|
SE
Amplifier Output Impedance - by Eduardo de Lima
(originally
published in Glass Audio, 3/97)
PART 1
Introduction
Much has been said about triode SE amplifiers with no negative feedback -
how good they sound, how lively they present a musical performance and so
on. Two easily measurable characteristics that make this type of
amplifiers sound different are, the amount of distortion produced with its
particular spectrum, and the high output impedance. This raises the
question of whether they sound so good and musical because of these
characteristics or in spite of them.
The first time I listened to such an amplifier with no feedback was
through a loudspeaker that apparently was not much affected by the high
output impedance of these amplifiers. Since I was really impressed with
the sound I heard, I decided to do some measurements to understand what
was going on.
After making these measurements, I became more deepely involved with the
subject, thinking about the design of a SE amplifier and the loudspeakers
to use with it. Based on this work, my intention here is to examine the
output impedance (Zout) and its role in the interface between SE
amplifiers and the loudspeaker.
Listening To a SE Amplifier
Just after I finished a 300B SE amplifier kit, I connected it into my
system and was really impressed with what I heard. I had never heard the
violins and the voices in such a natural way. Although I have other
speakers and amplifiers around, the amplifier and loudspeaker I was using
in my system at that time was a Quad II with same parts upgraded, and a
speaker I had designed and built in the mid 80s using a Kef bass unit, a
Peerless mid and a JVC ribbon tweeter. This loudspeaker has only suffered
minor changes and parts upgrade during the years. Although an old design,
for me it still sounds good. It is not a high efficiency loudspeaker, but
with the 300B SE amplifier I have been able to listen at levels that I?m
used to without any problems (I have to admit that usually I don?t listen
very loud).
After some days, I decided to look at the whole system trying to find
clues to explain the differences between the amplifiers. I measured the
Zout of the amplifier and found it to be almost 4.0 ohms. I knew the
loudspeaker very well , and looking at the notes I made at the time I
designed it, I remembered that it presents an almost purely resistive
input impedance with a magnitude between 6.8 and 10.1 ohms from 100Hz to
20Khz . It is a closed box design with about 87 dB/W/m average sensitivity
and a critically damped resonance (Q=0.5) at 39 Hz.
Using this loudspeaker driven by a SE amplifier with almost 4.0 ohm of
Zout, the big difference I should hear would be the stronger bass
caused by a less damped resonance. From the mid bass up, the expected
differences in frequency response would all fall inside a 1.1dB total
range (-0.5 dB / +0.6 dB referred to the nominal 8 ohm impedance). I
compared the loudspeaker frequency response from 100Hz up with a low
impedance conventional transistor amplifier and with a 3.9 ohms resistor
in series, simulating the SE amplifier output impedance. We also have to
consider the drop in the high frequency response of the amplifier of about
1 dB at 20 Khz.
I think that the differences I had heard were much bigger than what could
be expected from my frequency response plot. Surprisingly, at least for me
at that time, the most dramatic differences were in the mid range, with
violins and vocals sounding remarkably open as stated before. The bass was
stronger as should be expected, but this was a minor difference compared
to the midrange sound. I have to say again that all these thoughts and
measurements occurred several days after the initial listening tests, when
the differences in sound were first noticed.
My reaction to this listening experience seems to be just like most of the
described reactions to SE amplifiers. The fact that the loudspeaker used
is reasonably insensitive to the high Zout made me conclude that we have
to look elsewhere to find the reason for the good sound of SE amplifiers.
This is why I started to look more closely at this characteristic of SE
amplifiers in general. If I were to design my own SE amplifier, I could
use this experience. Probably if we can lower the Zout without destroying
the other aspects of the SE sound, we may be able to use these amplifiers
with more predictable results with many more loudspeakers.
The Output Impedance Of Typical SE Circuits
I considered a practical equivalent circuit for a single ended output
stage with simplified circuits at mid, low and high frequencies. These
models were based on the description given by Terman (ref.1). I only
changed the values to what they are at the secondary of the transformer
instead of at the primary like in the book. Also, to calculate Zout, RL (the
load resistance) is left out. From what I could test, these transformer
equivalent circuits are good approximations. Only the equivalent circuit
for high frequencies starts to became inaccurate at the highest
frequencies. It does not take into account the distributed capacitance of
the primary and secondary, therefore it can not predict a high frequency
peak in the frequency response that appears in some of the transformers.
