Analog filter design metgod questions

Make the reactances at f_-3dB the same magnitude and opposite sign as the low pass prototype.

For instance, a 50-ohm filter with f_-3dB = 1 MHz might have a 5-uH inductor someplace. Replace it with C=1/((2 pi*1MHz)**2)* 5uH) ~5 nF, if my mental arithmetic is holding up today.

Cheers

Phil Hobbs

you need THE BOOK

Mark

Gag me with a spoon >:-} ...Jim Thompson

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Get a copy of my favorite filter book...

"Synthesis of Filters" Jose Luis Herrero & Gideon Willoner

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 :-)

But excellent for handling depth of stop bands, etc. ...Jim Thompson

Nah, I like Zverev. (Of course I've been using it on and off since

Cheers

Phil Hobbs

I've used it, thus the gag ;-) ...Jim Thompson

Thanks. I have access to this book, but ploughing through it is quite an exercise.

Thanks, I have been using these tricks for years.

at is if I start with a

Thanks. Will try it out. Math does not bother me. I started out in my career as a physicist.

If you have a low pass transfer function H(S), the change S->1/s gives you a high pass transfer function G(s)=H(1/s). (Note upper -LP- and lower cases -HP-)

Attenuations are unchanged and frequencies are related by jW=1/jw, i.e. w=-1/W.

After this LP to HP transformation you (often) have to perform a frequency scaling, i.e. translate G(s) to G(s/wo). Now, whatever was happening at w=1 will now be happening at w=wo

Others have suggested some textbooks, and this is the way to go if you want to understand. Once you know what you are doing, even wikipedia (and perhaps my explanation) looks useful

HTH, Pere

On a sunny day (Tue, 23 Jun 2015 10:20:05 +0200) it happened o pere o wrote in :

FYI if you use an opamp to subtract the output from the lowpass you are left with the highpass. That reduces the problem in half :-) Same for bandpass-bandstop. :-)

Oh, okay. From a matho's POV, then, the usual filter transformations are based on a conformal mapping in the s plane:

LP -> HP s' = s_0**2/s (swap inductors and capacitors, keeping the magnitude of the reactance at s_0 the same)

LP -> BR s' = s_0/(s_0/s -s/s_0) Maps s_0 to infinity, zero to zero, and infinity to zero. (Keep the LP components, but series-resonate every C at s_0, and parallel-resonate all the inductors.)

LP -> BP s' = s_0**2/s - s**2/s_0 Maps s_0 to the origin, and both 0 and infinity to infinity. (Keep the LP components, but parallel-resonate all the capacitors and series-resonate the inductors)

(I think those are right. I just did it on the hoof.)

The BR and BP filters have the same FWHM as the lowpass prototype, because although the response is two-sided, the reactances change twice as fast, so the BW nets out the same.

These transformations are good starting points when you mostly care about amplitude, but they're not much use with linear-phase filters. Instead of the phase being linear with frequency, it's nicely hyperbolic instead.

Zverev has tables with pre-distorted coefficients for good bandpasses.

Cheers

Phil Hobbs

Right! But you have to be able to do the subtraction with enough precision to get significant stopband attenuation and this may not be so easy...

Pere

Just to add on that, the LP -> BP transformation only works for sufficiently high percentual bandwidths or equivalently, low filter Q. Otherwise element values become impractical. For moderate to high filter Q, the coupled resonator approach is the way to go and you may obtain several flavors of frequency (and phase) response. Furthermore, pre-distorted (coupling) coefficients may even give a nice response for finite Q rsonators.

Pere

The problem is that you generally wind up with only a single-pole characteristic when you do this, on account of the phase shifts.

Cheers

Phil Hobbs

Predistortion wrecks the return loss, and reduces sensitivity. I have never found a modern case where I thought it was worth it. Digital equalization post-ADC seems to be a better approach.

Hmm, interesting. Could you say more about that?

Cheers

Phil Hobbs

t is if I start with a

What you are asking for is in virtually every filter design book. I am pre suming you have at least one. The Omar Wing book can be downloaded.

Or Steve Winder's book:

I recommend purchasing Winder's book. It is simple and easy to read, and n ot expensive. It is good for filter newbies. IIRC, there is an error in t he elliptic BPF derivation from LPF proto.

The LPF>BPF and LP>NF is constrained to geometric symmetry due to the natur e of the transformations.

As someone else pointed out, as the BW gets under 20% or so, the standard t ransformation to BPF is unworkable, as component spread (really, L-spread) becomes intolerable. Then, the coupled resonator approach becomes a nice pr actical solution to that problem. In the background, it amounts to inserti ng immittance inverters in between each resonator of the standard transform ation. Then, single element impedance matching on the ends turn it into a parametric filter. Works great.

Many filter design books strangely ignore coupled resonator filters. Zverev covers the coupled resonator approach. There is a very good chapter in We s Hayward's Intro to Radio Frequency Design on coupled resonator filters. The Williams/Taylor book has coverage too.

If you are only going to buy one filter book, the Williams/Taylor book woul d be the one. But then, one really needs much more than one book for this t opic. If you get all the books you need, then the Williams/Taylor book bec omes a bit redundant. It is a bit cookbook-ish. It is not really a *deep* b ook.

Simplistically: It is usually the corners (BPF) that droop due to finite Q. So the "middle, " where response "peaks," is pushed down to match the corners by the predis tortion. (There is no way to bring the corners up by predistortion techniqu e; we are assuming a given or fixed component Q.) Since the elements are mo stly reactive, the pushing down of the middle area response amounts to refl ecting that energy back to the source rather than transmitting it to the lo ad. "Reflecting" is the same thing as saying the return loss is degraded. After all, the return loss approaches 0 dB in the stopband.

A passive filter works based on the principle of reflection. Ideally (pure reactive elements), what is not transmitted is reflected, and vice versa. This amounts to the famous Feldtkeller energy equation for filters. It is at the root of why return loss gets degraded for predistorted filters.

If the filter is pre-LNA (or post PA), then the amount of middle "push-down " will come straight off the noise figure and link budget. It won't hurt t he corner sensitivity because it is already down. It will probably not mat ter if, for example, it is an IF filter. If the equalization is done post ADC, then the noise profile will look bathtub-like (without predistortion).