[printed copies available from VAC]
Introduction
VAC Technical Monographs are provided to help
anyone interested in vacuum tube electronics to better understand the
issues involved in the design of truly "high end" amplifiers.
They are a direct response to the (unintentionally) inaccurate impressions
created by the marketing arms of manufacturers and other writings, fraught
with misunderstanding and outright inaccuracies regarding basic concepts
of tube electronics, laws of physics, operation of circuits, measurement
standards, and historical attribution. It is our intention to create an
unambiguous and accurate reference for many of these issues. As such,
these Monographs should prove valuable not only to individuals who are
just becoming aware of these issues, but also to many experienced
audiophiles who are awash in the competing claims.
To ensure accuracy and provide the reader with a source for even more
information on these topics, extensive reference will be made to
authoritative works in the electronics field. Thus, the thoughts presented
herein are not merely the random musings and recollections of one
individual, but a condensation of the accumulated wisdom of a great many
authorities.
Naturally, no one work is ever exhaustive, so the reader may encounter an
omission, or even spot an error (hopefully only typographical in nature).
We are anxious to clarify any fuzzy points and correct any inaccuracies.
As such, we encourage all interested readers to correspond with us on such
points. After all, the goal here is to enlighten, not to confuse!
Readers with little electronics background will probably wish to check
into some of the introductory sources contained in the "Recommended
Readings" at the end of this Monograph.
Finally, remember that in audio electronics there is never one uniquely
and absolutely correct way to design an amplifier. Design always entails
compromise. The real question is which parameters are compromised and to
what degree. The best way to judge audio equipment remains familiarity
with live acoustic music. Listen, and let the sound be your guide.
OF TUBES AND
IMPEDANCES
To start with, let's define resistance as the obstruction to the flow of
electricity offered by a particular device or substance. What then is
impedance? Technically experienced readers know that impedance is a
complex quantity, with both a resistive and a reactive component. For the
purposes of this Monograph, the non-engineer is invited to think of
impedance as like resistance but specified for a particular frequency of
alternating current.
The vacuum tube is often referred to as an inherently high impedance
device because it performs best when presented with relatively high
impedance loads, generally in the range of 1,000 ohms to 20,000 ohms. This
makes it unsuitable for directly driving a modern loudspeaker, which has a
rather low impedance, typically in the range from 1 ohm to 16 ohms.
The difference between a high impedance load and a low impedance load is
in the relative proportions of voltage and current that make up a given
power (wattage). These proportions are dictated by Ohm's law (see Appendix
A). Figure 1 shows how the current and voltage required by a load to
achieve 100 watts of power varies with changes in the load impedance.
As we can see, 100 watts at 5000 ohms (typical for a tube) requires 707
volts at .14 ampere, while the same power at 10 ohms (typical for a
speaker) requires 28 volts at 3.5 amperes. Even a fairly large audio power
tube such as the KT88 has a maximum current rating of only 230
milliamperes (.230 ampere). Obviously, it can deliver only a very small
amount of power directly to a loudspeaker.
ENTER THE OUTPUT TRANSFORMER
The need to trade the tube's high voltage/low current output for the
speaker's high current/low voltage demand requires a translating device
called a transformer. The transformer (simplistically) consists of two
coils of wire wrapped around a magnetically permeable metal. The tube's
output is connected to one coil (called the primary), while the load is
connected to the other coil (the secondary).
In a sense, the transformer is the electronic equivalent of the lever,
substituting voltage and current for weight and distance. When the primary
and secondary coils consist of differing numbers of turns, the proportions
of voltage and current in the two coils also differs. If the primary coil
has more turns, there is less voltage in the secondary coil than in the
primary. However, there is also more current in the secondary than in the
primary. Thus, by having more turns in the primary coil than in the
secondary coil we can reduce the voltage available to the load while
simultaneously increasing the current available to the load. Appendix B
shows the mathmatical relationships of this transformation.
This exchange of voltage for current implies a change in impedance. This
is referred to as the impedance ratio, and it is a function of the square
of the ratio of turns in the primary and secondary coils (the square of
the turns ratio).
Thus, the impedance that the tube "sees" through a transformer
is a function of the transformer's turns ratio and the impedance of the
load attached to the secondary. We may refer to the impedance of the load
presented to the tubes as the transformed or reflected load.
WHAT IMPEDANCE SHOULD BE REFLECTED TO THE TUBE?
Now that we know how to transform a given load impedance on the secondary
into any arbitrary value on the primary, it would seem that our task of
matching a tube to a speaker is simple. Unfortunately, two factors
complicate matters: determining the optimum load for the tube, and coping
with a loudspeaker whose impedance is not the same at all audio
frequencies.
