Hi Glen,

I put together a couple of circuits, shown in the accompanying drawing, as APFL and APFH, then did a Bode plot, and a group delay plot, also enclosed. Results were as expected (the spikes are SPICE truncation errors, and are only a few nanovolts in size).

I then strung together a dozen of each, and did a composite Bode plot. As may be seen, it's not a bandpass filter, but is lowpass, band-limited by the string of APFL components.

Apologies.

I uploaded the wrong drawing and simulation results, so here are the correct images. (Conclusion is still the same, though)

Mark,

Thank you. Very impressive use of SPICE.

This helps visualize the progressive combination of the many Low-Pass with the many Hi-Pass.

We had not considered the 'band-limiting' possibilities.

.

The difference in your design and my design is that

the two filter blocks are Low-Pass ( 007 Hz ) and High-Pass ( 700 Hz).

and my filter blocks are in parallel.

* This generates the desired Band-Pass effect, which I thought would occur

when a large group of same-frequency APF were used..

* If these Hi/Lo block signals are combined via summing OPA circuit,

then a Band-Pass and a Dual-Notch function is accomplished.

* If these Hi/Lo block signals are combined via a differential OPA circuit

then Band-Pass ONLY is accomplished.

.

Therein is the "Question" which puzzles me.

Why does my All-Pass-Filter produce Dual-Notches,

when using Lo-Pass = 007 Hz summed with Hi-Pass = 700 Hz.

.

In my mind, it seems that

the Lo-Pass (007Hz) should not have interaction with the Hi-Pass (700Hz) .

I have run SPICE on various patterns

where I designed Lo-Pass from 3.5 Hz up to 650 Hz,

with quickly diminishing results

as far as the Dual-Notches are concerned.

.

We are interested in the 700 Hz Pass-Band (+ \ - 100 Hz sidebands )

which is well within the 741 OPA capabilities.

We emplement the R+C reactance prior to the OPA, in a direct fashing.

We emplement the R+C reactance outside of the Negative FeedBack Loop.

We avoid the Negative FeedBack loop inherent delay of aprox. 7 nSeconds.

.

So, my circuit generates Dual-Notches, and this is

(1) the desired function.

(2) an unexplained function.

.

---------------------------

My previous project, which produced both Band-Pass and Dual-Notches

was prototyped and run successfully daily is displayed in the attached images.

The AFX project was Introduced on this RGN page:

https://www.researchgate.net/post/Are_there_any_Analog_Active_Audio_Filters_that_match_any_Digital_Signal_Processing_filters

You may find the AFX project schematics an easy quick read on my website at

http://www.geocities.ws/glene77is/index.html

Primary diagrams are attached at the top of this page you are reading.

The AFX was a long project, and received contribution comments from :

Barrie Gilbert, Erik Lindorf, Lutz Wiggenheim, Josef Punčochář, Cyril Mechkov. ,

.

I changed the circuit values to give 0.007Hz for APFL, and 700Hz for APFH.

Here's what I got on a wideband sweep:

Mark,

Your latest Transient Plot looks more like what I have been getting.

Really surprised me !

Is this anomaly interesting ?

Try generating a Bode plot, on the Log graph,

that is where I get Band-Pass visualizations,

which can justify these experiments.

Rather than only the Transient Plot, emphasizing the Phase shifts.

I understand your caution about the simulator truncating numbers.

With PartSIM.com I can also generate a Bode Plot on a Linear Graph

which accentuates the depth of the Notche ( never approaching zero on a graph).

PartSIM calls the Linear Graph visualization a "Magnitude Plot".

Even so, if a number goes impossibly down to -105 dB,

the depth of the Notch below -48 is not important.

I can easily follow a filter circuit with another MFB Active filter Q=10

and push sidebands down another -27 dB.

PartSIM will present a normal Bode Plot on a log graph,

accentuating the upper parts of the Band-Pass signal.

The Notches do sit near the zero line, at the bottom, and cannot be trusted.

So, trying to avoid math errors, I run PartSIM for a Bode Plot, with Phase data.

PartSIM presents a Linear Graph, starting at zero, and showing -dB down,

accentuating the lower parts of the Band-Pass signal.

The bottom of the Notch plot points is not important,

as the Notches are very useful if they only drop down -48 dB from zero.

Try generating a Bode plot, that is where I get Band-Pass visualizations.

Rather than only the Transient Plot, emphasizing the Phase shifts.

You did use 12 LO and 12 HI, 007 vs 700 ( what I call "Un-Balanced" )

but you may still be running the two groups in Series.

On the PartSIM Simulator I have run SPICE on

(1) Parallel vs Series groups

(2) Un-Balanced vs Balanced tunings

(3) Summing OPA vs Differentiating OPA methods of combining all signals.

Observing the results ( which do not approach zero , inviting an error )

I have settled on Parallel, Un-Balanced, Summing OPA.

On the Un-Balanced Tuning for the AP-Lo,

I have run comparisons using 003.5 Hz up to 650 Hz versus AP-Hi=700 Hz.

