Passive Fifth Order Bessel Filter Circuit Realization

[Farah]

Hi All,

I am trying to design a fifth order Bessel Low Pass Filter with a cut-
off at 48.8e6 Hz.

I calculated the transfer function and checked it in Matlab to make
sure it met my specs. I got:
Transfer function:

945
--------------------------------------------------------------------
3.05e-041 s^5 + 5.802e-032 s^4 + 5.15e-023 s^3 + 2.612e-014 s^2

+ 7.452e-006 s + 945

How do I realize a low pass filter circuit from the above transfer
function?
I know how to do it for a second order filter cos the standard form of
the transfer function would be:
(1/LC) / (s^2 + s (1/CR) + (1/LC)) which could easily be designed for
a R and L value after selecting a C value.

But, how to do it for a fifth order transfer function. Is there any
such equation for a low pass filter of Nth order from which I could
find the values of the L,R,C components?

Thanks,
Farah.

 

[The Phantom]

Hi All,

I am trying to design a fifth order Bessel Low Pass Filter with a cut-
off at 48.8e6 Hz.

I calculated the transfer function and checked it in Matlab to make
sure it met my specs. I got:
Transfer function:

945
--------------------------------------------------------------------
3.05e-041 s^5 + 5.802e-032 s^4 + 5.15e-023 s^3 + 2.612e-014 s^2

+ 7.452e-006 s + 945

How do I realize a low pass filter circuit from the above transfer
function?

Consult a good book on network synthesis.

I know how to do it for a second order filter cos the standard form of
the transfer function would be:
(1/LC) / (s^2 + s (1/CR) + (1/LC)) which could easily be designed for
a R and L value after selecting a C value.

But, how to do it for a fifth order transfer function. Is there any
such equation for a low pass filter of Nth order from which I could
find the values of the L,R,C components?

It would be easier to get a trial version of a filter design program (such
as http://www.filter-solutions.com/download.html) and just design a filter
to your specs. The program will give you the realization.

 

[[email protected]]

Hi All,

I am trying to design a fifth order Bessel Low Pass Filter with a cut-
off at 48.8e6 Hz.

I calculated the transfer function and checked it in Matlab to make
sure it met my specs. I got:
Transfer function:

945
--------------------------------------------------------------------
3.05e-041 s^5 + 5.802e-032 s^4 + 5.15e-023 s^3 + 2.612e-014 s^2

+ 7.452e-006 s + 945

How do I realize a low pass filter circuit from the above transfer
function?
I know how to do it for a second order filter cos the standard form of
the transfer function would be:
(1/LC) / (s^2 + s (1/CR) + (1/LC)) which could easily be designed for
a R and L value after selecting a C value.

But, how to do it for a fifth order transfer function. Is there any
such equation for a low pass filter of Nth order from which I could
find the values of the L,R,C components?

Thanks,
Farah.

In the dark ages, you would use a filter table. The table has a
diagram with the topology. The columns are L and C. Actually L1, C2,
L3 or C1, L2, C3 etc.[For a lowpass, you could start the filter with a
series L or a parallel C, hence there are two solutions.

All the filters are designed for 1rad/sec. You scale the frequency and
impedance as needed. Sometimes the Bessel is scaled to 1 second rather
than a 1 rad/sec corner frequency.

I did a bit of googling and this topic is too boring for the net.
However, any good engineering library will have a book on ladder
filter design.

I will say anytime I tried to build a passive filter higher than a few
Mhz, I didn't get the expected response. The inductors are very non-
ideal. I suspect people that build these high frequency ladder filters
have a great deal of practical experience in choosing components.

BTW, you are going to need a LCR meter to measure the inductors you
wind.

This is the best book on the subject:
http://www.amazon.com/Handbook-Filter-Synthesis-Anatol-Zverev/dp/0471986801