GC_ET_AFX_CW_FiltDIQ.html

2021-07-18   10:38:25

       "AFX"   the post-Filter Phase Sensitive circuit :
    

            Discussion of Circuit-Notch Concept (click)

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       Note:    in the following diagrams, R2 is the R(freq) for adjusting f(center).  
                   ie, R2 is at the source/drain connected to ground,  for MFB resonant node. 
       Note:    the -1dB level is equivalent to 900 mV level and barely audible. 
       Note:    the -3dB level is equivalent to 700 mV level in these Bode Plots. 
       Note:    [ (BW@-12dB - BW@-3dB )/9dB  labeled as :    "v" = slope of best fit ] 

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*** Goal:  "N"arrow and "W"ide passband signals.  

"N" and "W" passbands are achieved ,
with Roofing Filters,
with Quad MFB filters,
with the Differential and Integration stages. 

(1) Differential produces "N"arrow double-notched  passband. 
* Stage 'UDIF'    ( DIFFerentiating Fx01 with Fx04 )  to produce a "N"arrow double-notched signal. 

(2) Integration produces "W"ide Flat-Topped Steep Skirt passband. 
* Stage 'UINT'    ( INTEgrating #3 negative and #4 positive signals )  to produce a "W"ide flat-top steep sided signal. 

 
Note: Below specs are from PartSIM, and the schematics / plots are from ngSPICE. 
Note: Author did the initial build-up on ProtoBoards, and measurements compare favorably. 
Note: Author has used variations of these circuits since 2013 in his Amateur Radio Station.

These  specs  show both the "cQ" (calculated "Q" specific to each designed stage) , 
and the "mQ"  (measured "Q" as it accumulates progressively through the circuit) . 

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***  the reader should note these filter characteristics  : 

***  The DIFFerential and INTEgration Filter Stages have passband curves that are NOT Gaussian curves.  

      The "Q" of the passband, based on BandWidth at -3dB down to -12dB does not compare with regular band-pass circuits. 
      A modified slope-of-best-fit is used to better describe these bandpass curves.  
      This is the calculation : [  (BW@-12dB - BW@-3dB ) / 9dB   = v   :    "v" = variance = a slope-of-best-fit ]

***  The basic un-tuned DIFFerential stage produces a "N"arrow signal, via a Subtraction Operation, 
          with two -48dB notches at aprox. +/- 90 degrees from f(700) sidebands.  
           When preceeded by Roofing-Differential Filters, the Dual-Notches are pushed down -25 dB and -50 dB and -75 dB. 
          This is a f(700) narrow stage.   

*** The un-tuned INTEgration stage produces a "W"ide signal, via a Summing Operation, 
          with a flat top, and steep side-bands. 

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***  Based on the AFX circuit with a Single Roofing-Differential-Filter. 

***_ Differentiated  "N"arrow Output
***_ Dual Notch= 550 Hz & 900 Hz  , which is aprox.  +/- 90 degrees from f(700)
***_ Basic Measurements:  (measured cumulative "Q" across Quad MFB and the Differential Dual-Notch stage )
      'mQ' (measured 'Q') = 8 (aprox)    
      'BW' (-3dB)   =   85 Hz
      'BW' (-12dB) = 185 Hz
      'BW' (-60dB) = 350 Hz
 
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***  Based on the AFX circuit with a Single Roofing Triad Filter. 

***_  Differential "N"arrow passband has these characteristics:  
***_  BandPass shape is NOT gaussian. 
***_  Sideband falloff is -48 dB per octive (non-gaussian ).
***_  BW=89--196__ variance=12 (Hz passband spread per dB attenuation 0dB to -12dB)  
***_    BW @ -3dB = 90Hz
***_    BW @ -12dB = 185Hz
***_    BW @ -48dB ( Notch-to-Notch ) =385Hz 
***_ 535Hz Low Notch  and  920Hz High Notch.  
***    NOT a Quadrature Filter by design and NOT Conceptually a Quadrature Filter. 
***_ 920Hz is -27 dB under Fx04 passband curve. 
***_ 920Hz is -48 dB down from 1.0 Volt standard "0 dB" signal. 

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***  Based on the AFX circuit with a Single Roofing Triad Filter. 

***_ Integrated  "W"ide Output has these characterisics:
***_ mQ=3.9,  T=101, BW=180 
***_ BW=179--390, variance = 24 (Hz passband spread per dB attenuation) 
***_    BW @ -3dB = 179 Hz
***_    BW @ -12dB = 390 Hz


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***  When the DIFferention stage is combined with Roofing filters, we have these results :
*** (  here bode plots are based on the AFX circuit with a Single Roofing Triad Filter ). 
 

****   This is the QUAD MFB FILTER  plus DIF and INT stages : 
The filters are Fx01 , Fx02 , Fx03 , Fx04 . 
The calculated 'Q' are Q=2.0 , Q=2.5 , Q=3.0 , Q=5.0   ( calculated )
The measured  'Q' are Q=2.0 , Q=3.5 , Q=4.5 , Q=7.0   ( cumulative measured )

****   These are the DIF and INT stages  Plus  the  Q20 sharp stage :

              



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*** Notes on Bode for  DIFFerential "N"   and    INTEgration "W"
***  Differentiated "N"arrow is double Notched.
***  Integrated "W"ide is flat topped.  

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*** DIF stage operates by subtracting :   Fx01 - Fx04
***   and produces  Notches which are -27dB below Fx04
*** effective Notch Depth = -48 dB 
*** BW=86--190___v=12
*** Notch=533 @ -50dB
*** Notch=920 @ -50-dB
*** StopBand= -48dB

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*** INT stage operates by summing Fx03+Fx04  
*** BW=176--369___v=-22
*** StopBand = -19dB to -42dB


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Below:  
Narrow Differential signal is BLUE   and   Wide Integrated signal is BLACK 
   


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*** Below : early design with NO Roofing-Filter :
*** the Bode for Fx01 (black), Fx04 (blue), and the Dif "N" (red) .  
*** At 925Hz , the Dif "N" (red)  versus  Fx04 (blue)    is  -27 dB. 
***    This is a log scale plot so the real curve difference is difficult to visualize.  
   