After measuring the required parameters for one transformer, I used the
complete practical equivalent circuit with a circuit simulator for
calculating the magnitude and phase of the Zout. This was followed by the
actual measurements at some frequencies. Although the incremental primary
inductance (Lp) is not a very constant parameter, the measured results
were close to the simulation values. Only at the highest frequencies was
there some appreciable difference. Measuring other transformers confirmed
that these curves were fairly typical of this kind of output transformers.
The decrease in the Zout at low frequencies came together with a rapid
rolloff at the low end frequency response of the transformer. One very
interesting example has been the review of a commercial 300B SE amplifier
which has a 2.5 ohm Zout at 1Khz, 2.7 ohm at 20Khz and 0.76 ohm at 20Hz.
This low value of Zout at low frequencies may look like a good
thing but only happens because the primary inductance of the output
transformer is probably much lower than it should be for extended low
frequency response. This is confirmed in the frequency response plot shown
in the review. The amplifier is 9dB down at 20Hz. The low value of the
output impedance at 20Hz only shows that the limiting low frequency factor
is the output transformer, not any other coupling in the amplifier.
SE Amplifiers with good output transformers should have the Zout with a
more extended region of flat impedance. The phase plot except for the
frequencies extremes should be resistive. The region of flat impedance
with resistive behavior corresponds to the region where the equivalent
circuit is valid. We will use this extremely simplified model in all the
following analysis. This is a very important assumption, and one that has
to be made to simplify the first visualization of the effects of the high
Zout. As we go along I will try to show when we should expect this most
simplified model to fail, making the use of the other equivalent circuits
necessary.
As a first approximation to calculate the output impedance of a tube
amplifier with no negative feedback, we can simply divide the plate
resistance by nē (n = turns ratio between primary and secondary of the
output transformer). Several books state as a practical rule that output
triodes should be loaded with an impedance of about three times its plate
resistance for maximum undistorted power output (although some theoretical
calculations find a ratio of two to one. ref.3, ref.4, ref.5). If this
rule is followed, the Zout of SE amplifiers with any triode will always be
about the same. At first look, its value should be one third of the
nominal load impedance of the output tap of the transformer, or around 2.7
ohms for an 8 ohm tap. But we should look more carefully using the
simplified model and take into account the transformer resistances. To do
this, we will choose one output triode and work out an example. Lets pick
a typical 300B SE amplifier and do same quick calculations. The 300B
according to the WE manual has a 700 ohm plate resistance. Using an output
transformer with a 2.5K primary reflected impedance we can calculate the
output impedance. We need to measure or estimate its primary and secondary
DC windings resistances and use it in the following formula:
Zout = (rp + R1) + R2 ( 1 )
nē
where nē = Zp - R1 ( 2 )
R2 + RL
Zout = Output impedance
rp = Output tube plate resistance
RL = Nominal load resistance
R1 = DC Resistance of the primary of the output transformer
n = Ratio of primary to secondary turns (it can be measured directly)
R2 = DC Resistance of the secondary of the output transformer
Zp = Reflected primary impedance
If we estimate R1 to be 200 ohms and R2 to be 0.5 ohms, for Zp of 2500
ohms and a RL of 8 ohms, using formula (2) we get n2=270. Using formula
(1) we arrive at the value of 3.8 ohms for Zout.
I have actually measured many parameters of four output transformers for
use in single ended applications and calculated its Zout when used with
300B tubes. These Zout measures were taken at 1Khz. All the results were
within 10% of the calculated values. The measurements of low values of
resistances like 0.6 ohms using a digital multimeter may introduce a
sizable error. Although I have not further investigated the differences
between measured and calculated Zout, I believe they can be explained
mainly by this factor and by the fact that we didn?t account for the Rp of
the particular 300B tube used for the measurements, relying on the 700
ohms value given by the manual. All the transformers were measured with
the same 300B tube and changing the tube during one measurement gave just
slightly different results.
