post #1 were composed of 6 resistors (no capacitors, no inductors) would you be able to calculate the voltage at the right end of it all with a voltage of V1 volts applied by the source at the left end?

If you can do that, please do it and show your work. For this let L1 = 2 ohms, C1 = 3 ohms, L2 = 4 ohms and C2 = 5 ohms."

Do you know any DC circuit analysis techniques, such as superposition, mesh and nodal analysis?

Do you know how to apply those techniques to AC circuits?

Is this homework from a course you are taking at an educational institution, or are you self studying?

Please do not ignore these questions.

I'm beginning to get the feeling that you may be somewhat over your head with this problem.

 

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.

The product of two separated responses regardless of order is only valid when the two sections are independent of current flow effects, which means the second filter can not load the first filter at all if the product rule is to be used. If the impedances are such that the input impedance to the second filter is sufficiently higher than the first section (like maybe 10 times higher) then the product rule is an approximation but still not exact.
The only way to get the exact analysis is to do a complete analysis of the entire circuit, and for this circuit it looks like the impedances are too comparable to use the product rule.

 

Hi MrAl,

Why and how you representing the imaginary part is for amplitude of peak voltage?. Always, do we need to consider like this?. Or Is there any specific thinks are there to be considered like this?.

Why and how you calculated the phase angle from the real part?.

Please, could you answer those questions.

If there is a single source in the circuit the phase angle of that source can be taken to be zero.
When you have the real and imaginary parts the exact formulation is as follows:
Amplitude=sqrt(Real^2+Imag^2)
PhaseAngle=atan2(Imag,Real)

and from that if there is only a real part and no imag part then the phase angle is zero unless the real part is negative and then the primary phase angle it is 180 or -180 degrees.

You can convert all AC sources of a single frequency into it's real and imaginary representation using that above, solving for each alone.

The complete analysis of the circuit depends on a general network analysis technique. The simplets way is to work in the Laplace domain.

If this is truly a 4th order network, then you will have 's' to the power of 4 in the denominator as well as a coefficient and other terms. In general the denominator will look like this:
a*s^4+b*s^3+c*s^2+d*s+e

although all but 'a' may end up being equal to zero, but 'e' is almost always present too.
For a network like yours, there are probably no zero coefficients.

You cant use the product of two filter sections unless the impedance of the second filter is much higher than the first, and even then it is just an approximation.

To find the files in the most general way, you would form 4 equations based on the output response desired, then solve for the 4 components. IF there are more components then you have to form more equations and solve for those too.

There might be some simpler formula for this particular network, but it would most likely only work for this very network and not any other. This means it is better to learn a more general way to calculate the output response. Once you do that, you can calculate all sorts of things you might need.
You can also graph the output to make sure it looks like what you expected.

 

"If the circuit you gave in post #1 were composed of 6 resistors (no capacitors, no inductors) would you be able to calculate the voltage at the right end of it all with a voltage of V1 volts applied by the source at the left end?

Yes, the calculated voltage would be right side and the applied voltage would be left side.

Do you know any DC circuit analysis techniques, such as superposition, mesh and nodal analysis?

I have idea.. But, I need to go through them again.

Do you know how to apply those techniques to AC circuits?

I don't know.

Is this homework from a course you are taking at an educational institution, or are you self studying?

Homework.

 

What University are you attending? What is the name of the course you are taking which gave you this problem as homework?

It is very unusual for homework to be given without preceding instruction in methods to solve the homework. Have you not been taught methods of AC circuit analysis before being asked to solve the circuit of post #1?

 

What University are you attending? What is the name of the course you are taking which gave you this problem as homework?

It is very unusual for homework to be given without preceding instruction in methods to solve the homework. Have you not been taught methods of AC circuit analysis before being asked to solve the circuit of post #1?

I'm not going to university. I'm going to private institute where they don't have proper curriculum. They will teach randomly, because they aren't paid and they are teaching to students who can't afford the university fees. Whenever they have time they will teach, that's it.
I'm also learning my self most of the topics.
If you help me it would be valuable.
I hope you understand my situation.

