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Transfer function for a dual band pass filter (small task from network theory)

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niki

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In the past it was more difficult to find a transfer function for a given specification. With today's powerful computers, that shouldn't be a problem anymore...
As a small example, the specification for a dual band pass can be found in the appendix. A transfer function with minimum order and an LC network are required.
Have fun.
dual_bp_specs_edaboard.png
 

Does network theory consider labour cost of 0% tolerances and specs for group delay error and yet has 4.5dB slope with 2.5dB ripple hmm. , so component error tolerance also demands margin to meet this spec. 10th order Chebychev? Sorry I'm not familiar with methods they teach you, but there are many simple programs but not for this. e.g. active filters from ti.com and LC filters from falstad https://tinyurl.com/y9shwbhh
 

Does network theory consider labour cost of 0% tolerances and specs for group delay error and yet has 4.5dB slope with 2.5dB ripple hmm. , so component error tolerance also demands margin to meet this spec. 10th order Chebychev? Sorry I'm not familiar with methods they teach you, but there are many simple programs but not for this. e.g. active filters from ti.com and LC filters from falstad https://tinyurl.com/y9shwbhh
The slope with 4.5dB has a ripple of 0.05dB! As motivation I included the plot with tolerances of +-2% for all elements in the LC network.
I agree. There are many tools and this task should not be a problem. I'm just an old-fashioned filter designer who wonders about today's methods of network synthesis.
Attempts to implement the transfer function with an RC active network (e.g. cascaded biquads) result in "shocking plots". The question still remains: how to find the transfer function and the LC network.Dok3.png
 

The normal (classical) procedure is to start with the bandpass-lowpass transformation.
As the next step, we can find the corresponding lowpass functions - and apply again the lowpass-bandpass transformmation.
 

This is a common answer that does not solve the problem! First read and understand the problem correctly and then make recommendations.
Please show me a result.
 

First read and understand the problem correctly and then make recommendations.

Thank you very much for your nice reply. I am not sure at the moment if I will be motivated to follow your advice...
 

As motivation I included the plot with tolerances of +-2% for all elements in the LC network.

Specification and results looks a bit theoretical to me. Have you included finite Q for real world components?
 

Specification and results looks a bit theoretical to me. Have you included finite Q for real world components?
The specification is somewhat challenging so that a standard off-the-shelf solution is not simply possible (missing in most engineers' curricula). But the filter can also be realized with lossy elements. The plot again shows the yield analysis with lossy elements.
Next topic would be the realization with an RC active network and a monte carlo analysis. Here begins the great amazement...
ddd4.png
 

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The gain slope part of the filter can't be effectively implemented with standard band pass topologies, it's demanding for equalizer topologies like staggered pole-zero pairs.
 

The gain slope part of the filter can't be effectively implemented with standard band pass topologies, it's demanding for equalizer topologies like staggered pole-zero pairs.
Not quite right. It also works with a lossless LC network.
 

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O.K. you say it can be effectively implemented e.g. by standard low-pass topology. But it's not using a commonly known filter prototype. So how did you design it?
 

Not quite right. It also works with a lossless LC network.

If you realize the 4.5dB slope with a lossless network, this will cause (heavy) mismatch in the pass band, which isn't acceptable in most cases.

But it seems that you want our attention for your design methodology, so please go ahead.
 

If you realize the 4.5dB slope with a lossless network, this will cause (heavy) mismatch in the pass band, which isn't acceptable in most cases.

But it seems that you want our attention for your design methodology, so please go ahead.
Finally someone mentions the connections between reflection and transmission in a lossless LC network. Of course this gives a great reflection... the power has to go somewhere. The user must decide whether he can live with it or whether another solution is necessary.
A few days ago an experienced RF engineer showed me an LC low pass filter, which he designed with a ripple of 0.5dB. He answered my question about the matching with: I tuned the filter to 30dB return loss! It took me a while to explain to him that his filter design had nothing to do with the tuned filter. His answer: "This was not part of my curriculum".
Almost all engineers have access to the most powerful tools, but the basic knowledge is often missing.
 
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    FvM

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If you realize the 4.5dB slope with a lossless network, this will cause (heavy) mismatch in the pass band, which isn't acceptable in most cases.

But it seems that you want our attention for your design methodology, so please go ahead.

Many LC filters have large reflections in the "passband" without the user being aware of this. All phase-optimal filters (e.g. Bessel) have a monotonous increase in reflection in the "passband" (passband is not exactly defined).
The appendix contains a possible LC network with the desired amplitude response. There are several solutions for this network with identical insertion and return loss (lossless and reciprocal, but not equivalent). Graph 2.png
This plot shows S11 of 3 different networks with identical insertion loss and return loss.

The second network has realistic losses built in to show the influence on the amplitude response. Only few engineers know the classical approximation theory and can generate such transfer functions (despite modern tools). The synthesis of the LC network is also a small challenge for today's engineers.
 

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Here's a Ltspice circuit of the first network.

Can you explain the meaning of the inductor parameter aL for the lossy circuit? qC and QL means frequency independent losses, I presume.
 

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    niki

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Simple implementation of frequency dependent losses.
qlqc.png
 

400MHz CATV repeater amplifiers have always had remote controlled slope equalization filters to compensate for frequency dependent losses in cables for each feeder and distribution amplifier.
 

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