I observe that 007 Hz generates the best Dual-Notches and Band-Pass.

My AP schematic ran the 12 LO and 12 HI in parallel.

Using my approach of parallel, I did simulations for

(1) "summing OPA"

(2) "Differential OPA".

Using "Parallel" + "Summing OPA" produces a better Band-Pass

and generates the "Dual Notches".

Dept of notches is not important, when they drop to -48 dB,

because I can follow this with a Multi-Feed-Back (MFB) Q=10

which will drop the sideband signal down another -27 dB.

( see my AFX schematic above on this RGN page for the MFB example.)

Attached are some fresh images.

Why does my All-Pass-Filter produce Dual-Notches,

when using Lo-Pass = 007 Hz summed with Hi-Pass = 700 Hz.

You are very skilled in your use of SPICE.

Interesting to banter these things back/forth.

Those are Bode plots. Y scale is linear, x scale is log. The troughs of the lowest plot are between 48 - 58 dB down. The fuzzy upper plots are about 100uV peak to peak so, basically, flat.

I am driving the two chains in parallel - see below.

I'll try an impulse response and FFT to see if there's any more information there.

The principle is very simple: adding signals with the same amplitude and different phase. For a phase shift of 180 ° (+ 360 °; + 720 °; ... etc.) we obtain a minimum of transmission. The basic theory (in Czech only :-( ) is in: https://www.researchgate.net/publication/281620035_Fazovaci_clanek_s_posuvem_0_az_kpi_a_synteza_frekvencni_zadrze

Mark,

That schematic looks right, if I decipher the notation correctly.

Am missing the Bode Plot in your post.

Please resend the Bode Plot.

This discussion is getting us on the Same-Train-Track

and I am interested in the results.

Joseph may have seen right to the core understanding of this topic.

Joseph,

Welcome, your comments are always welcome.

Perhaps, you have gone right to the core Theory,

which we know must control the truth of our experiments.

You wrote

"For a phase shift of 180 ° (+ 360 °; + 720 °; ... etc.)

we obtain a minimum of transmission."

I agree that is what we are looking at.

As an old student, I wonder if I have read the theory

and its application correctly.

Here is the rationale behind my "question" :

(1)

We found in reading E.E. texts is that

AllPass (phase-shifting) filters have frequency responses which must be " zero at w=0 and at w=pi ".

From our research,

(First)

This means that AllPass Filters cannot be used for

Low-Pass nor High-Pass nor Band-Pass designs.

This would be because the resulting combination of waveforms are homogeneous ; ie, the combinations are always simple phase shifts, with no frequency / amplitude changes.

(Second)

However, to my surprise,

My All-Pass circuit generates the Notches + Band-Pass .

Here is the direction I have taken, and David has been good assistance

by exploiting his SPICE skills to "mirror" my work ,

and keeping possible SPICE errors in check.

So,

David and I are now using the same schematic, and hopefully ,

observing the same Bode and same Transient Plots.

* If we confirm that SPICE is telling the linear truth,

* then these results will be pleasant, indeed.

It will not be that we have discovered something 'new',

rather that we are extending our understanding of the All-Pass circuit.

Barrie would say that Curiosity has made the Apprentice happy , indeed !

My last RGN project, which you discussed several years ago, "AFX",

(1) utilized All-Pass Filters for phase-alignment,

(2) then Differentiated two of the signals

in order to generate Dual-Notches around Band-Pass at f(0).

I prototyped that circuit, and have used it on my radio station frequently.

My "AFX" project circuit works Very Good !

Thank you for your previous comments.

As a whole, the "AFX" project went forward nicely,

with the group help from Barrie, Cyril, Joseph, Lutz, Erik.

The Bode plot is apf007700.gif included earlier

In case it has vanished, here's the bode plot. The top two traces are the responses halfway along each chain, the next two are responses at the inputs to the T-pad summer. The bottom trace is the result of the sum. As mentioned earlier, the fuzzy traces appear to have transition regions, but the mean value of each is 998mV, the positive and negative excursions being only +/- 50uV, so you can call them flat.

Incidentally, in case it's not obvious, each zigzag in the phase (red) trace is one rotation of the phase vector through 360deg. Spice resets it to zero each time, hence the zigzags.

Mark,

You are thorough.

You have demonstrated the proper analysis of this variant All-Pass Circuit.

.

Being an elder geezer, I have become 'set in my ways'

and I missed the obvious. Just in case you had not noticed.

.

The "pattern" I see is being driven by this concept :

All-Pass (phase-shifting) filters have frequency responses

which must be " zero at w=0 and at w=pi ".

We are observing this concept in the Bode and Transient plots.

.

I think that this definition is going to be the solution to my "question".

SPICE is telling the Linear Truth about my All-Pass circuit.

The circuit appears to be functioning as drafted into SPICE.

No mistakes here.

.

Your responses have been experimentally the best, and very interesting to me.

Joseph is a life-long E.E. and focused on the controlling theory.

