1 / 43

Active Filters, EQs & Crossovers

Active Filters, EQs & Crossovers. Dennis Bohn Rane Corporation. It’s All About the Mathematics. Electronic filters are all about the mathematics. You cannot escape the math. We will study the math; … you will love the math. Simplified Laplace Transforms.

roland
Download Presentation

Active Filters, EQs & Crossovers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Active Filters, EQs & Crossovers Dennis Bohn Rane Corporation Rane Corporation

  2. It’s All About the Mathematics Electronic filters are all about the mathematics. You cannot escape the math. We will study the math; … you will love the math. Rane Corporation

  3. Simplified Laplace Transforms • Represents complex (frequency dependent) impedance, i.e., magnitude & phase • Uses the Laplace Operator, s, where s = complex frequency variable = jω = j2πf • Resistor Impedance = R (freq. independent) • Capacitor Reactance = 1/sC • Inductor Reactance = sL • Allows writing a circuit’s transfer function by summing circuit currents using Kirchoff’s Law Rane Corporation

  4. Transfer Functions (TF) • Transfer functions mathematically describe the frequency domain behavior of filters. • TF = ratio of Laplace Transforms of a circuit’s input and output voltages: T(s) = Vout(s) / Vin(s) Filter Vin(s) Vout(s) Rane Corporation

  5. Filter Transfer Functions • General filter transfer function is the ratio of two polynomials: Rane Corporation

  6. TF Poles & Zeros • “Zeros” = values that make numerator equal zero, i.e., the roots of the numerator. • Makes amplitude response rolloff 6 dB/oct. • Shifts phase +90°/zero (+45° @ fc) • “Poles” = values that make denominator equal zero, i.e., the roots of the denominator. • Makes amplitude response rise 6 dB/oct. • Shifts phase –90°/zero (–45° @ fc) Rane Corporation

  7. Audio Filter Order • The order or degree (equivalent terms) is the highest power of s in the transfer function. • For analog circuits usually equals the number of capacitors (or inductors) in the circuit. • 2nd-order most common. • For common audio filters the order equals the rolloff rate divided by 6dB/oct, e.g. 24 dB/oct rolloff = 4th order (24 6 = 4) Rane Corporation

  8. Audio Filter Order (cont.) Rule: 6 dB/oct & 90° per order Examples:1st-order = 6 dB/oct; θ = 90° ( 45° @ fc) 2nd-order = 12 dB/oct; θ = 180° ( 90° @ fc) 3rd-order = 18 dB/oct; θ = 270° (135° @ fc) 4th-order = 24 dB/oct; θ = 360° (180° @ fc) … etc. Rane Corporation

  9. Why 6 dB/octave Slope? The impedance of a capacitor is half with twice the frequency, i.e., XC = 1/sC = 1/2fC The impedance of an inductor is twice when frequency doubles, i.e., XL = sL = 2fL Twice or Half Impedance = 6 dB change Twice or Half Frequency = One Octave change Rane Corporation

  10. Why Phase Shift? • Phase shift is the flip side of time • It takes time to build up a charge on a capacitor -- that’s why you cannot change the voltage on a capacitor instantaneously. • It takes time to build up a magnetic field (flux) in an inductor -- that’s why you cannot change the current through an inductor instantaneously. • All this time = phase shift Rane Corporation

  11. Why 2nd-Order? • Maximum phase shift is 180 degrees • Guarantees circuit is unconditionally stable • No oscillation problems under any conditions • Get higher order circuits by cascading 2nd-order sections … or • Design 4th-order section to mathematically emulate two cascaded 2nd-order (Rane’s L-R) Rane Corporation

  12. Normalized Transfer Function Low-Pass (LP) =(2 poles) Amplitude 2 poles = -12 dB/oct Frequency Rane Corporation

  13. Normalized Transfer Function • Bandpass (BP) =(1 zero, 2 poles) 1 pole = -6 dB/oct 1 pole = -6 dB/oct Amplitude 1 zero = +6 dB/oct Frequency Rane Corporation

  14. Normalized Transfer Function High-Pass (HP) =(2 zeros, 2 poles) 2 poles = -12 dB/oct Amplitude 2 zeros = +12 dB/oct Frequency Rane Corporation

  15. Coefficients Determine Performance • Butterworth: maximally flat passbands2 + 1.414s + 1 • Chebyshev: steeper rolloff w/magnitude rippless2 + 1.43s + 1.51 • Bessel: best step response, but gentle rolloffs2 + 3s + 3 LP = = Rane Corporation

