Download The Tube CAD Journal, August 1999

This Issue
We were hoping to let the Circular/Balanced/Bridge
amplifier rest and not make an appearance this issue,
but it is here in an article on tube buffers. Expect more
on this topology next month as well, for we are not
nearly done excavating this vein. The circuit from the
July article, "Unbalancing Acts," is back in the same
buffer article. In this same article you find the secret to
optimizing the White Cathode Follower as a Class A
output stage. Headphone fans take note.
I have found that many tube circuit neophytes and,
unfortunately, far too many tube gurus have only the
Grounded Cathode amplifier under their belt, so to
speak. Good as this circuit is, a bigger repertoire is
welcome. (I am saddened by sights such as the earnest
tube fancier wasting his time trying different brands of
the same valued plate resistor in an attempt to make
the 12AX7 based line stage he owns better drive the
15 feet of high capacitance interconnect to the
amplifiers.) The aim of this journal is to increase the
vacuum tube circuit vocabulary of the readers.
Reader Rowan has asked for some direction in
building a tube microphone preamplifier. Two
topologies are shown.
In the last issue, reader Ian made a great suggestion:
a tube amplifier that would mimic the mixed class of
operation of the Pass Labs Aleph amplifier (SE / pushpull Class A). This month we have a brief follow up
by presenting a current source alternative to using a
choke.
Remember, if you have a request or suggestion of
your own for either an article topic or circuit, please email:
Editor
The Cathode Follower
A Quick Overview
Right after the Grounded Cathode amplifier, the
second most common tube circuit in use is the
Cathode Follower. The simplest buffer that can be
made with tubes, it is used to match a signal from a
high impedance source to a low impedance load.
In This Issue
1
4
8
9
11
14
18
Cathode Follower
White Cathode Follower
Plate Follower
Broskie Cathode Follower
Circular/Balanced/Bridge amplifier
Tube Microphone Preamplifier
E-Mail
Publishing Information
Glossary of Audio Terms
The circuit is single-ended and Class A by design,
as there is only one active device. The plate is, in AC
terms, but not in DC terms, grounded and thus the
Cathode Follower other name: the Grounded Plate
amplifier.
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The assumption here is that the B+ connection has
the same signal content and impedance as the ground.
The input signal is given to the grid while the cathode
is loaded by a resistor that leads to ground or a
negative power supply.
The gain is always less than unity, the output
impedance is roughly the reciprocal of the
transconductance, and the PSRR is roughly equal to
the inverse of the mu.
An intrinsic distortion correcting mechanism known
as degenerative feedback keeps the Cathode Follower's
distortion low. It works this way: any departure from
the desired output voltage will subtract from the input
voltage and result in a countervailing change in current
flow. In other words, if the cathode is forced more
positive, the grid will effectively become more
negative relative to it and thus less current will flow
through it, which works to decrease the output voltage;
on the other hand, if the cathode is forced less positive,
the grid will effectively become more positive relative
to it and thus more current will flow through it, which
works to increase the output voltage.
In other words, the Cathode Follower relies on the
tube's transconductance to keep its output voltage in
line with the input voltage. Thus, the greater the
transconductance, the lower the output impedance.
many solid-state devices, as they exhibit such very
high transconductance figures that running them at an
equally high current for any length of time would melt
the devices.
In addition to running a Cathode Follower with too
little current, many make the mistake of not using a
grid stopper resistor. Cathode Followers can exhibit
some wild oscillations that result from long inductive
leads connecting to the grid that are easily stoppable
with a 100 ohm resistor soldered right at the grid's
socket tab.
Bad Rap
Unfortunately, in spite of low distortion, a cathode
follower can sound bad if sloppily designed or
improperly used.
One advantage a Grounded Cathode amplifier has
over the Cathode Follower is that the plate resistor and
the cathode resistor (if it is not capacitor bypassed)
both lower the transconductance of the triode. This
would seem to constitute a disadvantage, but a high
transconductance that is not matched to a high current
draw, in my opinion, worsens the sound. I like to use
as much current as there is transconductance, which is
not possible with
<PREVIOUS
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pg. 2
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Another mistake often made is to over-estimate the
driving ability of a Cathode Follower. For example,
don't expect a 12AX7 based Cathode Follower to drive
a 600 ohm load to 10 volt peaks just because it has a
600 ohm output impedance. Let us assume that half of
the 1 mA of idle current through this Cathode
Follower can be delivered to the 600 ohm load. The
resulting peak voltage is disappointing:
.0005 x 600 = .3 volts.
An idle current of 33 mA would be needed to make
the 10 volts peak figure easily possible. The key point
here is not to make the mistake of thinking solely in
terms of voltage--current is equally important in a
buffer's design
Sometimes too high a current draw leads to a
compressed sound. Actually, this fault has nothing to
do with the design or function of the Cathode
Follower, but with sloppy power supply practice. For
example, let us imagine a common tube lineup: a
12AX7 configured as a Grounded Cathode amplifier
with a 150k plate resistor that then cascades into a
12AU7 based Cathode Follower with a 15k cathode
resistor. Makes sense. Does it not? A high gain, low
current amplifier at the front, followed by a high
current, low output impedance buffer.
< PREVIOUS
pg. 3
Everything looks good until we see that the both
stages tie together at a power supply connection with
relatively high series output impedance. So when the
12AX7 tries to pull its plate voltage down, the
12AU7's cathode will follow, but as the 15k resistor is
ten times smaller in value than the 150k resistor, the
change in current it produces in response to the input
signal will tend to swamp out the change in current the
150k produces in response to the same signal.
The key point here is that while the Cathode
Follower works in voltage phase with its input signal,
it works in negative current phase to the Grounded
Cathode amplifier. So while the 12AX7 tries to pull
down its plate voltage by the increased current
conduction, the 12AU7 lets go of ten times more
current, which allows the power supply connection to
drift upwards, which subtracts from the output.
