Oscillators & Filters

• Note:
  • This investigation started when I needed some filters for the bioAmp project.
    To start, I needed a 60-Hz notch filter for the bioAmp output,
    then some narrow bandPass filters to do a hardware transform of EEG signal
    into brainWave frequency slots.
  • then, in order to design and test various filters,
    I needed a sweep-freq (ie. VCO) oscillator.
    Such is the way projects expand...

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• Oscillators:
  • 555 oscillators:
  • Test 555 IC's
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  • Basic (2-resistor) astable:
  
  • freq_Hz = ( 1.44 * 10⁶ ) / ( ( R₁ + ( 2 * R₂ ) ) * C_uf )
  • NOTE: "Duty cycle" is often defined as "mark/space ratio".
    However I'm using the term in more intuitive sense of "% - high".

          t_H-ms = 0.693 * (R₁ + R₂) * C_uf / 1000
          t_L-ms = 0.693 * R₂ * C_uf / 1000

          D_%-Hi = t_H / (t_H + t_L)

  • C₂ nominal 0.01 uf
    

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  • Basic (1-resistor) astable:
    
    
    • not verified... f = 0.72 * R₁ * C_uf
    • Duty cycle nom 50%, though output load resistance will affect it.
    • Note: as drawn, this circuit is set up for VCO operation with variable voltage into pin-5.

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  • VCO mod:
    Starting from the Basic-2R circuit above,
    remove the 0.01 cap from pin 5,
    connect a pot between +V and gnd,
    with the wiper input to pin 5,
    and the output freq will vary according to the pot setting.
  • Op-amp oscillators:

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• Filters:
  • Basic Filters:
    • 
      
    • Filter cutoff freq:
      f_c = 1 / ( 2 * pi * R * C )

    • A curiosity I don't yet have an answer for:
      You could build a filter with eg. R = 1k and C = 1 uf,
      and you could build another filter with R = 500 ohm and C = 2 uf
      and they would both have the same cutoff freq, about 160 Hz,
      but are there other consequences to changing component values like this?
      Different bandwidth, ie. different Q
      Q = (center freq) / bandwidth

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  • Twin-T Filters:

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  • Notch Filter:
    • 

      In this configuration, both the low-pass and high-pass filter sections
      are tuned to the same freq, resulting in the "notch" that gets rejected/grounded.

    • Notch frequency:
      f_N = 1 / ( 4 * pi * R * C)

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• Links:
  • https://www.electronics-tutorials.ws/filter/filter_7.html

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