The Zout of these amplifiers with triode output tubes can only be lowered
(without using feedback) by changing the output transformer parameters.
Increasing nē and lowering R1 and R2 will make the Zout decrease. How low
can we get? Lets go back to the 300B example. The biggest part of the
impedance is made up by the tube Rp (around 700 ohms for the 300B) divided
by nē. Higher nē means higher primary reflected inductance. Usually 300B
amplifiers use 2K5 to 3K primary reflected impedance. The higher this
impedance, the lower proportionately would be the Zout. Therefore if we
want to lower the Zout, we should pick a transformer with a higher primary
reflected impedance. In the WE manual, 300B tubes are shown operating with
loads up to 6K5, although the 6K and 6K5 data is shown only at maximum
dissipation ratings. Therefore it looks like we can assume that 5K is a
reasonable high target. An amplifier using a transformer with this primary
reflected impedance should be better from the standpoint of output
impedance. But we will need to use higher voltages to keep the output
power, and its harder to have good frequency response from output
transformers of higher primary impedance.
To see what happens using higher turn ratios, we can calculate the Zout
for an hypothetical transformer the same way we have done before. Lets use
a 5K primary, and estimate a R1 of 150 ohms and a R2 of 0.4 ohms. For the
8 ohm tap nē will be 577. We will end up with Zout of 1.87 ohms. Since
the characteristics of this hypothetical transformer are of one very
optimized for low Zout, I believe that 2.0 ohms should be about the lowest
we could expect from a 300B SE amplifier with no feedback and still
reasonable output power (for a 300B). Also, for any other output triode
and even for parallel use of tubes, we probably cannot get much lower Zout
unless we deviate even more from the old rule about load impedance for
maximum undistorted power output (?undistorted? here usually meaning 5%
distortion).
Everything I have said above applies to the nominal 8 ohm tap. The 4 ohms
tap will usually have half of the Zout of the 8 ohm tap. Actually what we
have described above for the 5K transformer is like using the 4 ohm tap in
an amplifier with a 2K5 output transformer. Therefore when using speakers
rated as 8 ohms, if you are willing to sacrifice the output power, you can
see how it will sound with a lower output impedance using this tap. But it
should be clear that an amplifier designed to reflect a 5K impedance from
8 ohms should have details in the output transformer and the biasing and
power supply such that it would be optimized for the right impedance,
extracting more power and being a better overall solution if done right.
And, of course, you could have still a lower output impedance using its 4
ohm tap!
I have to say that this whole issue of which output tap should be used and
of specifying the nominal loudspeaker load is not a simple one. With tube
amplifiers using the tap that better reflects the average loudspeaker
impedance will usually result in more output power. To get lower output
impedance the 4 ohm (or lower) tap is always the better option regardless
of the loudspeaker impedance. Balancing these points, and also the
change in frequency response extension and the different amount of
distortion for different power levels among other factors is not easy.
This is why listening to all tap options is sometimes the only way to
decide which tap is better for a loudspeaker with a particular amplifier.
Looking At The Effects Of Hight Output Impedance
As we have seen, the lower limit on the value of the Zout of the SE
amplifiers, being high, makes it very important for us to consider its
effects on the system response. Driving a loudspeaker with a high Zout
seems to be a bad idea. Loudspeakers, in general, have been designed under
the assumption that they will be used with amplifiers that closely
resemble an almost perfect voltage source, which means Zout close to zero.
Although contacts and cable resistance usually make reducing the Zout of
an amplifier below some point like 0.1 ohm useless, in the SE amplifiers,
as we have seen, we are talking about values around 4 ohms. This value of
Zout interacting with typical loudspeakers input impedance will produce a
deviation from the loudspeaker intended frequency response of several dB.
From the midbass up, we can calculate the probable maximum deviation from
the original frequency response if we have the amplifier Zout value and an
input impedance curve of the loudspeaker. We can roughly look at what will
happen with the loudspeaker response as a kind of ?modulation? of the
frequency response curve via the input impedance curve ( although not
correct, I can think of no other way to quickly describe the effect).
