Equivalent capacitance for LC low pass filter

Could some electronics guru here provide some hints/ suggestions on this problem ? I would like to determine the equivalent capacitance of a LC ladder type low pass filter. At low frequencies, the inductors are short circuits, and at high frequencies, the capacitors are short circuits and the inductors are high resistances. Any hints, suggestions would be helpful. Thanks in advance.

Reply to
amal banerjee
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There are two basic sorts of low-pass filters: Those based on cascading of T sections and those made of Pi sections. They are expected to be loaded by their characteristic impedance/resistance. They can also be seen as delay lines or part of a transmission line. HTH

Reply to
bilou

I don't understand the question. What do you mean "equivalent capacitance"? If there was a single value of capacitance that was in any way equivalent to an LC filter, there would be no need for the L in LC.

Can you explain what you are doing? Or is this some sort of homework assignment? What did the professor tell you about "equivalent capacitance"?

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Reply to
Ricketty C

Use a simulator. Learn about polar plots and Smith charts. Some filters make nice little twirls.

Jeroen Belleman

Reply to
Jeroen Belleman

I think he wants to understand input impedance vs frequency for an LC ladder LP filter.

A ladder filter with equal LC values will have a load impedance to reduce the ripples in the bandpass a few octaves before the breakpoint as the pole-zeros are staggered but not smooth like Butterworth or Cauer/Bessel/Elliptical filters.

Here is a Ladder LPF simulation where you can drag the "out" line to plot the attenuation at the input or output . The input attenuation is the inverse of impedance and the phase response at the input is 0 until the frequency reaches the pole-zeros before the breakpoint of the high bandstop.

Since each stage is a complex load to the previous source complex impedance ,the divider ratio determines the overall transfer function.

If you remove the load R which dampens the response, these pole-zeros become maximum Q.

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> Falstad's > Circuit > LC Ladder > customized with phase response & 14 pole

Reply to
Tony Stewart

at high frequencies, the capacitors are short

e"? If there was a single value of capacitance that was in any way equival ent to an LC filter, there would be no need for the L in LC.

ignment? What did the professor tell you about "equivalent capacitance"?

I am trying to create an accurate SPICE model for a spiral rectangular|squa re inductor based on the Greenhouse formalism(which takes into consideratio n the mutual inductance in between each parallel pair ofstraignt line inductor segment). So, for any selected inductor segment, each adjacent parallel segments gen erate a mutual inductance component that is added to the sel-inductance for the segment, and conversely, each parallel inductor segments on the opposite side generate a mutual inductance component that has to be subtracted from the self-inductance for the segment. These calculations are long-winded, but straight-forward. The equivalent circuit model for a single inductor segment consists of a series inductor and resistor, and two shunt capacitors, one each at the end of inductor and capacitor. The induct ance is a sum of the self-inductance as well as mutual inductance values fr om all adjacent and opposite parallel inductor segments. So, to construct t he equivalent circuit model for the entire spiral inductor one could attach the individual segments end-to-end. While looking through the literature on the same topic, I found some authors mention an "equivalent capacitance" that would enable one to use the equivalent circuit model for an "equivalen t" single straight inductor. Hence my question.

Reply to
amal banerjee

Why not the modified Wheeler method.

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There is a calculator built into Saturn PCB design (free for this) using the above method.

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Reply to
Tony Stewart

Are you planning to use the same Polysilic substrate? I don't see any test results to validate the simulations which look much higher than I would expect. I would write the authors to ask for simulation vs actual with updates. What substrate are you planning. This is not a simple ladder filter.

Reply to
Tony Stewart

The calculations for both the minimum loss substrate planar inductor and lossy substrate planar inductor are complicated but straightforward. It is far easier to write one's own C language code to do these calculations. One has a very tight control over what is going wrong. For example, incorrect input is easily detected when looking at the output - the GIGO peinciple.

Reply to
amal banerjee

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