Joseph,

Perhaps, someday, you will edit an E.E. textbook

so that it has this more inclusive definition of All-Pass Filters :

"AP circuits can function as Phase-Shifters,

and Low Pass , High Pass, Band-Pass Filters."

.

BTW, you went thru school 20 years after I did !

I wish you good life !

.

Thanks again for your comment.

Your quick solution to this "question"

reminds me of Barrie's quickness in seeing solutions.

.

I am just an old Apprentice ,

caught hiding in the closet

of the Master's Workshop.

.

Joseph is correct. I think the thing works as follows:

The APFL component outputs a phase angle of zero (with respect to its input) below its transition frequency, and -180deg above its transition frequency.

The phase becomes 360deg after each pair of APFL components, so since there is an even number of components in the channel, the final phase angle at the end will be 360deg.

The APFH component outputs a phase angle of -180 below its transition frequency, and zero above it. As before, the phase becomes 360deg after each pair of components, so the output phase of the channel will be 360deg.

So, we have two channels, each delivering an output whose phase is zero (with respect to its input), at frequencies above and below the transition region. At these extreme frequencies, the composite output signal at the T-pad is 2/3 of the input signal.

During the transition bands, the phase of one signal is changing rapidly, while the other stays at zero. There are six pairs of devices in each channel, which is the total number of 360deg phase shifts. As the phase vector rotates, the sum of the signals rises and falls, causing the sidelobes seen at either end of the output response curve.

With respect to the foregoing, calling these circuits ‘high-pass’ and ‘low-pass’ is misleading, as it is equally possible to interchange the component values, such that the ‘high-pass’ transition frequency is below that of the ‘low-pass’, without affecting the operation of the overall circuit.

To continue, since we only need one pair of devices per channel, we reconfigure the circuit as per the enclosed, without changing the component values.

The result is that all the sidelobes disappear, since we only have one phase change. The Bode plot shows just two notches at the transition points.

SPICE netlist for the final circuit:

xy

.ac dec 1000 1e-6 10meg

*#iplot all

*#run

*#quit

.print ac v(1) v(4) v(3) v(6) v(7)

*.tran 1000n 10m 0 1000n

*.print tran v(1) v(4) v(3) v(6) v(7)

x1 1 2 apfl

x2 3 1 apfl

x3 4 5 apfh

x4 6 4 apfh

r7 3 7 1k

r8 6 7 1k

r9 7 0 1k

r10 9 2 1

r11 9 5 1

v1 9 0 ac 1

** vol:2 vinl:5

.subckt apfl 2 5

e1 2 0 1 3 1e4

r1 5 1 100e6

r2 3 2 10k

r3 5 3 10k

c1 1 0 23u

.ends apfl

** voh:1 vinh:5

.subckt apfh 1 5

e2 1 0 3 2 1e4

r4 3 0 9.8854k

c2 5 3 23n

r5 5 2 10k

r6 2 1 10k

.ends apfh

.end

See "Obr.8" and "Tabulka 7" - the "third row" - in my paper "above". Very simple solution indeed :-)

Here it is :-)

Mark,

I follow your verbal description well.

I really appreciate your repeated comments

and your perseverance to a clear result.

.

When PartSIM opens again, I will do another design,

using two AP-L and two AP-H , per your design.

I will be observing for Depth of Notches,

and frequency of placement around f(0)=700Hz.

My "AFX" has notches at 524 Hz and 905 Hz.

dropping to -60 dB ( depending on surrounding circuitry ).

.

Thank you, again, for sharing your expertise.

I read your "profile" and say that you are doing very well.

.

I am just an old Apprentice,

caught napping in the Master's WorkShop.

Josef,

Obviously, you have been around this tree many times,

and your academic position is well earned !

You Understand the Concept,

and thus you place the "concept" before the experimental results.

I wish I had been under your tutelage , in my beginning years of school.

.

When PartSIM opens again, I will do another design,

using two AP-L and two AP-H , per NotchWithPhaseUnit PDF .

I will be observing for Depth of Notches,

and frequency of placement around f(0)=700Hz.

My "AFX" has notches at 524 Hz and 905 Hz.

dropping to -60 dB , a very useful position and signal level.

.

Thank you, again, for sharing your expertise.

Barrie was right in spending his time in our group of seven.

.

I am Just an old Apprentice,

caught wandering in the Master's WorkShop.

Glen Ellis The depth of the first notch is about 90dB:

Freq Mag (dB) Phase (deg)

6.9952E-03 -6.3331E+01 2.6795E+02

6.9968E-03 -6.6908E+01 2.6688E+02

6.9984E-03 -7.3077E+01 2.6361E+02

7.0000E-03 -9.1507E+01 1.5851E+02

7.0016E-03 -7.2350E+01 9.5868E+01

7.0033E-03 -6.6542E+01 9.2981E+01

7.0049E-03 -6.3087E+01 9.1979E+01

The second notch is almost the same:

Freq Mag (dB) Phase (deg)

