Hi,

I have read in many places that the different types of filters; Butterworth, Chebyshev and Bessel are design using inductors and capacitors. However, I did not find much information using resistors and capacitors to build them. I came across a simulator that calculate the coefficients of the second order filter for Butterworth, Chebyshev and Bessel but did not know what's the algorithm for the calculation. Anyone have any idea on the modeling method on different types of filters using the same circuit as attached? Thanks

Regards,
lkgan

 

The difficulty with building the filter topologies you describe with only resistors and capacitors is that they all rely on the components of their transfer function having a quality factor of greater than 0.5, that is to say a damping factor of less than 1. It's not really possible to build a circuit using just Rs and Cs that is underdamped - the way to do it without using inductors is to use op amps. Using op amps in an active filter configuration allows feedback to be used to give a higher quality factor without having to use inductors.

 

Yep, what Bitrex said.
RC for active filters, LC for passive.

By the way, there's a good LC filter design program out there called "Elsie" that will design LC filters for you; available in a Student Edition that will do up to a 7th order (7 poles) as freeware.
Link: http://www.tonnesoftware.com/elsie.html

There's another freeware LC filter designer out there; AAED Filter Design that also supports crystal ladder filters; very handy if you need a very narrow passband or notch.
Link: http://www.aade.com/filter.htm

 

The difficulty with building the filter topologies you describe with only resistors and capacitors is that they all rely on the components of their transfer function having a quality factor of greater than 0.5, that is to say a damping factor of less than 1. It's not really possible to build a circuit using just Rs and Cs that is underdamped - the way to do it without using inductors is to use op amps. Using op amps in an active filter configuration allows feedback to be used to give a higher quality factor without having to use inductors.

Hi bitrex,

For phase locked-loop application, the loop filter is built using R&C components. The simulator I found is PLL Design Assistant. It manage to design Butterworth, Chebyshev and Bessel using R&C components, but I have no idea how the coefficients are derive from the transfer function, can't find the formulas in google too. The damping factor for loop filter in PLL is usuall 0.7 right? So doesn't really matter to use L.

Yep, what Bitrex said.
RC for active filters, LC for passive.

By the way, there's a good LC filter design program out there called "Elsie" that will design LC filters for you; available in a Student Edition that will do up to a 7th order (7 poles) as freeware.
Link: http://www.tonnesoftware.com/elsie.html

There's another freeware LC filter designer out there; AAED Filter Design that also supports crystal ladder filters; very handy if you need a very narrow passband or notch.
Link: http://www.aade.com/filter.htm

Hi SgtWookie,

The problem of using the LC filter in PLL is that the L value will be huge for such a low bandwidth filter design. For eg, if I want to design a 3kHz loop filter bandwidth, the inductor will be impratically huge.

 

Hello,

The attached PDF has a lot of information on PLL design, including a part on loop-filters.

Bertus

 

PLL loop filters are typically lead-lag. They have a single pole and a single zero, with maybe a second pole at a higher frequency, to reduce phase jitter due to residual phase detector ripple.
They are generally not Butterworth, Chebyshev, etc.

 

PLL loop filters are typically lead-lag. They have a single pole and a single zero, with maybe a second pole at a higher frequency, to reduce phase jitter due to residual phase detector ripple.
They are generally not Butterworth, Chebyshev, etc.

Hi Ron H,

You are right, but the simulator, PLL Design Assistant software written by Michael Perrott did classified the loop filter shape as Butterworth, Bessel, Chebyshev and Bessel. Please take a look at the attached document from page 9 until 13. User can select the filter shape by just clicking the radio button. The thing I do not understand is what's the algorithm to calculate those coefficients using the same circuit architecture.

 

Hi Ron H,

You are right, but the simulator, PLL Design Assistant software written by Michael Perrott did classified the loop filter shape as Butterworth, Bessel, Chebyshev and Bessel. Please take a look at the attached document from page 9 until 13. User can select the filter shape by just clicking the radio button. The thing I do not understand is what's the algorithm to calculate those coefficients using the same circuit architecture.

Read more carefully, especially p.6. The references in this document to Butterworth, Bessel, etc., refer to the closed loop transfer function of the entire PLL, not of the loop filter. The loop filter must be designed to achieve the desired overall PLL closed loop filtering characteristic, but the two are not identical. Even in a basic PLL, the closed loop transfer function includes VCO gain (and the 1/s term introduced by the VCO) , phase detector gain, the F(s) of the loop filter, the error amplifier gain, if any, and the attenuation caused by the frequency divider in the feedback loop, if one exists.
Regarding the algorithm (or mathematical operations) required to calculate the loop filter components, given the G(s) of the PLL, that's beyond my capabilities, at least without a lot of studying.

 

Hi Ron H,

Thanks for pointing out the important point. I really missed that out and it confused me for some time. Actually I have tried designed out the 3 types of shape for the G(s), Butterworth, Chebyshev and Bessel, and tried measuring their performance on a PLL, phase noise and lock time, but doesn't see much difference. Since you are mentioning that the shape are for the closed loop transfer function, then how about the loop filter coefficients? What are they called? Isn't it the type of loop filter (Butterworth, Chebyshev and Bessel) that determined the shape of the whole closed loop system?

Regards,
lkgan

 

By the way, the simulator is able to download at the following link:

http://www.cppsim.com/download.html

Do let me know if you need other information and thanks for the discussion.

 

I'm afraid you are getting beyond the limits of my knowledge about PLLs.

 

Hi Ron H,

Alright, thanks again for pointing out an important point that I have overlooked and for the discussion.

Regards,
lkgan