A loudspeaker is far from a constant impedance, and can
vary appreciably at different frequencies. Figure 2 shows the impedance
vs. frequency curve for a popular high end louspeaker. The manufacturer of
this speaker states that is should be considered to be a load impedance of
6 ohms (the nominal impedance), but in fact it presents an impedance that
varies from a low of 2.25 ohms to a high of 13 ohms at different
frequencies within the audio spectrum.
As you might suppose, the performance of a tube also varies with the load
impedance presented to it. In particular, the maximum power output
available varies with load impedance, as does the distortion produced by
the tube and the relative levels of the harmonics that make up the
distortion. This performance is affected by other operational conditions
as well. For example, a pentode tube may be operated as a pentode, or it
may be connected to perform as a triode tube. It acts differently in these
two modes.
Consider the performance of a push-pull pair of EL37 power
pentodes as shown in Figure 3. Here the tubes are operating in the pentode
mode, which is rarely done in the output stage of high fidelity power
amplifiers. It is at once obvious that the tube performs well over a very
narrow range of load impedances. A designer might select 4000 ohms as
optimal since power output is maximized and distortion (THD) is minimized.
However, one might also argue for a slightly lower load impedance,
sacrificing a bit of output power for a reduction in fifth harmonic
distortion, which is subjectively more offensive than the second or third
harmonics.
What happens when we connect the speaker from Figure 2 to this EL37
stage? Since the speaker is rated at 6 ohms and we think the tubes should
be presented a 4000 ohm load, we might wind our transformer such that 6
ohms on the secondary is reflected as 4000 ohms to the tubes connected to
the primary. This solution is confounded by the impedance curve of the
speaker, since the impedance may be as low as 2.25 ohms and as high as 13
ohms at different frequencies. As a result, the reflected impedance to the
tube may be as low as 1500 ohms at one frequency and as high as 8667 ohms
at another. Both of these numbers are so extreme as to be off of our
performance graph for the EL37. In fact, there is no way for this tube,
operating as a pentode without negative feedback, to accommodate an
impedance swing of this loudspeaker.
Figure 4 shows the performance of the same tubes connected
as triodes. While the power output is substantially reduced, sensitivity
to changes in load impedance is also drastically reduced. Power output is
still maximized for loads between 3000 and 5000 ohms. If we were to wind
the output transformer to reflect 6 ohms as 4000 ohms, we still could not
accomodate the entire impedance swing of the speaker.
However, suppose we wind the output transformer such that 6 ohms on the
secondary reflects as 6000 ohms to the tube. Now we can then effectively
accommodate all of the speaker's impedance range. True, the peak of 13
ohms at its bass resonant frequency and the peak at 1500 hertz will be off
to the right of our graph, where available power is reduced. Fortunately,
even though power is reduced, the distortion level will not be excessive,
and overall sonic performance may be subjectively acceptable.
There are other ways to operate an output stage than as
straight pentode or triode. An example of this is the ultra-linear (or
partial-triode) circuit, in which negative voltage feedback is provided to
the screen of the tube from a tap on the transformer's primary. Figure 5
shows the relative insensitivity to load impedance for an ultra-linear
output stage using a push-pull pair of EL34 power pentodes. Power output
from an ultra-linear circuit is greater than for the same tubes connected
as triodes, while the measured distortion over a wide range of load
impedances is comparable to that of triodes.
Another output circuit was popularized in the U.S. and the U.K. by
McIntosh and Quad, respectively. This circuit, called "unity coupled"
or cathode-coupled, is similar to the ultralinear circuit, in that
negative feedback is applied to the tube from a winding on the output
transformer. Now, however, the feedback is current feedback, and it is
applied to the cathode rather than the screen of the tube. The relative
merits of the ultra-linear and cathode-coupled circuits have been debated
at length with no clear winner emerging (see Reference article by
Williamson & Walker, also article by Wireless Engineer staff).
The application of negative feedback around the output stage will improve
on the performance shown in Figures 3, 4, and 5, making the tubes somewhat
less sensitive to changes in load impedance.
ARE MULTIPLE MATCHING TAPS NECESSARY?
In the preceding section we saw that it is possible to accommodate a
fairly wide speaker impedance swing with a tube output stage. To do so,
however, requires a very careful choice of turns ratio, such that the
impedance swings will be reflected within a range in which the tube works
well. Clearly, a single turns ratio for a particular amplifier ("one
size fits all") will work well with a relative minority of
loudspeakers, and will have major difficulty with many loudspeakers.