Magnitude Plot of Dual-Notch Effect           Goal is Ideal Brick-Wall Effect

           

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Below: 
***  "UDIF" NARROW DIFferential stage details 

***   where Filter#4 (mQ=7.0)    is subtracted from    Filter#1 (mQ=2.0)
***   easily producing dual -48 dB notches at aprox. +/- 90 degrees : 
***   StopBand is aprox. -45 dB to the limits 
***   Notch Band-Width is aprox. 350Hz.  

*** Experiments to Narrow the Notch Band-Width tighter are ( here ).

*** Ratio of Resistors is important but not critical :    
                         [  (+) 300K : 15.9K    and   (-) 100K : 100K  ] 
***      notice that a very small amount of Fx01 signal is used,  5% tolerance.
***      Ratio depends on the f(LoNotch) and f(HiNotch), which has been tested at 535 & 935  and variations.
***      BandWidth of Dual-Notches is Dependent on the Q and the Q-spread of the Quad-Filters.
***      Quad-Filters with a Same Q=3 for all four filters produce 530 & 930 , and work very well.
***      Principle effect will be noticed on adjacent very strong signals, where 1000 W can be reduced to sound like 1 Watt.


 

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Below: 
WIDE:  "uINT" stage is a INTegration of Fx#3 positive and Fx#4 negative.
Still in development, but earlier versions have worked well, according to the O'scope. 
Ear can hardly hear the effect.

Functionally,  Fx04 is an inverted signal to Fx03,  
          and both are INTegrated (summed) by the 'uINT' OpAmp.
       Fx04 is inverted and a 10% signal is used to form a notch into Fx03. 
       Notice that a small amount of Fx04 is used to compress the Fx03 peak.
*** The Ratio of Resistors is important.
This produces a "W"ide signal with a very broad top and steep skirts. 
This Bode shows a 1/2 dB dip in the passband ( below audibility ). 


“W” / “N”   via a single Switch. 
#6 INT stage produces Very Broad Top of 175 Hz.
#6 INT stage produces a sideband skirt nearly as steep as the "N" stage. 

Final  INTegrated  stage "W"ide    ------------ mQ=4, BW=175, v=16, K=-24

SPICE requires : R( 100K / 61K / 145K )
Constructed circuit requires : R( 100K / 33K / 100K ) 


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*** Bode for ALL complex waveforms ,  as described so far. 



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*** Bode for  Sum"W", Dif"N".

***    #5 UDIF and #6 UINT stages are the Differentiating and Integrating stages. 
*** These are untuned stages, and produce a very Non-Gausian BandPass. 

*** Bode for Fx03, Fx04, Summed to produce the "W"ide signal.
*** "N"arrow Differential signal is "blue" with double notches,
*** formed by subtracting Fx01 and Fx04.
*** "W"ide signal is the red flat-topped trace. 

   


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*** NOTE about the special DIF and INT stage characteristics : 
*** The DIFFerentiantial and INTegration stages do NOT generate  gausian curves. 
*** The DIF and INT stages combine two signals to produce non-Gausian curves.
*** The DIF and INT stages are NOT tuned resonant filter circuits.  
*** The DIF and INT stages are Phase Sensitive Operational Circuits, 
          receiving two signals, operating, and producing a single signal out. 


*** The INT stage produces a "W"ide signal, with a flat top, and steep side-bands.  

*** The DIF stage produces a "N"arrow signal, with dual  notches surrounding 700Hz 

***  Graphical Concept for the Dual-Notches     
*** Where the wave-forms cross,
      there is zero difference in amplitude,
      and the Differential OPA produces a Notch ! 


*** Below is a "Magnitude Plot" which emphasizes the dB relations.

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*** COMBINING   Filter#4  with  UDIFferential dual-notch  with  Sharp Q20 stage ***

*** Below is a "Magnitude Plot" which emphasizes the dB relations.
       Green trace is "roof"
       Red     trace is "Filter #4 "
       Blue    trace is "Dual-Notch"   

*** Below is a "Magnitude Plot" which emphasizes the dB relations.

*** Green Fx04    +    Orange Dif    +    Blue Q20 

*** Read this carefully ! 
### Below:
***  The additional Q20 stage deepens the 'Dual-Notch' pattern by more than -30 dB. 
*** Orange Notch is UDIF     ...    Red Notch is UQ20  at -88 dB down !
*** Practical Results:
      at the base of the RED Notch  a 600 Watt RF signal would sound like a 1 Watt RF signal. 

*** Triples are from DIF Stage   at +/- 20 %  component specs. 
*** upper-wide Blue Fx04    vs.   variable-Dif   vs.   variable-Q20 

*** which demonstrates component specification tolerance !!!  

*** Q20 stage produces this Bode plot : 
*** note that the Q20 sidebands have a variance of 7   (  ie, BandWidth spreads by 7 Hz per -db attenuation !!!  )
*** Narrow BLUE is the UINT stage   ...   Narrow BLACK is Q20  with stop-band => -98 dB ! 
*** has NO dual-notch ! 

*** Int vs Q20



***  Future Development plots  taken from current proto-type tests ***

*** Fx04 + Q20 is not so good. 

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These are the  author's  AFX  core Narrow Filter Circuits: 
(*) the   uDIF Differential Narrow Dual-Notch  
(*) the  very Narrow Q20 sharp filter with variable f(0).  

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