On Correlation Between Residual DHT Filament Hum and AC Frequency. Distortioninduced hum in directlyheated triodes.Copyright © May 2004. Author: Dmitry Nizhegorodov (dmitrynizh@hotmail.com). My other projects and articles
1. AbstractThis document describes a series of followup experiments to the experiment demonstrating that the amplitude of residual filament hum in Directly Heated Triode (DHT) voltagegain stages is independent of filament AC frequency, [1]. The followups are done with much better precision and exercise a range of tests with a large collection of DHT tubes. All data shows that under normal conditions (class A or AB, normal plate current, filament current providing sufficient emission) triodes generate hum that represents distortion of filament AC signal.
2. IntroductionIt is a known phenomenon that DHT voltage amplification stages with ACheated filaments develop a hum but little is known about why exactly it happens. My last year experiment suggested that the cause is likely not the lack of infinite mass of filaments, as was rumored. For an example, see [2]. I described my findings to Steve Bench and he encouraged me to continue.I wanted to explore the issue through a set of different experiments, involving different tubes and filament regimes. My main goals are to determine whether the filament hum is solely due to distortion introduced by the tube or that a degree of thermal hum is present at low frequencies. I also wanted to try out various hum cancellation techniques that can be devised once it is clear that the hum nature is distortion.
3. Main Ideas and Plan of ActionsIn the previous experiment, the main idea was to identify the single most telling parameter that separates thermal noise from harmonic one. The parameter is AC frequency and the experiment was setup to measure hum with several filament frequencies. Here, we'd like to find out whether the nonthermal hum is indeed predominantly harmonic and how well composite tube models can be used to calculate the hum. The following measurements, conditions and parameters seem promising to experiment with:
4. The SetupTo meet the new requirements, we assembled more machinery. A borrowed highspeed computer with DSP software provided both signal source and FTT analysis facilities. An isolation transformer was used to position a signal generator and the sources independently (no ground connection). A Tektronix 475 scope was sitting at that ground, too. A 60W EICO HF60 tube amplifier capable of driving lowohm loads was sitting at that ground. The amplifier was tuned for lowest hum. Originally, the idea was to feed the amp on the common ground, and its secondary windings were made floating. The feedback was disconnected, but that bad distortion figures. After the isolation transformer was added, the the amp was returned to to stock configuration.Another EICO HF60 was used as a workbench. The advantage is that it provides fixed biasing circuitry, tuberegulated PS (low highfrequency noise) and very high B+. Its 8 pin sockets can be used for 6B4Gs. A 4 pin socket was mounted. The driver stages of HF60, tuned for lowest distortion, delivered the signals to the DHT grid. A singleended 3K OPT was originally tried as a load, but then it was found that Acrosound 300, the OPT of Eico HF60, runs into no noticeable saturation under the conditions of the experiments, and it was used as the load. A Tektronix 464 was used to measure the signals on the grid and cathode pins or on the plate (through a DCdecoupling 1mF orange drop polyprop capacitor). The output signal from 5 Ohm load resistor was fed into PC's sound card through a resistive divider (a 10K potentiometer). The signal from the PC was connect do the input of either HF60. When it was connected to the filament HF60, the PC was disconnected from the main ground. Each Eico was connected to wall AC via autotransformer. Here is a simplified map of the setup:
5. DHT Tubes used in the experiments
6. Frequency and filament voltage sweep studyThis experiment was the most involved. The main parameter in the study was the level of the 2nd harmonic of the filament AC signal, as computed via realtime FFT. The sensitivity on the sound card was selected to reach the 0 level at 1 VRMS, or 1.4 V amplitude. The level of 0 dB on the plots correspond to that.The filament frequency varied from 20 Hz to 10kHz. The amplitude varied from 10% above tube's nominal filament voltage down to the level where no output signal was detected. Additionally, biasing and B+ varied for selected tubes.
7. Main findingsAfter all tubes were tested, it became clear that under normal biasing conditions, filament hum of all tubes is independent of the filament frequency. Each tube produced slightly different hum, dependent on its individual parameters. Also, the level of hum was dependent on biasing, B+, filament voltage. Only the second harmonic was reliably detected and that is shown on the plots below. Starved filaments produce less hum but that is proportional to reduction of amplification, especially when AC voltage drops under 70% of nominal. Under all such conditions, the phase of the 2nd harmonic is aligned with the filaments AC (that is, peak to positive peak, peak to negative peak).
When filament voltage is around 50% of nominal, emission drops so low that tube is not amplifying (plate signal is a small portion of grid/cathode signal, and at that level the phase and the amplitude of the hum fluctuate greatly. More on that in the next sections.