To overcome this problem, many designers specify that the secondary
winding of the transformer have multiple tap points on the coil. These
taps are led out to separate connectors to which the audiophile may attach
the loudspeaker. Selecting different taps changes the number of utilized
turns in the secondary, thereby changing the effective turns ratio of the
transformer. The user may thus position the loudspeaker load in different
portions of the output tubes' performance curve. When a tap is labelled X
ohms (i.e., 2, 4, or 8 ohms), it means that a resistance of X ohms
connected to that tap will reflect to the tubes as what the designer
considers to be the optimal value.
Some good sounding single tap amplifiers exist. In general, such
amplifiers pick an average value for loudspeaker impedance (say 5 to 6
ohms) and fix the turns ratio accordingly. A speaker in the impedance
range from 4 to 8 ohms will be matched to the tubes fairly well provided
that its impedance does not vary too much with frequency. Fortunately,
many modern speakers have a well controlled impedance curve, staying
between 4 and 12 ohms. Also, a speaker with a widely varying impedance may
still be well matched provided that the transformer is by chance wound to
exactly the correct ratio for that particular speaker. Unfortunately, many
high performance speakers fail to meet these criteria, and available power
will be substantially reduced and/or distortion increased.
Single tap amplifiers, therefore, limit the user in choice of
loudspeaker, now and in the future. Some manufacturers can reconfigure
their transformer connections at a user's request, although the choice of
alternatives is in some cases limited to a single questionable value, such
as 1 ohm. Such amplifiers also represent an unknown on the used market, as
it is not easy for a perspective purchaser to know what custom
reconfiguration has been carried out.
CRITICISMS OF MULTIPLE TAP TRANSFORMERS
Given all of the technical disadvantages of the single tap amplifier, why
are they still manufactured? In some cases, the answer may be cost, the
single tap unit being slightly easier and less expensive to wind. (In a
high quality tube amplifier, the transformers are the most costly
components, and are often the focus of cost control attention.) In other
cases the designer may have elected to use a replica of a "classic"
transformer, lacking the expertise, finances, or time necessary to design
a high quality unit for the specific application.
Occasionally a designer will utilize a single tap approach due to well
intended misunderstanding. One occasionally encounters the assertion that
if we connect a loudspeaker to a 4 ohm tap, power will be lost due to the
unused portion of the secondary winding from 4 ohms to 8 ohms. Fortunately
for the audiophile, this is not the case. Power can not be dissipated
unless current is flowing. For current to flow, there must be a complete
circuit. The unused portion of the winding is not included in a completed
circuit. Hence, no current flows through the unused section of the
secondary and no power is lost.
Another criticism of a multiple tap transformer involves the wire size
(diameter) required to carry a given level of current. As Ohm's law
indicates, the current required for a particular power level is greater
for a lower impedance. For example, in a 100 watt amplifier, 5 amperes
must flow into a 4 ohm load, while only 3.5 amperes is required for an 8
ohm load. Accordingly, the section of the secondary up to the 4 ohm tap
must be wound with a wire large enough to support a 5 ampere current flow.
A smaller wire size will probably be used in the section of the secondary
to 8 ohms. If we omit the 4 ohm tap, the smaller wire size could also be
utilized in both sections of the secondary, and the transformer could thus
be slightly smaller, lighter, and less expensive. Fortunately, the use of
the slightly larger wire size needed for the low impedance tap introduces
no significant difficulties to the competant transformer engineer, and the
transformer performance need not suffer apart from cost.
Similarly, if one had no need for the 8 ohm tap we could wind the
transformer stopping at 4 ohms, again with a savings in cost and size.
However, we have already seen that there is a genuine need for alternate
taps. Fortunately, the savings from omitting a higher impedance tap is not
as great as one might at first imagine. For example, since the impedance
ratio is a function of the square of the turns ratio, fully one half of
the secondary exists in the winding up to 2 ohms! A relatively small
proportion of turns is needed to reach 8 ohms, so omitting the 8 ohm tap
is of little consquence. Small capacative and inductive effects are again
easily dealt with by the competant transformer engineer, and the
transformer performance need not suffer apart from cost.
LOOSE ENDS
The tube performance graphs shown in this Monograph depict the
performance of representative tubes operating under specific circuit
conditions. The same tubes operated with different voltages may display
somewhat different results. However, the comparative performance between
triode, pentode, and ultra-linear operation will hold true for a given set
of operating conditions.