6.9952E+02 -6.3531E+01 2.7002E+02

6.9968E+02 -6.7216E+01 2.7000E+02

6.9984E+02 -7.3746E+01 2.6996E+02

7.0000E+02 -9.2115E+01 9.0488E+01

7.0016E+02 -7.1868E+01 9.0035E+01

7.0033E+02 -6.6280E+01 8.9999E+01

7.0049E+02 -6.2908E+01 8.9978E+01

Josef Punčochář SPICE says your notch is about 63dB

Freq Mag (dB) Phase (deg)

3.3651E+02 -4.4053E+01 2.7219E+02

3.3729E+02 -4.8023E+01 2.7311E+02

3.3806E+02 -5.5519E+01 2.7695E+02

3.3884E+02 -6.3478E+01 7.2598E+01

3.3963E+02 -5.0607E+01 8.5943E+01

3.4041E+02 -4.5599E+01 8.7516E+01

3.4119E+02 -4.2441E+01 8.8050E+01

Aha ! The Saga of APF continues !

.

The theory behind combining rotating-phases holds true, obviously.

.

I only require use of the Notches nearest the f(0)=700Hz in my project.

In my radio receiving equipment, I have

(1) "Roofing" filters prior to

and

(2) MFB Hi-Q Active Band-Pass filters after

the main filters ( which in the case of "AFX" are four MFB Band-Pass ).

.

It is good news that you obtain good results using only two pairs of AP .

Attached is my current project All-Pass circuit, with 24 AP stages.

I look forward to seeing the results I obtain at PartSIM.

.

Part of my project goal was to see if I could use All-Pass-Filters

to replace the phase-aligning function of my four MFB Band-Pass stages.

Results of this APF project shows that , in general, this is possible.

When PartSIM opens up, then I will run further simulations

utilizing the suggested 2-APL and 2-APH.

.

I observe that the Dual-Notches in my "AFX" project were 525 and 875.

Quadrature frequencies are 525 and 875.

f(700) >> f(L)=525Hz and f(H)=875Hz.

.

Same aprox. position for the current "APF", but resonance is 692Hz..

Quadrature frequencies are 525 and 875.

f(692) >> f(L)=519Hz and f(H)=865Hz.

.

Glen Ellis and Mark Sitkowski, thanks for very interesting debate. "Phase units" were my great hobby before about 30 years. But results was described in Czech only. Some you can see on RG too: https://www.researchgate.net/publication/281625619_Fazovaci_clanky_s_operacnimi_zesilovaci_a_jejich_pouziti

https://www.researchgate.net/publication/281625355_Pasmove_propusti_s_fazovacimi_clanky_s_prenosem_zavislym_na_ciniteli_jakosti

https://www.researchgate.net/publication/281625430_Zapojeni_pasmove_propusti_s_vazbou_typu_bootstrap

Pictures and "math" is the same in all languages :-))

Josef

Joseph,

Yes !

I recall my introduction to "Serious Boot-Strapping ! "

This old Apprentice was allowed to "rub elbows"

with an elite "Group of Five" Engineers.

.

Interestingly enough, if you set the upper and lower transition frequencies to the same value, the notches disappear...

Yes,

The Mystery requires more Mastery to behold the SECRET !.

I have a short series of Schem and Plots where I explore this case.

See my website.

...

Joseph mentioned in one of his papers

that if the parallel phases match ( balance )

then the AF(low) cancels the AF(high) .

Thjs will produce a Gaussian Band-Pass, at best.

But nobody ever pursues All-Pass to that target.

...

I recall the RGN sessions on Active Boot-Strapped Band-Pass Filters,

several years back,

wherein we used positive Band-Pass filtered feedback

to quickly generate a Null circuit, or a Band-Pass circuit, or an Oscillator !

...

Alas !

I am still locked out of PartSIM.

So, this old geezer will have to tinker on some other toy this PM.

Perhaps I should turn on my Ham Radio rig, and listen to Morse Code

wafting on wings of magnetic feathers, as I have for 60 years,

and I may find some new ham friend from some faraway enchanting land.

...

You have a good day, pal.

Barrie Gilbert encouraged me to "Explore, Experience, Be Thankful ! "

...

If you need a simulator, you can download all the stuff I use from www.designsim.com.au (for free...)

Mark,

Thanks for the tip.

I have only MicroSoft XP, and most Sims require something larger, later,

for a Downloaded embeded install. I like the idea of the On-Line type.

PartSIM was designed for small student projects, way back,

but I have run as many as 32 OPA filters in a single design,

with 27 probes. Have given PartSIM a real test.

I will check it out, this PM.

.

This is something I must check on, since the other option is to do hand calculator crunching , which would be a week each mod on my projects.

Even if done that way, you cannot hand-calculate a project with dozens of OPA filters, combined as innovative groups, and expect that effort to enable you to visualize , intuitively, the results. As Barrie Gilbert related, An Intuitive Idea involves "putting on the robes of the electron ' and touring the circuit in your mind, understanding the many feedback loops and relationships. Then the calculations can describe the moving , living, circuit functions.

Sorry, soap box is over. Old geeky geezers get side-tracked ....

.

