From: hill@rowland.org (Winfield Hill)
Subject: Re: pink noise generator!!!
Date: 16 May 1998 21:50:20 GMT
Organization: Rowland Institute for Science

 Matthias, 04940116@fbe.hs-bremen.de says...
> Has anyone a schematic for a pink noise source?

 There's a simple schematic in the Art of Electronics, see fig 7.61,
 page 452.  This is a -3dB/octave pink noise filter circuit which uses
 5 resistors and 4 capacitors.  This circuit is pink to within 0.4dB
 from 9Hz to 16kHz (sorry, the book over-states its accuracy).

 To improve this circuit's accuracy to 0.3dB and extend it to over
 100kHz, change the 2.49k to 3.32k, the 2.9nF to 3.0nF and add 1.5nF
 across the 3.3Meg resistor.  Now a -45 degree phase shift is
 maintained for nearly 4 decades.

 I designed a higher-performance pink-noise filter than the one
 described above, and presented it here 9 Nov 1997 23:23:41 GMT.

  "Pink-noise should have a -3.01 dB/octave and -10.0 dB/decade
  intensity vs frequency slope, and a 1/f power spectral density
  characteristic.  This article describes a nearly perfect pink-noise
  filter, intended for use with common flat-response white-noise
  generators.

  "My design uses two sets of R’s and C’s for each frequency decade,
  twice the usual amount.  In all, 10 pairs of R’s and C’s are used
  (all scaled by the 4th-root of 10), with an additional R to set the
  maximum gain at 0.25Hz and an additional C to maintain a decreasing
  gain above 300kHz.  While it may seem that five-decades-worth of
  filters is excessive, this is necessary to maintain a constant -45.0
  degree phase shift from 4Hz to 65kHz (within 1 degree), insuring an
  accurate pink-noise response over the entire audio range. 

  "The audio version of my filter is AC coupled and has 0dB gain at
  325Hz.  The filter has 0.1dB (1.2%) accuracy from 18Hz to 18kHz
  (or +0.25/-0.1 dB from 10Hz to 50kHz).   

                             ,----- C11 -----,
                             +- R10 -- C10 --+  etc etc
                             +   -      -    +
                             +-- etc - etc --+
  good G = -1                +   -      -    +
  inverting                  +-- R2 --- C2 --+
   opamp --- 18.2k - 100uF --+-- R1 --- C1 --+
                             +----- Ro ------+
                    Ro=470k  '-- -           |
                                     out ----+------ OUT
                          gnd -- + 
                                    5MHz FET opamp
    R1  C1  100nF  499k
    R2  C2   56nF  274k
    R3  C3   33nF  158k
    R4  C4   18nF   88.7k
    R5  C5   10nF   49.9k
    R6  C6   5.6nF  27.4k
    R7  C7   3.3nF  15.8k
    R8  C8   1.8nF   8.87k
    R9  C9   1.0nF   4.99k
   R10 C10   560pF   2.74k
       C11   680pF

  "A DC-coupled audio version (no 100uF capacitor and Ro = 422k) has
  0.1dB accuracy from 15Hz to 25kHz.

  "The filter's capacitors are from 560pF to 0.1uF, and a 100uF *
  18.2k = 1.8s AC coupling time-constant is used to retain most of the
  low-end accuracy.  Ceramic and electrolytic capacitors may be suited
  for some audio applications, where their ac impedance is so low no
  voltage change occurs across the capacitor (e.g. the 100uF coupling
  capacitor).  However, in a filter network like this, mylar or other
  film capacitors are required, selected for accuracy.

  "With its rushing waterfall sound, wideband audio pink noise, also
  called 1/f noise, is pleasing to the ear.  With minor shaping, it
  can sound similar to wind, rain, streams and with further processing,
  even artificial surf.  However, these applications do not need an
  accurate noise source.  

  "By contrast, accurate pink noise is very useful for many types of
  laboratory measurements.  One very useful feature of pink noise is
  its frequency-independant level, when passed though any fixed-Q
  filter.  A common third-octave filter is one example, and is popular
  for in-room loudspeaker testing.  An inexpensive fixed-Q tunable
  switched-capacitor filter, such as an LTC, could be swept in search
  for room resonances.

  "If the capacitors in the DC version of the filter are increased by
  a factor of 100 (i.e. ranging from 56nF to 10uF), we get a filter
  useful for a 0.005Hz to 2kHz 1/f noise generator, with 0dB gain at
  33Hz.  Low-frequency 1/f noise is useful for simulating electronic
  flicker-noise and VCO oscillator phase noise, as well as vibration
  testing."

 After posting this design, a reader, Rodger Rosenbaum, wrote to me
 describing even better constants, obtained using Chebychev filter
 design concepts.  Perhaps someday I'll describe those results, if
 he doesn't first.  But the above design is far better than most.

 All pink-noise filters need a white noise source to generate pink
 noise.  Amplified transistor reverse emitter-base breakdown can be
 used for a source (see below), as can higher-voltage zener diodes.  

                   +V          
                    |          
                   5.6k        
                    |          
   ,------+-- 47k --+-- 1uF --+-- out
   |      |         |         |
  0.1uF   E         C        100k
   |        B --- B           |
  GND     C         E        gnd
            Q1      |  Q2
                   GND   

 V+ should be at least 15V, and any npn small-signal transistors can
 be used.  Q1 is the noise generator and its collector is usually
 left open.  One should be aware that identical type components may
 not have even similar noise properties (!), and that the noise
 intensity may vary with time as well.  The mechanism of noise
 generation is microplasma avalanches occuring on a sub-nanosecond
 time scale, creating random current pulses into Q2's base.

-- 
Winfield Hill    hill@rowland.org       _/_/_/            _/_/_/_/
The Rowland Institute for Science     _/    _/   _/_/    _/
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