calculate the Q factor of LC bandpass

the

that

I can usually do 1 pole in my head. Two poles to 4 poles i can do with pencil and paper. Beyond that i don't bother, i use table based design or software. Never had to go past 8 poles, but that was a bitch to tune with

out

A single peak is possible in theory. It is not likely to be realizable in production quantities. Doing it one off may be reasonably achievable. (How close do the peaks have to be before you cannot tell then apart? / How good is your measurement gear?)

?-)

Bessel and Butterworth LC bandpass filters are easily done in production.

Something's obviously got into the water today. (Maybe St. Patty's came a bit early for some folks?)

Four-pole bandpasses are like camels--they come in one-hump and two-hump varieties. Plot the response of rickman's filter with the component values Lp = Ls = 10 uH, Cp = Cs = 8.2 nF, Rs = RL = 50 ohms. It has a nice smooth single peak right around 555 kHz.

If you want a sharper one, try replacing the shunt section with

Or as John says, look up the response of a Bessel filter.

Cheers

Phil Hobbs

Take away the 50 Ohm resistors (as the question was originally posed by "rickman") and it's double-hump like crazy.

And it was Walter Brennan, not Gabby... I always mix those two up, particularly in really old movies ;-) ...Jim Thompson

What's remarkable (at least to me) is that you can design an LC lowpass filter, then easily map it into a bandpass. All you do is pick a center frequency Cf, and add C's to series-resonate all the L's at Cf, and add L's to parallel resonate all the C's at Cf. That shifts the zero-frequency point of the lowpass up to Cf, so the bandpass is twice as wide as the lowpass prototype.

Seems too easy.

filter,

lowpass

The general technique is called conformal mapping, which used to be used a lot for solving Laplace's equation because it can map geometries with corners and stuff into circles or rectangles or half-spaces. It's used less now, mostly because it only works in 2D.

That works great except for linear-phase filters. The frequency warp is nonlinear, so a Bessel or equiripple delay LPF maps into a beautiful approximation to just the exact delay curve that you don't want. ;)

Cheers

Phil Hobbs

filter,

lowpass

You can hack in a couple of elliptical notches that add delay peaks, both to flatten the delay and improve the skirt attenuation. Of course, there's not much market for narrowband FSK modems these days.

...Jim Thompson

filter,

lowpass

It is easy, at least if you are not too stringent on the fractional bandwidth of the bandpass filter. If you want a narrow filter, with this approach you end up with unrealistic component values, and have to resort to the coupled-resonator approach.

Pere

two-hump

ohms. It has a

lowpass filter,

frequency Cf,

parallel

the lowpass

I'll bet you even still remember all the neat tracks that you can do with a complex Riemann sphere.

My favorite filter system is inverse Chebychev.

filter,

Cf,

lowpass

Not that I recall!

The Type 2 one, with the ripples in the stopband? IIRC I've only ever seen those used in antenna design, to minimize sidelobes, so I've obviously missed their sterling qualities for other stuff. Could you enlighten me?

Cheers

Phil Hobbs

If it has, pleas tell me how. I'm pissed off with having to use Berkeley Spice 3f to do PZ analysis.

Hearsay... I haven't looked for it, but I seem to recall it being mentioned on the LTspice list. ...Jim Thompson

-- | James E.Thompson | mens | | Analog Innovations | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice:(480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at

are

I would literally try the same file in LTSpice. It may work. And you should get some possibly helpful diagnostic messages if it doesn't. This should work best from CL.

?-)

two-hump

component

ohms. It has a

lowpass filter,

frequency Cf,

parallel

the lowpass

used

with

used

with

Gosh, you mean you didn't learn about interesting transforms of the complex frequency plane (rotations of the complex Reimann sphere before transforming back)? It can be handy for understanding going between s and z transforms.

is

Well my favorite trick is placing the maximum attenuation notches just where i want the to block narrowband interfering signals. Like harmonics of power line frequencies. Then if needed another filter could restore much of the pass response in the stop band (initial design has to be low minimum stop band loss. They are also fairly good at approximating a brick wall filter with high minimum stop band loss. I think the phase is well behaved in the pass band as well.

I would have to find my book of tables to setup some spice examples.

?-)

filter,

Cf,

lowpass

Conformal mapping and calculus of complex variables I know about. Transforming between s and z is pretty simple too, because exponentials are entire functions. I expect that the terminology used in EE vs physics and math classes is probably different. (The only EE courses I ever took were Bracewell on Fourier transforms and Steve Harris on nonlinear optics, both in grad school.) Or perhaps I've just forgotten.

I see. I've very occasionally done that with elliptic-type filters, but they ring like anything. I'll keep your method in the bag of tricks, and maybe try it out next time.

Cheers

Phil Hobbs

filter,

Cf,

lowpass

That sounds like the "General Parameter Filters" technique in my favorite filter book...

"Synthesis of Filters" Jose Luis Herrero & Gideon Willoner © 1966 by Prentice-Hall, Inc., Englewood Cliffs, N.J.

Library of Congress Number: 66-27547

(Peruse the old/used bookstores...

Math intensive, transforms required, not for those who can't already do a hand-math filter design with Laplace (and need to fall back on FilterPro :-) ...Jim Thompson

I did. It didn't.