On Correlation Between Residual DHT Filament Hum and AC Frequency

Copyright © Nov 2003. Author: Dmitry Nizhegorodov (dmitrynizh@hotmail.com). My other projects and articles

1.   Abstract

An experiment demonstrating that the amplitude of residual filament hum in Directly Heated Triode (DHT) voltage-gain stages is roughly independent of filament AC frequency, is described. The residual hum typically has frequency twice of AC frequency and is proportional to tube non-linearity and filament voltage. The experiment suggests that all AC-heated DHTs develop such residual hum of twice of AC frequency since all triodes have significant 2nd harmonic distortion in the voltage range involved. These question validity of explanations referring to bad cathode design and insufficient filament mass. The findings justify the triode models developed in [][], permit simple analytical estimates of the residual hum provided in [], and support hum-neutralizing topologies developed in []. The experiment can be readily reproduced by anyone with sufficient skills and require either a DHT tube stage on a a bench or a SET amplifier with DHT power stage and a low-noise B+, an audio-range oscilloscope, a 10W+, low-distortion audio amplifier, a Sine-wave generator. The setup of the experiment is described in details.

2.   Introduction

It is a known phenomenon that DHT voltage amplification stages with AC-heated filaments develop a characteristic hum which can not be neutralized with hum-balancing potentiometers. Here we assume that the power supply contributes absolutely no hum component and that the input is producing none as well. We also assume we deal with a single, single-ended, DHT voltage gain stage such as a cathode gain stage loaded with an output tranformer, either with fixed bias or with a bypassed autobias resistor.

The amplitude of the residual hum varies greatly, depending on tube construction, B+, tube parameters, load, etc. The issues is very critical in SET comunity where low-poer amplifiers drive extremely high efficiency speakers. There are myphs surrouning thissue and various sources report various levels of residual hum but it can not be zero. Some sources claim that applying some measures removes teh hum.

In our findings (in the context of studying hum in Welborne Moondog 2A3 SET amplifiers, and when B+ is hum free and DHT's input carries no hum) the level is quite high and can be measured and studied. A typical example is B+=350V, tube=2A3, filaments at 2.5VAC, 60HZ. The residual hum is ~30mVAC 120HZ at the plate. With a 3K:16 transformer as the load, this results in ~2 RMS of output hum. When two amps drive a pair of ultra-efficient speakers (> 105 dB/W/M), the hum is audible in listener's spot.

What is the source of the hum? It can be proven by instantaneous disconnect of the filament AC or by use of DC, that the source of the hum is filament AC and not something else. There were evidences and/or beliefs that this AC signal is due to low mass of filament structure and is due to filament heating up and cooling down at the rate of filament AC. Change of filament temperature with twice of filament AC frequency (ACF) causes change in emission. There were no other explanations available to us up to the point of writing (Nov 2003). The emission theory assumes there is a noticeable phase shift in the residual AC component (a delay).

3.   Background of the experiments

In my measurements done for the 2A3 output stage of Moondog SET amplifiers, I found that the residual hum component has no or almost no phase shift regards to the AC line signal. At first, I was uncertain about this due to equipment situation (dual mode sync in my scope was not working), and I firmly believed, follwing Steve Bench web material, that phase schifts are apparent. Indeed, there were schifts w.r.t to B+ due to phase-delay introduced by choke. but not w.r.t filament CA. After obtaining a better scope and also running a Lissajou proved it is true. This prompted my thinking about the nature of the hum. Another important consideration was that at some point I developed a simple "theoretical" explanation for the AC hum phenomenon in single-ended DHT circuits. This is related to my ideas of studying DHT triodes with a technique I call composite tube models. According to my findings based on composite models, non-linearity of triodes must result in hum that is proportional to distortion and to filament voltage amplitude. Since DHT tubes generate mostly 2nd harmonic component, the hum is of frequency twice of the frequency of the filament AC. The amplitude of the signal can be calculated analytically based on tube data and my models. SPICE simulation suggests that a 2A3 triode develops on its plate around 10..30 mVRMSAC of 2nd harmonic of filament AC, which is in the range of the signal I scoped in Moondog.

4.   The Idea of the Experiment

Is filament hum in a typical DHT stage mostly thermal or mostly caused by 2nd harmonic? In section [] I provide some analytically derived explanation of relative impact of both processes. However, how this can be resolved experimentally?

The idea is as follows: the 2nd harmonic component is largely frequency-independent, at least in audio frequency range and under normal operational conditions. Unlike that, the thermal/emission effect, due to gradual cooling of the filament between AC cycles must be highly dependent on frequency. Therefore, an experiment consisting in feeding the tube filament with AC of varying frequency would be telling about the impact of the effects. Even considerbly small change from 60HZ AC may show which effect contributes more, but it would be more preferably to measure the hum for a range of frequencies.

5.   Contemplating Requirements and Set-Up.

To be able to set the stage for this experiment, we firstly need to have a DHT tube running in class A operation with clean B+ and secondly provide frequency-varying AC supply to the filament.

It is fair to assume that a moded SET amplifier such as Moondog can provide a resonable setup. Otherwise, a breadboard with a DHT stage and some bench supply is needed.

The main requirements for the filament AC source is power, low distortion and DC/grounding isolation. For 2A3 tube AC must be 2.5VRMS, 2.5A. Hence the supply must be string enough to deliver around 7..9W of AC.

To make sure we cleanly switch from the "real" situation (A DHT SET amp, humming at 120Hz) to an eqivalent simulation, the first try must be with AC frequency 60Hz, 2.5VRMS, observing exactly the same level of hum as in the "real" situation.

Such clean transition would be an important requirement.