When I retired , I disconnected from my career which involved IT work in Relational Database design/adm, using Fox and T-SQL

extensively, on Z-80 CP/M systems and SCO-Unix and MS DOS systems.

.

Now,

I run Puppy Linux, based on the binary of Ubuntu 19.03, BionicBeaver ,

labeled UpupBB 19.03+15. PuppyLinux is designed for older CX,

and is easily run completely from USB flash drives.

I have tried my best to stay away from my "old haunts" of CX design/adm.

Has been hard to break old habits of four decades,

but my mind really needed a change.

I went back to Ham Radio (60 years licensed)

and bicycle riding (46 years)

with more zeal that my former career had allowed. ( x, -j zeal ! )

.

Buena Suerte !

.

Gracias.

There are ports of all this stuff to any Windows that can run Cygwin, any Linux and Sun SPARC. If you can install Cygwin on your XP box, it should work fine.

Manuals and executables all from www.designsim.com.au/dssdnld.html

Forgot to mention: 64-bit only (sorry!) and you'll need the Cygwin X11 libraries

Vaya con dios.

Mark,

Just viewed your "Vspice" project.

Very impressive and self motivated exploration of application of Spice Tools.

.

Yep !

My ntfs base system is XP, 32 bit.

Not 64 bit here.

My Four CX are 32 bit.

I will download the manual and read through, at your suggestion.

Thank you for the tip.

Maybe my "rich uncle" will send me a 64 bit computer !

.

Would like to install Ubuntu and try KiCad for Linux,

but even Ubuntu-17 for 32 bit requires more resources than I have.

The new versions of LTspice (supported) , require late versions of M$,

and my "ntfs" main partition has only M$-XP, and is 2005 model.

My other CX are 2001 and 2002. I must consider that my projects require a dozen OPA filters in the base design, and for real-time application in my Radio Station the design may require two dozen, so the SIM must be a serious version.

.

But, since you have verified that the Un-Balanced, Parallel, Summed version

of APF produces Dual-Notches and Band-Pass,

maybe I should just accept it.

.

For the frequency range 350 Hz to 1400 Hz,

can you post the Bode Plot Band-Pass, and the Magnitude plot.

I suspect that they will be very similar to my "raw" plots .

I will be able to compare the Notch Band-Width .

... Mine was aprox. 380Hz BW @ -60 dB.

I will be able to measure the -3 dB and -6 dB and -12 dB BW.

I suspect that they will be very similar to my "raw" plots .

...

Well, let's march on and see what the future holds.

No problem

Here's the circuit diagram and the simulation results.

As you can see, the two transition frequencies are too close together to give a sharp notch, since the two phase angles are 105deg and 251deg, and not zero and 180. The actual depth of the notch is -11dB, shown in the second result.

At what frequency would you like the notch to occur? I can bend the transition frequencies to achieve that.

Mark,

Thank you for this. PartSIM opened back up, this PM.

My target is a pair of Notches around the f(700) , aprox. 500 Hz and 900 Hz.

...

With the comments in mind, I setup a Shem series, beginning with 2 Filter Pairs.

We Sequenced through 2, 4, 6, 8, 10, 14, 16, 18, recording each Bode.

.

The progression of Bode f(0) and f(Hi-Notch) showed the pattern of interest.

Given a Filter Pair ( 7 and 700 ) each circuit generated a series of Notches.

At 2 Filter-Pairs the notches were very far apart, perhaps 20 KHz, not good.

When we used Filter Counts progressing up towards 18 Filter-Pairs,

then the circuit generated Notches that became closer together.

At Filter-Pair 16, the Dual-Notches around f(0) became most useable ;

ie, closer together , nearer to my target of 700 Hz..

.

Given this pattern of results,

I would predict that using 24 Filter Pairs,

would generate Notches closer together,

and thus be the same results I had obtained earlier,

wherein the f(0) was about 700 Hz,

wherein the f(Notch-Lo)=525 f(Notch-Hi)= 900, aprox.

.

This discussion has been Partially Solved by applying the All-Pass Filter Theory,

wherein co-mingling AP-Hi and AP-Lo produce notches in a defined series.

.

Defined : "Balanced Hi / Lo" = 700 Hz and 700 Hz.

Defined : "UnBalanced Hi / Lo" = 0.007 Hz and 700 Hz.

.

Unsolved is why a circuit with "Balanced Hi / Lo " seems notch free.

Unsolved is why a circuit with "UnBalanced Hi/Lo" generates Notches.

.

Mastery of this is a "mystery" , a riddle to be resolved. No Magic here !

.

Joseph's statement about All-Pass Filtter Theory still predicts this Behaviour.

Controlling theory from the professor who studied this in 1976.

.

I have attached this series of Schem and Bodes

showing the Apex creeping downward in f(0), Notches coming closer together.

These have a note on the Apex , and show it creeping down in F(0)

... from 2 FP to 18 FP , where the Apex shifts to below 700 Hz.

.

