Pink and blue/azure noise filters. - Page 1
Forum section: electronics / beginners

author: Greg Robinson
author_rank: Regular Contributor
timestamp: June 11, 2016, 07:01:06 am
content: Hi everyone,I've been working with some pink noise filters, and have found some references with design examples, such as this one byElliot Sound, but I have not found any information about the actual design process, such as selecting the break points of the lumped filter elements.I'd like to understand how to go about designing one of these filters rather than just simply copying an existing design, is anyone able to direct me towards such information?I'm also hoping to play with someBlue noisefilters, which you could describe as being the opposite of pink noise, with +3dB per octave/+10dB per decade. I haven't been able to find any reference designs, and have been having a bit of a brain-fart as to how to design one in the analog domain, seems my experiments in simulation with swapping low-pass RC filters for high-pass in a pink noise filter hasn't been working.If anyone could point me towards a reference or show a basic topology that would be greatly appreciated.Thanks for any assistance!

author: T3sl4co1l
author_rank: Super Contributor
timestamp: June 11, 2016, 01:48:20 pm
content: A 3dB/oct slope is characteristic of diffusion processes: many 1/f noise sources (imagine that!), ionic diffusion (battery impedance, electrochemistry), convection (self-similarity of turbulent noise, heat transfer) and other thermal diffusion, and even electromagnetic diffusion (skin effect, eddy current and core loss effects).Making a 1/sqrt(-f) or 1/sqrt(t) (the Fourier dual function) block isn't very easy, so it is approximated over a modest range by a rational function (poles and zeroes), i.e., an RLC filter. This is a polynomial approximation to 1/sqrt(f), so it can be expected to hover above and below the ideal value, and only be useful over a finite bandwidth. "The usual analog method is to use a parallel set of series RC sections, with the characteristic frequency of each successive section increasing by a fixed ratio (here x10, i.e., one decade) with an impedance that decreases by the square root of that same ratio (here sqrt(10))." AoE3 p.559-560Tim

author: Greg Robinson
author_rank: Regular Contributor
timestamp: June 11, 2016, 01:51:58 pm
content: Thanks for the Art of Electronics reference Tim!Need to go do some reading.

author: bson
author_rank: Unknown
timestamp: June 11, 2016, 11:05:50 pm
content: Quote from: Greg Robinson on June 11, 2016, 07:01:06 amIt's a basic inverting amplifier with a sort of RC ladder in the feedback loop. For an inverting amplifier, Vout=-Zf/Zs*Vin where Zf is the feedback impedance and Zs is the source impedance (10k in this circuit). The RC ladder is a low-pass filter, but the inverting amplifier turns it into a high-pass.The RC ladder is just a bunch of parallel impedances, each \$Z=R-j\frac{1}{\omega C}\$. For the last one, C=0.Clearly, the feedback network impedance becomes: \$\frac{1}{Z_f} = \sum_{i=1}^n \frac{1}{R_i-j\frac{1}{\omega C_i}}\$\$-\frac{Z_f}{Z_s}\$ becomes \$-Z_s \sum_{i=1}^n \frac{1}{R_i-j\frac{1}{\omega C_i}}\$ where n is the number or ladder steps, and the problem can be reduced to finding a solution to the series sum of reciprocals that produces an approximately linear response for a unity Zs=1. (The response is a low-pass. The -Zs factor then scales and inverts it into a high-pass.) All solutions are approximations. I don't have tables on hand, but I'm sure such exist. Personally, I'd find a pi or T filter that does the job... Not sure what the compelling reason for the elaborate RC ladder is, but if there's a good reason to use it I'd explore it numerically for different orders and value progressions just to get a sense of the tradeoffs and non-linearities.Anyway, that should help you get started with your own designs. This is a little more complex than plugging numbers into a formula, which is perhaps why it's not used more frequently. Another reason would be the cost of the elaborate ladder itself.I like the use of an inverting active high-pass filter. Its drawback is, well, that it's inverting, but for random noise it doesn't matter. If N is random, then so is -N and there is no entropy change. The big benefit here is that the bandwidth of the feedback loop can be limited to its operation as a low-pass, while the bandwidth of the op-amp high-pass filter is that of the op-amp at or near unity. If instead you used a basic pi/T passive high-pass filter in front of a gain stage to make up for the insertion loss of the passive filter you'd need gain which adds in op-amp noise (which may not be particularly random and highly modulated with the signal). And then you'd have the question of the bandwidth of the passive high-pass due to a real-world limited Q (i.e. parasitics). The inverting high-pass used elegantly avoids this and it becomes a matter of high-frequency creep (capacitive leakage) in the feedback and op-amp unity bandwidth.Anyway, I hope this is helpful...Hope I got the math right. Kinda hard to proofread LaTeX without preview.

author: bson
author_rank: Unknown
timestamp: June 12, 2016, 09:24:11 am
content: I've been on the hunt for a good white noise source, so quickly breadboarded a 2N3904 (TO-92) with 100k, and AC coupled (100uF electrolytic Vishay something-or-other axial 63V) to a 100k impedance active probe. Breakdown starts at around 8.25V supply voltage at which point noise builds up and levels off at 8.5V. Between 8.5V and 9V there's not much additional noise amplitude.Scoped out with a 512k point FFT and persistence mode (really slow, took maybe 30min):(The signal itself on Ch. 1 is omitted.)And just for kicks, the full 500MHz scope bandwidth (2.5GHz active probe)! Keep in mind this is on a breadboard with big leaded components, hence the rolloff. The spikes are almost certainly transmissions picked up by the breadboard and component leads.Looks like a potentially good wideband noise maker... I think I'm going to try it in SMD!