On Correlation Between Residual DHT Filament Hum and AC Frequency. Distortion-induced hum in directly-heated triodes.

Copyright © May 2004. Author: Dmitry Nizhegorodov (dmitrynizh@hotmail.com). My other projects and articles

1.   Abstract

This document describes a series of follow-up experiments to the experiment demonstrating that the amplitude of residual filament hum in Directly Heated Triode (DHT) voltage-gain stages is independent of filament AC frequency, [1]. The follow-ups 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.   Introduction

It is a known phenomenon that DHT voltage amplification stages with AC-heated 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 Actions

In 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 non-thermal 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:

vary filament voltage
This promises to be very telling.

vary filament signal shape
some complex signals are more telling than sine waves. If the noise is thermal then a square wave filament supply would be very telling. If it is exactly harmonic, complex waveforms may help to prove that.

vary operation point parameters
e.g. biasing,load etc. How that relates to hum? degenerative feedback reduces distortion, does it reduce hum? In absolute or in relative terms? etc.

compare many tubes of the same brand
this seem to help to find correlation between tube's distortion and hum. Do otherwise identical tubes but with different distortion levels hum differently? how does that correlate with distortion numbers.

compare tubes of the same kind/structure but different brands
this may augment the above

compare tubes of the same structure but of different filament voltage
;;; here we mean 2a3 vs 6b4g type of comparison. To some extent, ;;; 2a3 vs 300b is also interesting, but 2a3 vs 6b4g is the most ;;; interesting!

wider-band measurements
more data is better. what happens at 5 or 10KHz? At 10 Hz?

FFT data
measuring distortion accurately with a scope is not possible. A spectrum is telling not only because it gives quantitative data, but because unrelated noise can be easily separated. Especially needed for gathering distortion vs hum data!

Each of the issues mentioned would require an experimental environment allowing to run batches of tests varying a particular parameter or "variable". measuring data and making sure the rest is the same. The configuration must be flexible to accommodate various tubes and or parameters. The old configuration, described in [1], with a sine generator, subwoofer amp, stepdown transformer and a scope is not sufficient. A new machinery was assembled, as described below.

4.   The Setup

To meet the new requirements, we assembled more machinery. A borrowed high-speed 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 low-ohm 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, tube-regulated PS (low high-frequency 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 single-ended 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 DC-decoupling 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

Sovtek 2A3, current production
2 tubes were available. These tubes were used in the Moondog amplifiers.

Sovtek 6B4G, current production
monoplate 6b4g tubes, indistinguishable geometrically from Sovtek 2A3 tubes. 4 tubes were available for experiments.

NOS Svetlana 6B4G.
Dates are 1972 to 1985. Total 6 tubes were available. These are dual plate tubes very different from Svetlana monoplates. Each half looks similar to a single 45 section. The filaments of the sections are connected ion series (!), the grids and plates - in parallel. Yes, something that is very interesting to compare against the monoplates.

NOS RCA 30 tubes
Total of 4 RCA tubes.

Assorted 26 tubes
RCA, Tung-Sol. Total 5 tubes were used.

6.   Frequency and filament voltage sweep study

This 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 real-time 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 findings

After 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).

2f-hum-fg-60-600-6k.jpg Filaments AC and residual hum on dual-trace scope, signal levels do not scale. We clearly see 2nd hum harmonic (1st cancelled with the hum-balancing pot) The frequencies were: 60 Hz, 600 Hz, 6000 Hz. The hum is always At the same amplitude and degree. Tube used: 2a3 Sovtek monoplate, filaments voltage - 6VAC, B+: 350V, Ik: 52ma.

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.

all-tubes-data-plots.gif Hum data gathered for 3 randomly chosen tubes: Sovtek monoplate 2a3 #2, Sovtek monoplate 6B4G #4, Svetlana dual plate #1.

8.   Non-sine wave filament signals

triangle-1khz.gif Triangle wave form into filaments. Sovtek monoplate #1. The shape of the residual signal and its phase clearly proves it is a 2nd harmonic signal.

9.   Some extract from my email postings describing the approach

  SPICE 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 auto-biased at 55V, bypassed, B+ is 350V:

      NO         (HZ)     COMPONENT    COMPONENT    (DEG)       PHASE (DEG)

       1     1.000E+03    5.496E-01    1.000E+00    1.794E+02    0.000E+00
       2     2.000E+03    1.107E-03    2.015E-03    8.578E+01   -2.730E+02
       3     3.000E+03    3.560E-05    6.478E-05   -1.789E+02   -7.170E+02
       4     4.000E+03    9.717E-06    1.768E-05    6.474E+00   -7.110E+02
       5     5.000E+03    7.548E-06    1.373E-05   -1.599E+02   -1.057E+03
       6     6.000E+03    7.367E-06    1.340E-05    3.537E+01   -1.041E+03

  (2) cathode, same biasing and same B+ :

      NO         (HZ)     COMPONENT    COMPONENT    (DEG)       PHASE (DEG)

       1     1.000E+03    6.822E-01    1.000E+00   -5.639E-01    0.000E+00
       2     2.000E+03    1.461E-03    2.142E-03    9.163E+01    9.276E+01
       3     3.000E+03    4.676E-05    6.854E-05    6.075E-01    2.299E+00
       4     4.000E+03    1.672E-05    2.451E-05   -1.758E+02   -1.736E+02
       5     5.000E+03    6.841E-06    1.003E-05    3.160E+01    3.442E+01
       6     6.000E+03    1.104E-05    1.619E-05   -1.548E+02   -1.514E+02


  Obviously, AC distributed across the length of the filament results in 
  effective potential swing of 1/2 of that, for each "half-tube", 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
  3-triode composite, the one in the middle receives no cathode AC, and
  yet better approximation is 5-segment 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 2-tube composite is good enough, though. Two
  lowish-gain small-signal IHTs can model a 26, and a pair of el84s in
  triode mode can do an OK job "modeling" a 300b.

  SPICE-ing 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 2-slice composite DHT models:

  .SUBCKT 2a3-composite  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  
  E12 42 0  
  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
  C2 2 1 {CGP} ; GRID=PLATE
  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 half-way 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
  cathode-bypassed 26s driving most cathode-bypassed 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
  not-so-linear 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 non-linear tubes. Hence
  composite models may be able to simulate non-linearity, and in some
  sense, a koren-style triode model (which is pretty good for expressing
  non-linearity 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 
  distortion-induced 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 reduced-filament voltage conditions.

  I also studied non-sine 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 20-30dB 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 super-linearity 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  S-like,  and the "upper" side of 
  the S is extended all the way across the bias spot, and the  bias spot is 

  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 
  super-linearity spot"  and into the normal "in-phase" 2nd harmonic region.

  I thought you'll find these experiments interesting.

10.   Conclusions

This 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