Out of interest, Josef's circuit, with Ca=Cb=47n, and Ra=Rb=10k gives a notch frequency of 338.6275Hz, a notch attenuation of -73dB. (Simulated with a resolution of 10,000 points per decade)

3.3838E+02 -6.2287E+01 2.8512E+02

3.3845E+02 -6.5201E+01 2.9137E+02

3.3853E+02 -6.9235E+01 3.0540E+02

3.3861E+02 -7.3704E+01 3.4562E+02

3.3869E+02 -7.1425E+01 4.1817E+01

3.3877E+02 -6.6831E+01 6.3933E+01

3.3884E+02 -6.3478E+01 7.2598E+01

and a 6dB bandwidth of 428Hz

Mark,

Excellent. 388 Hz agrees with my plots, for starters.

This is one difficult way to design a Morse Code Audio Filter at 700 Hz !

.

My previous project "AFX" , on my website, is more direct,

and I hope I presented adequate theoretical foundation

about the Differential Notch Generator.

.

Will return in the AM to examine and appreciate your data , more.

...

I simulated your circuit, (8L + 8H) using your values for R and C, which I checked and found correct for 7Hz/700Hz).

However, I think your results only show part of the actual spectrum, which actually starts at about 1.3Hz, and goes on to about 3.6kHz.

Mark,

Right On!

"part of the actual spectrum" is correct.

The further spectrum, extending far out is useful in a tutorial sense.

.

The further spectrum was, not neglected, just not useful to my goal.

In the "GC_AP_1RL-24" design, the lower and upper lobes

are attenuated ( surpressed ) by Active Filtering.

.

The Goal of the "AFX" and this "APF' has been

to provide Pass-Band Filtering for the Audio Spectrum close to 700 Hz.

The 700 Hz is a good pitch for copying Morse Code from the Radio Bands.

Having Dual-Notches at 525 Hz and 900 Hz greatly aids in surpressing

un-wanted sidebands which may contain signals from adjacent radio stations.

Having a central f(700) Pass-Band of only 100 Hz Band-Width at -3dB

and perhaps 300 Hz Band-Width at -60 dB,

will greatly enhance the ability of a radio operator to copy Morse Code

from the radio bands.

.

There is much more interesting information

which I could relate about Radio Operations and Morse Code.

We have been around Amateur / Commercial Radio operations for 60 years.

All my Amateur experience has been with Morse Code Operations.

We could easily say too much, and digress from the AP Filter Project.

.

The attached PDF file illustrates such a AP Filter for copying Morse Code,

with Pass-Band close to 700 Hz,

including associated circuitry

( PreAmp, Roof-Filter, Active-Limiter, MFB Band-Pass Filters )

which were adapted from the "AFX" project, which is on my website.

(We have used "AFX" during he past four years in my radio station.)

.

This discussion has been Partially Solved by applying the AP Filter Theory,

wherein we should understand that

co-mingling AP-Hi and AP-Lo produces notches in a defined series.

.

Defined : "Balanced Hi / Lo" = 700 Hz and 700 Hz.

Defined : "UnBalanced Hi / Lo" = 7 Hz and 700 Hz.

.

Unsolved is why a circuit with "Balanced Hi / Lo " seems notch free.

Unsolved is why a circuit with "UnBalanced Hi/Lo" generates Notches.

.

Mastery of this is a "mystery" , a riddle to be resolved.

No amount of calculations will provide the answer.

... because Math and Calculations provide descriptions of existing phenomena

and enable us to predict future developments based on our experiments..

I still have to figured it out. ... No Magic here !

.

Mark,

Received a note from Joseph about one of his papers.

Now,

I am wondering if I could apply positive feed-back to an All-Pass Filter

so that my current All-Pass project with 24 stages could be more compact.

Call this a "All-Pass Filter Hi-Q version".

This would be "Applied Boot-Strap Technology", by Joseph's suggestion.

This is probably a silly question, but why not just use two tuned circuits..?

If you don't like inductors, a gyrator is easy enough to design...

Mark,

Don't know how to spell that ... 3177e ?

.

Tuned Active Filter circuits produce a Gaussian Band-Pass.

Multi-FeedBack (Dalyannis) Active Filters are the "cat's meow" for that !

.

My application requires very steep sidebands,

to kill near-by audio signals, surrounding f(700) .

Active Filters produce a Gaussian (Normal Curve) slopping passband.

The Dual-Notch circuit produces a Non-Gaussian Curve,

with a nearly vertical Pass-Band (side-band) shape..

.

Got to run, right now.

Tomorrow , pal.

Mark and Joseph,

I edited and re-rote the "Question" in order to simplify the issue.

Have you considered the humble bridged-T?

You can get much better results with that, and it's easy to make and a very simple netlist:

notch

.ac dec 10000 6 10000

*#iplot all

*#run

*#quit

.print ac v(2)

e1 2 0 1 2 1e6

r1 4 5 200k

r2 5 1 200k

r3 6 0 100

r4 7 6 100k

c1 5 6 2n

c2 4 7 1n

v1 4 0 ac 1

c3 7 1 1n

r5 2 6 50

.end

Some interesting facts about notch filters You can find too in:

https://www.researchgate.net/publication/324176166_Band_Stop_Filter_with_a_Synthetic_Inductor_with_Series_Resistance_and_a_Real_Operational_Amplifier

Article Band stop filters with real operational amplifier

Mark,

In radio Morse Code operations, use of a notch for nulling specific adjacent frequencies in the audio spectrum

is very useful. The Twin-T is deep, but not easily adjustable.

