From: hill@rowland.org (Winfield Hill) Subject: High-accuracy pink noise and 1/f noise. Date: 9 Nov 1997 23:23:41 GMT Organization: The Rowland Institute for Science Yesterday (8 Nov 1997) I posted an article in sci.electronics, "Re: Good Pink Noise Generator," reporting on the deficiencies of some widely-used pink-noise generators, and suggested some improvements. For example, I examined a circuit with which several users had expressed satisfaction, and with a SPICE simulation, found it to have errors of several dB. Furthermore I found the respected circuit we detailed in AoE (fig 7.61 page 452) to have 0.65dB ripples and only +/-0.4dB accuracy up to 16kHz, rather than 0.25dB from 10Hz to 40kHz, as stated. Here I present an improved pink-noise filter design, which indeed exceeds the above specs. 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 sounds 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. -- Winfield Hill hill@rowland.org _/_/_/ _/_/_/_/ The Rowland Institute for Science _/ _/ _/_/ _/ Cambridge, MA USA 02142-1297 _/_/_/_/ _/ _/ _/_/_/ _/ _/ _/ _/ _/ http://www.artofelectronics.com/ _/ _/ _/_/ _/_/_/_/