 

The network you showed will give you a 4th order once you have "added" up all the individual stages.
You need to know about complex numbers to handle this.
You then write down the network equations.
I usually start from the output end. As you move towards the input, draw a dotted line at the first junction where you have any components in parallel. Now write out the effective impedance for that part of the circuit so that you have an expression for that set of components. Then move again towards the input and add components which are in series and when you get a parallel path calculate the impedance again. Keep going until you reach the input.
Warning: the expressions for the impedances by themselves are very simple.
e.g. resistor is just R, capacitive impedance is a complex number (0,-j/(WC)) inductive impedance is (0,jWL)
you need to use complex arithmetic to add these.
After a couple of parallel combinations the expressions can become cumbersome!
To get you started can you write out the impedance for the combination of C2-R2-L2?

 

The network you showed will give you a 4th order once you have "added" up all the individual stages.

How to derive 4th order question?, to calculate the attenuation after the 4th order filter as the circuit is posted #1. Could you help me with this?.

 

Pinkyponky, if you take this course until you finish the AC circuit analysis you will be able to solve your problem. The Khan Academy courses are free; there are no fees: https://www.khanacademy.org/science/electrical-engineering

 

Pinkyponky, if you take this course until you finish the AC circuit analysis you will be able to solve your problem. The Khan Academy courses are free; there are no fees: https://www.khanacademy.org/science/electrical-engineering

I will take that course later. For me it will take a time to study the course and understand the classes and then implementing, It will take long time. Please could you help me with the 4th order equation?. So that I will calculate the attenuation value of 4th order equation.

 

I will take that course later. For me it will take a time to study the course and understand the classes and then implementing, It will take long time. Please could you help me with the 4th order equation?. So that I will calculate the attenuation value of 4th order equation.

Show how you would calculate the attenuation of this 4th order transfer function from 1/100 Hz to 100 Hz:

\(\frac{105}{s^4+10 s^3+45 s^2+105 s+105}\)

 

Show how you would calculate the attenuation of this 4th order transfer function from 1/100 Hz to 100 Hz:

\(\frac{105}{s^4+10 s^3+45 s^2+105 s+105}\)

Why your considering 1/100 Hz and 100Hz?.

Where those values (such as 105, 10, 45) came from, which are in above formula?. Is that real formula which is came from after the derivating the circuit which is in post #1?.

 

Why your considering 1/100 Hz and 100Hz?.

Where those values (such as 105, 10, 45) came from, which are in above formula?. Is that real formula which is came from after the derivating the circuit which is in post #1?.

This is not the transfer function of your circuit. It is a 4th order Bessel filter. The frequency range was chosen to contain the corner frequency. But all this is irrelevant. Can you calculate the attenuation at even one frequency, namely 1 Hz? Please show us.

 

This is not the transfer function of your circuit. It is a 4th order Bessel filter. The frequency range was chosen to contain the corner frequency. But all this is irrelevant. Can you calculate the attenuation at even one frequency, namely 1 Hz? Please show us.

I have a 2nd order transfer function and have calculated attenuation (but, there was a algebra mistake) for the 2nd order.

I need to have a transfer function for 4th order RLC series passive filter, to calculate the attenuation. Here, the problem is that I don't have transfer function and I don't know how to derive the 4th order transfer function from the circuit which is posted #1.

I have tried for 2nd order. now I'm asking you guys to provide the 4th order transfer function to calculate the attenuation after the 4th order filter. I don't know why I couldn't get help from you guys for this.

 

This is homework aid, not homework done for you.
But I'll try to help.
First, someone asked you if you could work out the output if all of the components were resistors. Can you do that?
Can you use complex numbers, (because that is essential to solve this problem).
If neither then you really need to take another look at your course or find some free ones, perhaps even on this site.
To start you off, the impedance of the right hand side of the network is
Z=R2+ZL2+ZC2
where Z is a complex impedance, ZL2 the impedance of the inductor L2 and ZC2 the impedance of the capacitor C2.
Now can you write the impedance of the next step leftward where ZC1 is in parallel with the impedance Z?

 

pinkyponky probably won't be back here. He posted his problem in another forum:
https://www.edaboard.com/threads/4th-order-transfer-function.400193/

without mentioning that it is homework, and he was given the answer right away.