.

http://www.geocities.ws/glene77is/GC_ET.html

.

One project I worked up is attached. Here is partial copy from my website, about a Gaussian Filter.

http://www.geocities.ws/glene77is/GC_ET_AFX_CW_Filt7N.html

*** Yet Another Analog CW Filter ***  AFX_AAN_Q34 *** with Gaussian Shaped Waveforms.

*** Twin Notch Filters around a CW Filter,  Max Notch "Q"=10+10=14 . *** The  AFX-AAN  has broader Top Band and Steep Sides at v=7 . *** *** The "AAN" Design utilizes Twin Notches for Narrow PassBand, rather than only narrow active-filters. *** This 11 stage design is better than the "7N" , but more complex than the standard AFX. ***

*** The main benefit is a good steep side-band curve down to -36 dB. *** The main problem is that the pair of Q=10 filters must be extremely accurately aligned *** (1) with each other ( exactly 650Hz or 750Hz )  else severe distortion of the notch will occur.  *** (2) with the f(700) center-band freq ,  the  offset is  only  +/- 50 Hz .    ***

In the Bode Plot, the two Notches are shown in positive (up-ward) but their effect is negative (down-ward).

Please note the Gaussian waveforms ( Green, Blue, Red ). Green and Blue are before the two Notches.

Red is the result of the Notches.

The Red waveform has very steep side-bands,

and the fall-off side-band remains near the zero level +/- an octave.

This is a 'good' result, AFX_AAN_Q34, generaing Gaussian waveform filtering.

There is aother 'good' Gaussian Notching filter on this page.

http://www.geocities.ws/glene77is/GC_ET_AFX_CW_FiltAAN.html

.

Not as good result as the "AFX" circuit "GC_ET_AFV-3RL-V4F-D-VQ-Man",

on this page : http://www.geocities.ws/glene77is/GC_ET_AFV.html

"AFX" ("AFV") uses Non-Gaussian Phase-Filtered wave-forms.

This one I built and have used in my radio station for several years.

The "AFX" design is more than simply a 'good' filter, it is spectacular.

I have attached the PDF of that web-page, for the "AFV"

[ http://www.geocities.ws/glene77is/GC_ET_AFV.html ]

In the "AFX" and "AFV" design, the Side-Band Extent is produced by Non-Gaussian Phase-Filtering,

and the Side-Band Extensions are down more than -60 dB, out to +/- Octave.

At BW=100 Hz, the side-band attenuation per -dB is 5 Hz. Side-band widens by 5 Hz for each -dB down.

This is called "brick-wall" .

The "AFX" wave-form is what is produced by DSP filters

after the signal has been run through a DAC to the ear-phones.

On my website, at this page http://www.geocities.ws/glene77is/GC_ET_AFX_CW_FiltRG.html

you will find the DSP workup which emulates and expands the idea.

That page is devoted to tthe Excellent Digital Model and Documentation as provided by Dobromir Dobrev , Ph.D , Bulgarian Academy of Sciences.

.

In radio operations, we have what is called a "pile-up" wherein a dozen stations will respond to a "DX" ( long distance ) radio signal, each attempting to be 'heard' and thus receive credit for having 'worked' some distant station or country.

So, sometimes this overly crowded situation arises in normal contacts,

wherein radio stations do not hear signals from some direction (maybe because using a beam antenna)

but I hear many signals because my antenna is a Long-Wire (broad-side directional).

I hear these various signals at various audio pitches ... Not a "single" signal causing "QRM" interference.

It is like being in a crowded room and only wanting to hear one single person, from out of the crowd of voices.

On top of that, signals vary in signal strength (QSB) constantly as the ionosphere fluctuates.

.

Thus, the use of narrow audio filters can be a great aid in copying Morse Code.

Thus, the use of Narrow Pass-Bands having attenuated side-bands extending +/- Octave are of great value.

In the developed circuits I use, the Dual-Notches have this type of side-band attenuation.

.

Hope that rambling tutorial helps in understanding the variety of Audio Filters, their applications,

and the usefulness of Audio Filtering in my several projects associated with my radio operations..

...

Joseph,

You are delightful and your diagrams are interesting.

I tried some of my ideas in SPICE, but it was fruitless.

However, I did greatly reduce the number of All-Pass stages, and got the same results.

I still wonder about "WHY?" the Un-Balanced arrangements of All-Pass Filters works,

especially in he light of the attached schematic. One AF-Lo (7Hz) and TEN AF-Hi (700Hz) .

One AF-Lo (700Hz) and TEN AF-Hi (700Hz) produces exactly same results !

.

This AM, I will study your diagrams ... good time for a pause.

Barrie , one time, cautioned me about projects that might be a "fools errand" !