Output-transformer-less (OTL) tube amplifiers are a special case. They
generally employ the lowest impedance power triodes possible. One such
tube is the 6AS7, originally designed for power supply regulation service,
which works well into a load impedance of 1000 ohms. Operating multiple
tubes in parallel reduce the optimum load. Two 6AS7 provide twice the
power into a load of only 500 ohms. Sixteen such tubes in parallel will
deliver their full power capability into a load of only 62.5 ohms. Thus,
if a sufficient number of tubes are employed, enough power may be
available to generate adequate listening volume when conneceted to a
loudspeaker in spite of the impedance mismatch. An unusual characteristic
of such a design is that it can deliver significantly greater power levels
where a speaker has an impedance peak, while conventional amplifiers
deliver less power at an impedance peak. Most speakers are not designed
for such an amplifier characteristic, which may help explain the frequent
observation that OTL tube amplifiers are quite picky about their
associated loudspeakers. OTL amplifiers also often employ circuit
connections somewhat different from the normal push-pull configuration.
The relative merits and demerits of these circuits are well discussed in
the literature.
In the last 25 years, some designers have sought to avoid output
transformers by replacing the output tubes with transistors, which are
much lower impedance devices. In effect, this is a hybrid design,
employing tubes in the front end and solid state devices at the output
end. This is no longer a pure tube amplifier, and thus falls outside of
the scope of this Monograph. Good test bench performance can be achieved
in this manner, but the sonic merits must be judged by each listener. In
some cases, using both vacuum tube and solid state technology results in
the sonic problems of both and the advantages of neither.
Some degree of overall loop negative feedback (from the output of the
transformer to an earlier amplifier stage) will improve on the measured
performance of any output circuit discussed in this Monograph, lowering
total harmonic and intermodulation distortion levels. However, additional
feedback loops multiply the order of distortion and can lead to less
desirable clipping behavior. For example, if an amplifier generates third
harmonic distortion, the introduction of a feeback loop will lower the
level of the third harminic, but will also introduce the ninth harmonic.
Since higher order distortion products and odd order distortion products
are subjectively the most offensive, feedback is best used in moderation.
The relative merits of the circuits presented here remain the same with
feedback.
All circuits referred to in this Monograph have had the load connected to
the plate circuit of the tubes, with the exception of the partially
cathode-coupled amplifier, in which the load is split between the plate
and cathode circuits. The ultra-linear may also be thought of as a
distributed load circuit, where part of the load is in the screen circuit.
However, this design is usually analyzed in terms of feedback to the
screen circuit.
Finally, this Monograph has not gone into the details of the construction
of loadlines on the plate curves of a tube, although this is commonly done
by engineers. Our discussion in this Monograph has been based on the
actual measured performance of an output stage, and thus subsumes this
more complex topic in a form that is more meaningful to the audiophile.
Nor have we discussed the effects of the reactance of a complex impedance
on performance, which also argues for careful impedance matching. Both of
these topics are well covered in the references.
BIBLIOGRAPHY
Recommended Background Reading
McIntyre, Bob, Vacuum Tube Fundamentals, Part I. The Audio Amateur, 2/86,
pages 26-36. (contains an excellent reference list)
McIntyre, Bob, Vacuum Tube Fundamentals, Part II. The Audio Amateur,
2/87, pages 25-29.
Moir, James, High Quality Sound Reproduction. Macmillan, 1958.
RCA Staff, RCA Receiving Tube Manual (RC-26). RCA, 1968. Pages 3-10,
13-14, 25-37.
References Used In Preparation of Monograph 90-9
Baxandall, P.J., High-Quality Amplifier Design - Advantages of Tetrodes
in the Output Stage. Wireless World, January 1948. (Also see correction in
February 1948.)
Corderman, Sidney A. & McIntosh, Frank H., A New 30-Watt Amplifier.
Journal of the Audio Engineering Society, October 1953.
Crowhurst, Norman H., Some Defects in Amplifier Performance Not Covered
by Standard Specification. Journal of the Audio Engineering Society,
October 1957
Dickie, D.P.Jr. & Macovski, A., A Transformerless 25-Watt Amplifier
for Conventional Loudspeakers. Audio, June 1954.
Futterman, Julius, An Output-Transformerless Power Amplifier. Journal of
the Audio Engineering Society, October 1954.
Futterman, Julius, A Practical Commercial Output-Transformerless
Amplifier. Journal of the Audio Engineering Society, October 1956.
Gibson, W.F., A Practical Cathode-Follower Audio Amplifier. Audio
Engineering, May 1949.