6.   Plan for the experiments

To drive filaments, I decided to use a suitable solid state audio power amplifier taking signal from an audio generator. The amplifier will send signal into a step-down transformer, whoch would send low-level, high-current signal into filaments. Thsi will also provide DC-isolation, as the filaments are not at the ground voltage level.

In the first setup I used a subwoofer amplifier rated at 300W into 8ohm load. The amp is therefore capable of delivering sqrt(300 * 4) = 35VRMS of signal before clipping. Since the filaments of a 2A3 triode are ecxactly 1.0 Ohm when hot and much less when cold, the solid-state amplifier would not like to drive it directly or via 1:1 isolation transformer. The step-down transformer was used in a junkbox, ina form of a 40W industrial filament transformer whith its 5VAC,6.3VAC and 2.5VAC secondaries connected in series, providing 13.8VAC from 117VAC, i.e, having the step-down ratio of about 8.5:1. This transformer may not be well suited for multi-kilohertz signals, but the intent was to measure signals in 20...6000 range - more than enough for the purpose of the experiment. With the ratio of ~8, a 30V signal boils down to 3.75V - more than enough voltage, and the current delivered can be enourmous (over 20 A).

As the source, Eico 379 audio generator would be used. The only apparent discomfort of this setup is the amplifier, which contained a built-in low-pass filter. It was temporarily removed.

7.   Equipment List

Moondog 2a3 SET amp, Tektronix 465 dual scope, OEM multimeter, PE 300W subwoofer amp, EICO 379 audio generator, a 117:13.8, 40W transformer (so far, read on for more experiments later on).

8.   Experimental Findings

As a preliminary step, I fed the filaments from the 2,5AC tap of the above mentioned 40W transformer connected to the wall AC, balanced the signal with the balancing potentiometer, and found no apparent change in shape and amplitude of the residual signal from the signal produced by the "stock" circuit of Moondog. The scope was connected to the plate of 2a3 via a DC-blocking 1 mF capacitor.

Next, I set up the frequency-varying filament supply module. The multimeter in RMS VAC mode was connected to the to the tube filament pins.

The machinery was arranged as follows:

which looks admittedly messy but it's the real snapshot. See part 2 for the continuation of the experiments, when/where a cleaner rig was constructed.

Next, I set the frequency at 60 Hz and, after obligatory balancing the potentiometer, found no apparent change in shape and amplitude of the residual signal. I found that the position of hum-neutralizing pot was highly dependent on filament voltage.

Next I set the voltage exactly at the same level I produced with the wall AC transformer (around 2.55V), balanced, and found no change in residual signal amplitude. The signal on the scope was:

the signal is slightly disbalanced; with stock 100 ohm balancing pot of Moondog precise adjustments were a pain! Later (see Part 2) I shorted the ballancing pot with 2 10 Ohm resistors, which helped greatly.

Next I started changing frequency, keeping voltage constant, and found no apparent correlation between frequency and residual hum voltage. I expected something like that, but was prepared to see at least some, but found none.

Here are scope screen shots showing the residual signal on the plate at 20 Hz, 30 Hz, 600 Hz.

some transformer saturation is seen

well-balanced snapshot

not well balanced; also, some RF pickup is apparent here

note that the levels of the 2x AC signals are pretty much the same, if you factor out disbalance.

9.   Some Fine (and Finer) Details, Possible Improvements and Suggestions

Balancing potentiometer has always been adjusted to neutralize the first harmonic component - sort of, as you can see some presence of it on all shots and a quite lot on 600 Hz one.

For 600Hz, the scope sweep is in 1ms/div position (sorry for the blurry shot), for the rest - in 10ms/div position, as can be seen from more vivid shots.

The vertical resolution on all shots is exactly the same and is is 30mV/div. It is actually 10mV, but the amplitude was about 1/3 of amplitude at the plate as a resistive divider was used to protect the scope. The divider was fed via a DC blocking condenser (shall we use this ancient name) which impedance is negligible small compared to the divider.

The shape of the signal at 20Hz is distorted because iron saturates.

The ratio of the step-down transformer (about 8) satisfactory but a smaller ratio coudl be used. Assuming the audio amp is rated for 4 ohms, the ratio can be as low as be 2. For a 8 ohm - it can be 3 or more. This is so because 2a3 tube has filament resistance of 1 ohm and transformed impedance is the square of turns. In reality, the amp develops its best signature when loaded with 8 ohms, hence the best ratio would be 3 or more. I did not have such transformer on hand, but the amp provided sufficient voltage swing to deliver 2.5VRMS after 8.5:1 reduction.

Interestingly, at frequencies above 200Hz the tube was singing loudly. This is very interesting and may help to explain why the 2A3s I experimented with are so microphonic.

I could use a 14W tube amp and avoid the step-down transformer, but the amplifier was humming and that was not a very good option. See below for more experimens involving tube amps.

10.   Conclusions

This experiment proves that residual hum in directly-heated triode output stages is mostly independent of AC frequency, at least in 30..600Hz range. Since the 2nd harmonic dominates, the hum is of frequency that is twice of the filament AC frequency: 120Hz in US, 100Hz in most of Europe. These experiments justify my theoretical findings about DHTs behaving as grounded grid differential amplifiers for AC signal. Thermal and magnetic hum does exist, but for in most mass-production tubes, filaments are large enough and short enough so that most hum is harmonic, and the level of harmonic hum masks the thermal and magnetic effects. This provides a justification for composite tube models, see [1], SPICE models for analytical computation of residual hum, see [2], and for ideas around hum cancellation in SE DHT amplifiers presented in [3]. 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.

11.   References

[1] composite-triode-models.htm

[2] filament-ac-harmonic.htm

[3] dht-filament-hum-cancel.htm

12.   Part 2: Extensive Harmonic Hum Study

click here to go to the part 2.

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