Therefore, I always try to listen for good ideas,

lest I trip and find my head in the sand !

.

Relatively easy way as change frequency of the double T. More precise description see (Czech only :-(( ):

Article Zádrže a propusti s nulou přenosu realizované s operačními zesilovači

That would be my suggestion too. I've had good results with parallel-T filters in the past, and the quick'n'dirty design I sent earlier (sorry about the frequency) does seem to meet your criteria.

First, please be aware that the resulting notch filter will be very non-minimum-phase (i.e. many zeros in the Laplace s-plane will have positive real parts), so the filter's step and impulse response are likely to distort waveforms much more than a simpler, minimum-phase realization. So please make sure this is really what you want.

As for analyzing the network, this can be done algebraically in the Laplace Transform domain. If the transmission gain function is

H(s) = [(n1(s)/d1(s)] + [n2(s)/d2(s)]

where n1 and d1 are the numerator and denominator of the upper allpass chain and n2 and d2 are the numerator and denominator of the lower allpass chain,

then the poles of H are all of the poles of the two branches (11 in total, if the top is one stage and the bottom is 10 stages).

The zeros can be found by a numerical root finder, where the polynomial n3 representing the zeros is

n3 = n1 * d2 + n2 * d1

That is, we rearrange H to put it in the form n(3)/d(3), where d3 = d1 * d2 and is the polynomial whose roots are all poles of both branches. The only potential messiness is finding the roots of the high-order polynomial n3.

I would use a computer algebra program like Maple to manipulate the polynomials into the proper form and then to take the roots of n3 numerically.

Once you have the roots of n3 (i.e. the zeros of the notch filter), you should see some complex conjugate roots with a 0 or very small real part (due to numerical accuracy limitations in the rootfinder), putting them on the imaginary axis in the Laplace s-plane. These represent the notch frequencies of the resulting notch filter, and the absolute values of the imaginary parts are the notch frequency in units of radians/second.

As a side note, this differential allpass structure is useful for synthesizing certain classes of lowpass filters, including odd-order Butterworth and odd-order Elliptic Function lowpass filters. However, this technique is mainly popular for making digital filters that have low sensitivity to coefficient quantization.

to : Robert A. Orban,

Thank you kindly. You have validated the SPICE results.

Your approach is Right to the Point.

.

H(s) = [(n1(s)/d1(s)] + [n2(s)/d2(s)]

is exactlly where to start understanding

this "Differential All-Pass Filter".

Everything else follows in natural order.

.

I follow the algebra, very well.

I am familiar with Active Filters.

However, use of this "differential all-pass structure"

in relation to "odd-order active filters"

is not in my understanding.

That will be my puzzle to learn.

But,

I am greatly encouraged that there is a rational analysis

for this unusual "differential all-pass structure".

This All-Pass project was an extension

of my earlier "AFX" phase-filtering project,

and my results were so unexpected.

In the "AFX" my analysis came together with the attached equation,

and all else followed in natural order.

The lesson learned is to "Start At The Beginning",

and always learn from engineers who have been around this tree before..

.

As an intellectual project for this elder engineer,

this little project has been refreshing.

It will continue now into the world of All-Pass Phase-Filtering Filteres.

To Robert A. Orban, ... Right to the Point.

Thank you for your generous and expert analysis and participation.

.

Fellows,

Thank you for your participation.

I am attaching your Bio Information to the current schematic,

as contributors to this project in this format :

Glen Ellis, Univ Tennessee, Memphis, TN, USA

Mark Sitkowski, E.E., Design Simulation Systems Ltd, Australia

Joseph Puncochar, E.E. ,VŠB-Technical Univ of Ostrava · Czech Republic

Robert Arnold Orban, Master E.E., Stanford Univ, California, USA.

.

The level of talent expressed in your "Answers" and C.V. is impressive.

.

I am just an old Apprentice,

and I have been caught tinkering in the Master's Workshop.

We are extending the "AFX" Filter Project

by examininging Phase-Filters and All-Pass designs.

We have uploaded several "Pre-Papers" on the major projects

under the topic "AFX" :

https://www.researchgate.net/post/Are-there-any-Analog-Active-Audio-Filters-that-match-any-Digital-Signal-Processing-filters

...

This "APC" Phase-Filter-Project is a continuation of the "AFX" Project,

and is thusly relevant to this current topic

about "Variant All-Pass Filters".

- - Analog Phase-Filters in Narrow Band-Pass Audio applications.

Three Sections are titled :

"AFX_Main-Filter-Project-210808-1832.PDF",

"AFX_Resonant-Filter-Project-210806-1600.PDF"

"AFX_Phase-Filter-Project-210903-0700.PDF"

2021 Oct 15...

.....We have a revised Pre-Print attached : 2021 October 26

Attached file.

This Project continues as an examination of All-Pass Band-Pass circuits.

...This "AFC" project is derived from our previous "AFX" project https://www.researchgate.net/post/Are-there-any-Analog-Active-Audio-Filters-that-match-any-Digital-Signal-Processing-filters ..

...