Subject: Noise Experiments Date: 21 Aug 1994 23:56:03 -0500 From: ritter@io.com (Terry Ritter) Message-ID: <199408220456.XAA28923@pentagon.io.com> Newsgroups: sci.crypt Lines: 226 NOISE EXPERIMENTS I recently spent the better part of several nights and days trying to see just how easy it really is to generate noise from a reverse- biased transistor B-E junction. I breadboarded several different circuits, and measured the amount of noise produced. The method does seem practical, but uses a number of parts and may require some testing and/or adjustment, because the noise depends upon non-guaranteed transistor characteristics. Day One My first successful circuit was: _ V+ _ | | | R3 R1 | | +---> V2 V1 | c |--------+--R2--+-----b Q2 e | | e +--b Q1 +--C1--+ | | c v | | v v Both transistors are NPN silicon. Q1 pretends to be a zener, and drops current across R1, presumably creating noise in the process. R2 biases Q2, but is so large that C1 is needed as a bypass. R3 is probably not critical. A production design would probably bias Q2 with negative feedback and just couple the noise in with C1. Here are the results for two configurations: V+ Q1 R1 V1 R2 C1 Q2 R3 V2 AC 1/ 11.3v 2N5088 100K 6.65v 1M .22 2N2222 12K 5.0v 56mv 2/ 10.0v 2N2222 100K 7.04v 1M .22 2N2222 12K 3.2v 168mv AC is the RMS noise output. Note that RMS is the power in the noise signal, and not the peak-to-peak voltage, which may be more related to what we need for subsequent processing. 56mv RMS seems to show an "average" amplitude of about 300mv p-p on the scope. Technically, the absolute amplitude exceeds the rms value about 1/3 of the time, with 5 rms exceeded about 1 time in a million, but the scope probably has a much larger bandwidth than the meter. If we work out the currents in 1/, Q2 must be running with a beta around 88, and if we assume that the small-signal gain is the same, we have about 640uv of RMS noise on Q1. Similarly, /2 shows Q2 with a beta around 89, and 1.88mv of RMS noise on Q1. Is AC really noise? Removing C1, or connecting it across Q1 had no affect on the DC levels, but reduced the AC value to the background level of 4mv. (The RMS meter showed 4mv on the supply.) Thus, the circuit was apparently neither oscillating nor collecting a significant amount of RF. In /2, R1 was changed to 10K and 470K; in both cases the noise was drastically reduced. Apparently there is some optimum current for maximum noise. Also in /2, Q1 was replaced with several different zener diodes. In all cases, the AC noise output dropped to background. Changing R1 to 10K did not seem to help. It is tempting to think that a transistor in "zener connection" is exceptionally noisy, but maybe real zeners just need more power. Day Two A noise source with a self-biasing amp: _ V+ _ | | | R2 R1 | | +--R4--+--R3--+---> V2 | | | | | | C2 | | | | | | | v | V1 | | c |----C1---+-------------b Q2 e e +--b Q1 | | c v | | v v Both transistors 2N2222 V+ R1 V1 C1 R2 R3 C2 R4 V2 AC 10.0v 100K 7.04v .22uf 12K 100K 10uf 100K 2.1v 168mv This gives a very reasonable output, at the expense of no automatic biasing for Q1. On the other hand, the biasing may be fairly stable, so this could be a good configuration. We can also auto-bias the noise source. This circuit is very similar to one in an article called "Truly Random Numbers" by H.R. Bungay and Robert Martin in an early issue of Kilobaud: _ V+ | R1 V1 | +------+------R3-----+ V2 | | | C1 | R2 | | | v | +---> V3 | | e c Q1 b-------------b Q2 c e (nc) | v Both transistors are 2N2222. V+ R1 R2 R3 C1 V1 V2 V3 AC 10.0v 12K 15K 68K 10uf 7.53v 7.7v 4.75v 80mv Note that this circuit trades off output amplitude for automatic biasing. The fixed zenering level fixes V1; feedback fixes V2 based on V1; R2 serves to move the output voltage nearer to center. This particular E-B junction appears to break down about 7v, but this is not a guaranteed quantity. The 2N2222 has a guaranteed minimum Vbe of 5v (a common value); I searched around and found a 2N1990 with a minimum guaranteed Vbe of 3v, but this particular transistor happened to have an even *higher* breakdown. It would be nice to find a "transistor" with a guaranteed low breakdown (say 2.5v) and then try to work from a logic level supply, but with the present components, a low ripple 9v or higher voltage supply seems necessary. If 80mv (RMS!) is not enough, we can try a simple amplifier: _ V+ | R4 | +--R5--+--> V4 | | | c ---C2-----R6---+------b Q3 |+ e D1 | | v v Q3 is 2N2222; D1 is a switching diode. V+ R4 R5 C2 R6 V4 AC 10.0v 4.7K 220K .22uf 0K 4.17v 1.07v Now we get peaks virtually to the 0 and 10v extremes. The scope seems to show a bandwidth change, however, so we might need to reduce C2 and increase C6, remove D1, or perhaps even use a high-frequency transistor. R5 tends to steady the output voltage to a reasonable mid value. Alternatives One alternative would be to use an op-amp to perform the final amplification; possibly it could perform limiting and digital conversion as well. Of course, if we are going to support one op-amp, we might as well support others, and then can eliminate all but the noise-source transistor. Of course the op-amp circuits will have their own costs. The number of components and the variability of the noise source in the reverse-biased junction approach may make the FM IF strip idea a very interesting alternative. Conclusion Several simple circuits can generate really-random noise from a reverse-biased transistor B-E junction, and then amplify this noise to near usable levels. Subsequent limiting and then pulse-width measurement (for example) would be one way to use this noise to generate really random values. --- Terry Ritter ritter@io.com
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Last updated: 1999-01-16