Trying to visualize it, you should keep in mind that because of the
difference in the effect of the peaks and dips of the input impedance of
the loudspeaker and also because of the complex nature of the impedances,
the peaks will be reproduced broader and the dips sharper in the frequency
response curve than in the original input impedance curve.
To calculate the change in the response we should use the following
formula:
D(f) = 20log ____Zin (f)___ (3)
Zin(f) + Zout
where, D(f) = deviation in dB at frequency f
Zin(f) = input impedance of the loudspeaker at frequency f
We can see that this formula will always give a negative value, which
corresponds to a loss for any value of Zout that is not zero. But we are
looking for the difference between the loss at the maximum Zout and the
loss at the minimum Zout. This will give the range of deviation from the
intended frequency response curve of the loudspeaker. Ideally we should
use the complex values of Zout and Zin but the output transformer model we
are using implies a resistive behavior for Zout. Also the peaks and dips
in the magnitude of the loudspeaker input impedance usually correspond to
points where its phase angle is 0 or very close to it. Because of these
facts using just the magnitude of the input impedance and assuming a
resistive behavior, it will give us the most probable maximum deviation
from the intended frequency response of the loudspeaker.
I went through 12 issues of Stereophile (Jan/95 to Dec/95) and looked at
31 loudspeakers that were tested and had the input impedance curve
published. The maximum values for input impedance had to be estimated as
the curves are limited to a maximum of 20 ohms. Considering only the
frequencies well above the low frequency resonance of the system, the
average loudspeaker had an input impedance varying from 4.3 ohms to 15.0
ohms. with the phase going from -28 to +29 degrees. Very seldom a
loudspeaker had phase angles of more than 45 degrees or less than -45
degrees (only 2 cases, the worst being a 55 degrees angle). This is
fortunate because the error introduced assuming resistive behavior will be
small.
Now we must look at what will happen at the very high frequencies. Should
the equivalent circuit be used here? With dynamic loudspeakers, the voice
coil inductance of the tweeters will usually have an effect on the phase
of the loudspeaker input impedance corresponding to an inductive behavior.
This is similar to the effect of the leakage inductance of the
transformers on the phase of the amplifier Zout. This will keep the
difference in phase angle small, and this reduces the need to use the
model for evaluating the effects of the high Zout at high frequencies with
dynamic loudspeakers. As long as the change in the magnitude of the Zout
at high frequencies is reasonable, we should have no surprises here and
can still consider the Zout resistive. This also holds even when impedance
compensating networks (Zobels) are used. Only with output transformers
with very limited high frequency response driving loudspeakers with
capacitive behavior (like piezo tweeters) we should need to take a closer
look at these frequencies, because of the probable high phase difference.
All the considerations above are valid through the frequency region far
from the resonant frequency of the woofer in the system. Near the resonant
frequency of the system, we can still try to use the same approach as a
rough guess but it may give wrong results. We can not just use the idea of
?modulation? of the frequency response curve via the loudspeaker input
impedance curve without further care. Not only does the falling frequency
response make it difficult to visualize the effect of the output impedance,
in vented systems the change in the alignment produced by the high Zout
will change not only the value but also the frequency of the impedance
peaks. There are other factors that also may have a big effect on the
frequency response of the system, including the primary inductance of the
output transformer, making the use of the equivalent circuit necessary to
understand what happens. But this alone deserves its own article which I
hope will follow this one soon.
References
ref. 1 - Terman - Electronic and Radio Engineering (1955) - pg. 341
ref. 2 - Stereophile - March/1995 - pg. 120
ref. 3 - Reich - Theory and Application of Electron Tubes (1944) - pg. 228
- 232
ref. 4 - Dammers, Haantjes & Van Suchtelen - Application of the
Electronic Valve in Radio
Receivers and Amplifiers. Vol II (1951) - pg. 97-101
ref. 5 - Langham - High Fidelity Techniques (1950) - pg. 38 - 41
(originaly published in Glass Audio 3/97 - Copyright Audio Amateur Corp.
1997)
|
