Analog Filters: a Compilation of Standard Transfer Functions (UPDATED 2)

[ballsystemlord]

I snapped up a copy of the Zverev bible of filters on eBay. I paid about €50, a bargain.
They often change hands for serious cash:
www.ebay.co.uk/sch/i.html?_nkw=zverev+filters&_sacat=0&_from=R40&_trksid=m570.l1313&_odkw=zverev&_osacat=0
Mine used to belong to a company called CTI, developers of early video cassettes.
Have I bought stolen goods?

Put it on your ebay watch list.

Are you talking about "Handbook of Filter Synthesis, Paperback by Zverev, Anatol I." or "Filtering in the Time and Frequency..., Zverev, Anatol "?
Thanks!

[mawyatt]

I snapped up a copy of the Zverev bible of filters on eBay. I paid about €50, a bargain.
They often change hands for serious cash:
www.ebay.co.uk/sch/i.html?_nkw=zverev+filters&_sacat=0&_from=R40&_trksid=m570.l1313&_odkw=zverev&_osacat=0
Mine used to belong to a company called CTI, developers of early video cassettes.
Have I bought stolen goods?

Put it on your ebay watch list.

I got a lot of mileage from a compact package called NuHertz.
Coilcraft offer a neutered version for free. www.coilcraft.com/en-us/other/coilcraft-lc-filter-designer-software/?srsltid=AfmBOoomVBWJYkQsiDeLAap-9x3D-TpijoFWUu5nwMpAGywv5GqgrllE

Maybe!! Don't lend out your version, they have a habit of evaporating

We had our hardback "borrowed" by an employee long ago, then left the company and didn't return the book. This left us with only the paperback version which we still have.

Wonderfull filter resource indeed

Best

[Analog Frontend Designer]

Hi,
recently I have stuck with a problem.
I need to derive a transfer function of third order filter section with absorbed first order stage and with transmission zero.
For second order topologies this is easy to do manually or find an example in handbook.
I know that Filter Solutions can provide a stages with absorbed real axis poles, but unfortunately not every employer/customer can provide it due to the high cost. Also this propgram doesn't cover some interesting topologies like one-opamp Friend general biquad etc.

Here is example of 3order VSVS circuit and similar absorbtion i would like to do with a Friend high-pass notch stage.
What i think - if trancfer function will be obtained, then at least several possible solutions may be simulated in term of sensitivity and better one chosen.

Maybe you know how to derive a transfer function from node equations without ugly manual math?

[gvz]

For those interested, here are some functions to compute Butterworth and Chebyshev order and coefficients I wrote a few years ago:

Code: [Select]

function n = butt_order(f_pass, f_stop, att_pass_dB, att_stop_dB)
    att_pass = 10^(att_pass_dB/10);
    att_stop = 10^(att_stop_dB/10);

    N = (att_stop-1)/(att_pass-1);
    D = (f_stop/f_pass);

    n = ceil(log(N)/(2*log(D)));
end

function g = butt_coeffs(N)
    k = 1:N;
    g = (2*sin((2.*k-1).*pi/(2.*N)));
end

function n = cheb1_order(wp, ws, ap, as)
    n = ceil(acosh(sqrt(10^(as/10)-1)/(10^(ap/10)-1))/(acosh(ws/wp)));
end

function [g] = cheb1_coeffs(N, apass)

    B = log(coth(apass/(40*log10(exp(1)))));
    Y = sinh(B./(2.*N));

    k = 1:N;
    b = Y.^2 + (sin(k.*pi/N)).^2;
    a = sin((2.*k-1).*pi/(2.*N));
    g = ones(1, N);

    for k = 1:N
        if(k == 1)
           g(k) = (2.*a(k))/Y;
        else
            g(k) = (4.*a(k).*a(k-1))./(b(k-1).*g(k-1));
        end
    end

    if(~mod(N,2))
        g(N+1) = (coth(B./4)).^2;
    end
end

LP to BP/HP/SP transformations are know and can be easily implemented.

I have used many times for passive filters.

These were taken from Valkenburg "Analog Filters" book,  Blinchikoff &Zverev "Filtering in Time and Frequency Domain", and Matthaei, Young and Jones "Microwave Filters, Impedance Matching Networks, and Coupling Structures" books.
Cheers,
g.

[sergey_g]

Maybe the following information will be useful to someone.
Many years ago, there was a need to make the simplest possible selective filter using an operational amplifier.
In the end, this is what happened:

[sergey_g]

From what I have checked recently -
By connecting different R the bandwidth of this filter changes while the central frequency remains unchanged.

[sergey_g]

The central frequency is determined by the formula see the figure.
Resistance r affects the magnitude of the output signal, but does not noticeably affect F.
For the maximum quality factor Q the formula was not found, the necessary equipment is not available.
When I could use a generator with a resolution of 0.01Hz, the achievable bandwidth
at a frequency of 1000 Hz it was 3 Hz, while the operational amplifier K544УД1 was used

[jaxon]

Excellent sorting work! This complete set of analog filter formulas and attached documents will save lots of time for circuit designers in practical development. Thanks very much for your generous sharing.

[Frederic]

I like to give some comments to the topic (active filters):

(1) MFB-topology:
* For bandpass applications, a simplification is posible with Y2=1/R2=0.
* The basic structure is not well suited for high-Q bandpass applications. Component spread and dimensioning (equal component values) can be improved when a second (inverting) gain stage is used which provides some positive feedback thru an additional resistor to the first node(Q enhancement, Modification is proposed by Deliyannis).

(2) S&K topology: If compared with the MFB-topolgy, this structure is rather sensitive to component tolerances - this applies in particular to the two gain determining resistors.
Therefore, it is strongly recommeded to use either the unity-gain option or a gain of "2" (with two equal resistors in the opamps negative feedback path).

(3) Comparison: Under ideal conditions, all available filter topologies behave equally. Differences can be observed under non-ideal conditions only (parts tolerances, finite gain of the opamps).
In general, the following can be stated: The MFB topology has pretty good passive and comparable bad active sensitivities. The opposite is true for S&K structures.

(4) Comparison to other known active 2nd-order filter circuits: There are two very popular topologies:
(a) State-variable (integrator-based, three opamps) ;
(b) GIC-based (Two opamps, Antoniou-block, "Fliege"-filter).

Comment: GIC-filter blocks are known to have the best properties of all 2nd-order blocks as far as sensitivity to non-ideal opamp parameters is concerned.

[EE_Audio]

Here are a couple of spreadsheets I made that automate the design of Sallen Key and MFB filters. The design process is to select the desired capacitor values and the spreadsheet calculates the resistors needed for the target Q, frequency, and gain. Capacitors are generally available in E6 or E12 values, whereas resistors are available in E96 values. You can unprotect the spreadsheet if you want to make changes. No macros were used, all formulas.