8. Nonsine wave filament signals
9. Some extract from my email postings describing the approachSPICE modeling (Koren triode model, with tube parameters I selected myself for the curves I trust) supports my distortion number range. I've just ran 2 simulations for 1KHz 3.5Vampl into (1) the grid of a 2A3, cathode is autobiased at 55V, bypassed, B+ is 350V: HARMONIC FREQUENCY FOURIER NORMALIZED PHASE NORMALIZED NO (HZ) COMPONENT COMPONENT (DEG) PHASE (DEG) 1 1.000E+03 5.496E01 1.000E+00 1.794E+02 0.000E+00 2 2.000E+03 1.107E03 2.015E03 8.578E+01 2.730E+02 3 3.000E+03 3.560E05 6.478E05 1.789E+02 7.170E+02 4 4.000E+03 9.717E06 1.768E05 6.474E+00 7.110E+02 5 5.000E+03 7.548E06 1.373E05 1.599E+02 1.057E+03 6 6.000E+03 7.367E06 1.340E05 3.537E+01 1.041E+03 (2) cathode, same biasing and same B+ : HARMONIC FREQUENCY FOURIER NORMALIZED PHASE NORMALIZED NO (HZ) COMPONENT COMPONENT (DEG) PHASE (DEG) 1 1.000E+03 6.822E01 1.000E+00 5.639E01 0.000E+00 2 2.000E+03 1.461E03 2.142E03 9.163E+01 9.276E+01 3 3.000E+03 4.676E05 6.854E05 6.075E01 2.299E+00 4 4.000E+03 1.672E05 2.451E05 1.758E+02 1.736E+02 5 5.000E+03 6.841E06 1.003E05 3.160E+01 3.442E+01 6 6.000E+03 1.104E05 1.619E05 1.548E+02 1.514E+02 respectively. Obviously, AC distributed across the length of the filament results in effective potential swing of 1/2 of that, for each "halftube", so to speak, and we again arrive at ~0.1% distortion for 10mV hum, ~0.3% for 30mV hum and so on. The "composite tube" approach is fun, and it does model a DHT pretty well. From a purely theoretical standpoint, a better approximation is 3triode composite, the one in the middle receives no cathode AC, and yet better approximation is 5segment composite, with 2nd and 4th receiving 1/2 of AC, 1st and 5th receiving full AC, and 3rd  none. Obviously, 1st and 2nd are out of phase with the 4th and 5th. When the number of slices is taken to the limit, we get real DHT. Of course, each "slice" must become wimpier and wimpier otherwise we produce a tube with unrealistically low Rp and high Ip. From a practical standpoint, a 2tube composite is good enough, though. Two lowishgain smallsignal IHTs can model a 26, and a pair of el84s in triode mode can do an OK job "modeling" a 300b. SPICEing such triode composites is fairly simple, as for instance, the parameter KP for the Koren models must be divided by the number of "slices" in the composite, which results in curves identical to the "base" tube, no other transfer function changes needed (I tried that, I've developed java applets to match the tubes). Here is one of my 2slice composite DHT models: .SUBCKT 2a3composite 1 2 3 4 ; P G K1 K2 + PARAMS: RGI=2000 ** audiomatica + MU=4.58 EX=1.512 KG1=1710.0 KP=40.8 KVB=1188.0 VCT=2.24 ; Vp_MAX=600.0 Ip_MAX=0.2 Vg_step=12.0 ** ??old + MU=4.2 EX=1.4 KG1=1500 KP=60 KVB=300 RGI=2000 + CCG=7.5P CGP=16P CCP=5.5P * cathode resistor is 1 ohm, the pins K1 and K2 are .25 ohms from the ends of it RFIL_LEFT 3 31 .25 RFIL_RIGHT 4 41 .25 RFIL_MIDDLE 31 41 .5 E11 32 0 VALUE={V(1,31)/KP*LOG(1+EXP(KP*(1/MU+V(2,31)/SQRT(KVB+V(1,31)*V(1,31)))))} E12 42 0 VALUE={V(1,41)/KP*LOG(1+EXP(KP*(1/MU+V(2,41)/SQRT(KVB+V(1,41)*V(1,41)))))} RE11 32 0 1G RE12 42 0 1G G11 1 31 VALUE={(PWR(V(32),EX)+PWRS(V(32),EX))/(2*KG1)} G12 1 41 VALUE={(PWR(V(42),EX)+PWRS(V(42),EX))/(2*KG1)} RCP1 1 3 1G RCP2 1 4 1G C1 2 3 {CCG} ; CATHODEGRID C2 2 1 {CGP} ; GRID=PLATE C3 1 3 {CCP} ; CATHODEPLATE D3 5 3 DX ; FOR GRID CURRENT D4 6 4 DX ; FOR GRID CURRENT RG1 2 5 {RGI} ; FOR GRID CURRENT RG2 2 6 {RGI} ; FOR GRID CURRENT .MODEL DX D(IS=1N RS=1 CJO=10PF TT=1N) .ENDS *$ To approximate the distribution of the AC potential across the filament, I used the avg(ACampl,0) which is ACampl/2 and which means the cathode pins are halfway into the cathode "resistor". The most pleasurable outcome from my experiments and models is an ability to guestimate which tubes might cancel each other. thus, most cathodebypassed 26s driving most cathodebypassed 300b will provide a better cancellation than driving 2A3s or 6B4Gs of _equal_ distortion (an order of magnitude range of distortion numbers in a a large batch is something I totally agree with) Yet another interesting direction in studying composite models may be in trying to tie them with triode [non]linearity as well as explaining