  16. Response Comparison Rane Corporation

  17. Q Effects Butterworth Q = 0.707 Bessel Q = 0.5 Rane Corporation

  18. Group Delay Comparison Rane Corporation

  19. Step Responses Butterworth Bessel Rane Corporation

  20. Active or Passive? • There exists no sound quality attributable to active or passive circuits per se. • TF determines the overshoot, ringing and phase shift regardless of implementation. • A transfer function is a transfer function is a transfer function … no matter how it is implemented -- all produce the same fundamental results as long as the circuit stays linear: same magnitude response, same phase response, same time response; however there are secondary differences. Rane Corporation

  21. Passive Less noise No power supply More reliable Less EMI susceptible Better at RF frequency No oscillations No on/off transients No hard clipping Handles large V & I Active Gain & adjustable No loading effects Parameters adjustable Smaller Cs No inductors Smaller, lighter & cheaper No magnetic coupling High Q circuits easy Active vs. Passive Rane Corporation

  22. Creating An Equalizer Input Signal In Out 1 BP BP Filter fc Rane Corporation

  23. Boost = Original + Bandpass Boost (Lift) 1 + BP Out In + BP 1 fc Rane Corporation

  24. Cut = Reciprocal Out In + Cut (Dip) BP 1 1 1+BP fc Rane Corporation

  25. Why 1/3-Octave Centers? • 1/3-Octave (21/3oct= x1.26) approximately represents the smallest region humans reliably detect change. • Relates to Critical Bands: a range of frequencies where interaction occurs; an auditory filter. • About 1/3-octave wide above 500Hz (latest info says more like ~1/6-oct); 100 Hz below 500 Hz Rane Corporation

  26. Creating A Crossover:Use LP & HP To Split Signal HP1 High Out Input HP2 LP2 Mid Out LP1 Low Out Rane Corporation

  27. 1st-Order & Butterworth Crossovers 1st-order plus 2nd through 4th-order Butterworth vector diagrams Rane Corporation

  28. Linkwitz-Riley Crossover • Two Cascaded Butterworth Filters • Outputs Down 6 dB at Crossover Frequency • Both Outputs Always in Phase • No Peaking or Lobing Error at Crossover Frequency Rane Corporation

  29. Creating A LR CrossoverCascaded Butterworth BW-HP BW-HP High Out Input BW-LP BW-LP Low Out Rane Corporation

  30. Linkwitz-Riley Crossovers LR-4 LR-2 LR-8 Rane Corporation

  31. Ray Miller (Rane)Bessel Crossover Rane Corporation

  32. Successfully Crossing-Over • Must know the exact amplitude and phase characteristics of the loudspeakers. • Driver response strongly interacts with active crossover response. • True response = loudspeaker + crossover • DSP multiprocessors à la Drag Net allow custom tailoring the total response. Rane Corporation

  33. Accelerated-Slope Tone Controls Rane Corporation

  34. Stop Kidding Yourself (Rick Chinn Request) Why low-cut and high-cut filters are a must for sound system bandwidth control; or, Why cutting the end sliders on your EQ doesn’t do diddly-squat. Rane Corporation

  35. Digital Very complex filters Full adjustability Precision vs. cost Arbitrary magnitude Total linear phase EMI & magnetic noise immunity Stability (temp & time) Repeatability Analog Speed 10-100x faster Dynamic Range Amplitude: 140 dB e.g., 12 Vrms & 1 V noise Frequency: 8 decades e.g., 0.01 Hz to 1 MHz Cheap, small, low power Precision limited by noise & component tolerances Analog vs. Digital Filters Rane Corporation

  36. Digital Filters and DSP Allow circuit designers to do new things. We can go back and solve old problems ... like the truth-in-slider-position bugaboo of graphic equalizers: • Proportional-Q was good • Constant-Q was better • Perfect-Q is best Rane Corporation

  37. Truth in Slider PositionProportional-Q Rane Corporation

  38. Truth in Slider PositionConstant-Q Rane Corporation

  39. Truth in Slider PositionPerfect-Q Rane Corporation

  40. PERFECT-Q™ & DEQ 60 Rick Jeffs Sr. Design Engineer Rane Corporation

  41. DEQ 60 Graphic 1/3-Oct EQ Rane Corporation

  42. DEQ 60 Features Rane Corporation

  43. DEQ 60 Performance Rane Corporation

More Related