Grannel, Arthur E., Transformerless 25 W Amp. Audio Amateur, Vol 5, 1982.
Hafler, David & Keroes, Herbet I., An Ultra-Linear Amplifier. Audio
Engineering, November 1951.
Hafler, David & Keroes, Herbet I., Ultra-Linear Operation of the
Williamson Amplifier. Audio Engineering, June, 1952.
Hayes, Kevin M., Tube Misinformation (letter). Stereophile, May 1989.
Kiebert, M.V., The "Williamson Type" Brought Up to Date. Audio
Engineering, August 1952.
Langford-Smith, F. (Editor), Radiotron Designer's Handbook. RCA, 1953
(Fourth Edition). Chapters 5, 13.
McIntosh, Frank H. & Gow, Gordon J., Description & Analysis of a
New 50 Watt Amplifier Circuit. Audio Engineering, December 1949.
Millman, Jacob, Vacuum-tube and Semiconductor Electronics. McGraw-Hill,
1958. Pages 400-436.
Moir, James, High Quality Sound Reproduction. Macmillan, 1958. Pages
285-306, 307-316.
von Recklinghausen, Daniel R., Mismatch Between Power Amplifiers and
Loudspeaker Loads. Journal of the Audio Engineering Society, October 1958.
Stanley, A.W., The Output Stage - Effect of Matching on Frequency
Response. Wireless World, August 1946.
Strandberg, M.W.P., OTL Vacuum Tube Amplifier. Audio, December 1961.
Sulzer, Peter G., A Survey of Audio-Frequency Power-Amplifier Circuits.
Audio Engineering, May 1951.
Tomick, D.J. & Wiggins, A.M., New Amplifier has Bridge-Circuit
Output. Audio, November 1954.
Tremaine, Howard M., Audio Cyclopedia. Howard W.Sams, 1969. Pages
543-544, 604.
Williamson, D.T.N., Design For a High-Quality Amplifier. Wireless World,
April & May 1947.
Williamson, D.T.N., High-Quality Amplifier - New Version. Wireless World,
August, October, & November 1949.
Williamson, D.T.N & Walker, P.J., Amplifiers and Superlatives, An
Examination of American Claims for Improving Linearity and Efficiency.
Journal of the Audio Engineering Society, April 1954. (Also printed in
Wireless World, September 1952.)
Wireless Engineer staff, Ultra-Linear Amplifiers. Wireless Engineer,
August 1955.
Graph Credits
Figure 3 after Moir, page 289.
Figure 4 after Moir, page 288.
Figure 5 after Moir, page 305.
Appendix A
The proportions of voltage across and current through a load are dictated
by Ohm's law, which states that the current flowing through a resistance
is equal to the applied voltage divided by the resistance (ohms). This is
usually written as
I = E / R
where I is the notation for current expressed in amperes, R is the
resistance in ohms, and E represents voltage in volts. It is also a basic
fact that power is the product of voltage and current, commonly written as
P = E x I .
Combining these two facts tells us that P = E2 / R. So, 100 watts at 5000
ohms (typical for a tube) requires 707 volts at .14 ampere, while the same
power at 10 ohms (typical for a speaker) requires 28 volts at 3.5 amperes.
For measurements involving alternating current, such as audio signals,
current and voltage are expressed by their effective or r.m.s. (root mean
square) values. For a sine wave, this is simply the peak value divided by
the square root of two.
Appendix B
Figure 6 presents a pictoral representation of a
transformer and its connections.
The voltage ratio between the primary and the secondary is determined by
the ratio of the number of turns in the two coils, written as
E2 / E1 =
N2 / N1
where N refers to the number of turns of wire and the subscript 1 refers
to the first coil, etc. Similarly, the current ratio between the coils is
also a function of the turns ratio, written as
I2 / I1 = N1 / N2.
Thus, by having more turns in the primary coil than in the secondary coil
we can reduce the voltage available to the load while simultaneously
increasing the current available to the load. Of course, some power is
lost in the transformer, so these ideal ratios do not hold exactly.
Using the formulae already presented, we can work out an impedance ratio
for the transformer. The impedance ratio winds up being the square of the
turns ratio, written as
R1 /
R2 = ( N1 / N2 ) 2.
Thus, the impedance that the tube "sees" through a transformer
is a function of the transformer's turns ratio and the impedance of the
attached load. We may refer to the load presented to the tubes as the
transformed or reflected load. If a transformer having a 10 to 1 turns
ratio is connected to a load of 8 ohms, the reflected impedance on the
primary coil will be 800 ohms.