why many linear tubes running in parallel often result in a notsolinear combined outcome... The answer may be in deviations of Mu and Gm across the batch, and it can be shown analytically. One of my java applets, for a composite tube sandwich, shows how misaligned parameters/geometry of a real tube (direct or indirect heated) may result in the kind of rounding up in the low right corner on the plate curves that we all hate and associate with nonlinear tubes. Hence composite models may be able to simulate nonlinearity, and in some sense, a korenstyle triode model (which is pretty good for expressing nonlinearity via its purely *phenomenological* parameter KP) can be shown to emerge as a composite of simple Vgk ^ 1.5 models (by the way, these simple models, very idealistic, may be responsible for the bad rap of tube SPICEing). I'll be happy if I eventually will be able to flesh out the math showing that. It appears that the thermal hum is measurable, but in real conditions, it kicks in any significant way only for small DHT tubes with very wimpy filaments: 30, 26. Power tubes such as 2A3 or 6B4G show predominantly distortioninduced hum all the way down to 20hz of filament AC. The way I was able to spot thermal hum in my batch of 26 and 30 tubes was based on simultaneous scoping of the filament signal and the hum, and when the phase starts lagging, we can proclaim that the thermal hum becomes measurable. Simultaneously, the amplitude increases somewhat too, and more after frequency drops. I ran many tests, under normal and reducedfilament voltage conditions. I also studied nonsine signals on filaments  very interesting stuff!! I'm also happy to tell you that I experienced your "starving filaments lessen distortion" phenomenon, but in a very interesting way. When applying slowly reducing filament AC voltage, I found that at some point, at around 60% of rated voltage, the phase of the 2nd harmonic hum suddenly flips 180 degrees! This happens rapidly: say, at 60% it is still the normal phase and at 55% is already reversed! When it goes through the transition, the hum drops 2030dB below its "typical" level and then backs up again. WHAT IS GOING ON  I was puzzled for few days. But then I realized: the lull in hum means that the loadlines have very equal spacing, and the inverse phase means that the loadlines are more dense toward the zero bias direction and less dense towards higher bias direction. When I looked at your starving filament loadlines where you explain the superlinearity phenomenon, I realized I ran into the same condition! The hum drops almost to zero when the loadlines around the particular biasing spot are very evenly spaced, just like you present on your plots; when the filament voltage drops just a bit more, the loadlines around the biasing spot will have very slightly "reversed" density gradient. This shows up as 2nd harmonic flipped 180 degrees! In other terms, the dynamic curve becomes Slike, and the "upper" side of the S is extended all the way across the bias spot, and the bias spot is downwardbent. If this is true, then we can play with biasing as well as filament voltage to get in and out of the sweet spot. Indeed, I was able to show that increasing the bias (after the phase flipped), causes the operating point to glide from the "inverse 2nd harmonic region" through the "Steve Bench superlinearity spot" and into the normal "inphase" 2nd harmonic region. I thought you'll find these experiments interesting. 10. ConclusionsThis experiment proves that residual 2x ACF (twice frequency of filament AC) hum in DHT structures is mostly independent of AC frequency, at least in 20..600Hz range, and suggests my theoretical findings about harmonic nature of DHT hum are correct. This provides a justification for SPICE models developed in [] for analytical computation of residual hum, see [], and for ideas of DHT SET amp design presented in []. In practical terms, hum is proportional to mu, to filament voltage and to harmonic distortion. This explains why a 6a3 (6b4g, 6c4c) tubes are roughly twice more humming comparing to 2a3. The emission theory would not be able explain that, as filaments have the same or comparable mass.
Author: Dmitry Nizhegorodov (dmitrynizh@hotmail.com). My other projects and articles