Conversely, when the first stage tries to push up its
plate voltage by the decreased current conduction, the
Cathode Follower conducts ten time more current,
which pulls the power supply connection downwards.
Of course, if the power supply were perfect, i.e. zero
impedance, this cancellation effect could take place.
The obvious strategy is to use a regulated power
supply. A more subtle move is to match the Cathode
Follower cathode resistor to the value of the plate
resistor of the first stage so as to cancel any net
variation in current presented to the power supply.
The final setback to the Cathode Follower is that
because it is intrinsically a single ended circuit, it can
only aggressively drive the output in one direction: up.
If presented with a difficult load, i.e. low impedance,
the Cathode Follower can be driven into twice or three
times its idle current, but it can only decrease its idle
current to zero conduction. This makes for an
asymmetrical output drive potential. A popular myth is
that this problem can be overcome by using a negative
power supply. But a negative power supply only
allows for a larger valued
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cathode resistor, which would serve to better
approximate a current source, but would do nothing to
increase the idle current limit to the negative current
swinging of the Cathode Follower.
White
Cathode
Follower
The White Cathode Follower
Mr. White's improvement on the Cathode Follower
was to create a buffer that boasted a much lower
output impedance and the ability to sink as well as
source current, i.e. push-pull operation. The lower
output impedance results from the use of a feedback
loop from the plate resistor to the bottom tube and the
use of two tubes allows the buffer actively to draw
current in both directions.
Because of the increased complexity of the circuit,
the math is much more complicated than that of a
simple Cathode Follower:
Gain =
As an example, given a setup that consists of a 6DJ8
with a bypassed cathode resistor of 200 ohms and a
10k plate resistor, the results are
Gain = 0.97
Zo = 3.44 ohms
PSRR = -65 dB.
mu² + murp/Ra
(mu² + mu + 1) + (mu+2)rp/Ra
Zo = 1 / [ (1 + mu)/(rp + Ra) + 1 + mu(mu + 1)/(1 + rp/Ra)
((mu + 1)Rk + rp)
]
PSRR =
2rp + (2mu + 2)Rk
[2rp+(2mu+2)Rk+Ra+murp+(mu²+mu)Rk] [(Ra+rp)/(mu+1)+rp+(mu+1)Rk)/(muRa)]
<PREVIOUS
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pg. 4
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If this seems too good to be true, that's because it is
too good to be true. Yes, the gain is almost unity and
the Zo is amazingly low, yet the circuit cannot deliver
very much current into a low impedance load, such as
a Grado headphone, 32 ohms. Imagine a car with 340
horsepower, yet which could only do 10 miles per
hour. Surprisingly, if we try to output more than a few
millivolts into the 32 ohm load, we will overdrive the
circuit, as we will break out of Class A operation.
Here is what happens in detail. Any variation in the
current flowing though the top triode will produce a
variation in the voltage developed across the plate
resistor. In turn, this voltage will be transmitted to the
bottom triode's grid, which can only see a few positive
volts before it is driven into positive grid voltage or, if
the voltage swings negatively, it is completely turned
off. The greater the value of the plate resistor, the
easier it is to overdrive the bottom triode, as a smaller
amount of current is needed to develop a large voltage
change across the plate resistor.
On the other hand, if we make the plate resistor
smaller in value, we gain dynamic headroom, but lose
the stellar specifications. In fact, if we set the plate
resistor to zero ohms, we end up with a classic
Cathode Follower with an active load, i.e. the bottom
triode. Of course, if the load we wish to drive is not a
punishingly low 32 ohms, the headroom issue is much
less of an issue. But if the load is a high impedance
one, such as a 100k potentiometer, then we must ask:
Why do we need to use a super low output impedance
buffer?
Optimal White Cathode Follower
We found that too large a value plate resistor limits
the potential output current from this buffer and that
too low a value reduces the buffer's specifications. So
the question is what would be the optimal value for a
given load and a given desired out voltage swing?
< PREVIOUS
pg. 5
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This was the question I had asked myself, when I was
disappointed by the results of an experiment wherein I
had built a White Cathode Follower with the aforesaid
tube and resistor values for driving a much more
reasonable load: the Sennheiser headphones, which
have an impedance of 300 ohms. After only a few
millivolts, clipping occurred. My expectation was that
the circuit should be able to deliver the idle current of
at least 10 mA into this load, if not almost 20 mA,
which would conform to classic Class A, push-pull
amplifier standards. I then replaced the plate resistor
with a 10k potentiometer with its center tab connected
to one of its outside tabs, which allowed for easy
adjustment of the plate resistor value.
After adjusting the potentiometer, I found the
optimal value according to the trace on the
oscilloscope to be 100 ohms. The lowness of the value
surprised me. I then wondered what the optimal value
would be for the 32 ohm load represented by the
Grado headphones. Even more surprising was that the
same 100 ohm plate resistor value yielded the best
performance into the 32 ohms, in spite of this load
being 10 times lower in value than the previous load.
Moving to the other extreme, I replaced the 32 ohm
resistor with a 3k resistor and retested. The 100 ohm
plate resistor value once again made for the biggest
and most symmetrical voltage swings. After some
mathematical introspection, everything made perfect
sense to me.
For any push-pull tube amplifier to work well, there
most be an almost identical signal presented to each
tube. (The signals must differ in phase.) In this circuit,
if the top triode sees an increase in its grid-to-cathode
voltage, then the bottom triode must see an equal
decrease in its grid-to-cathode voltage. How do we
ensure equal drive voltages for top and bottom triodes?
Let us start our analysis with the severest load
possible, not Grado headphone, but 0 ohms, in other
words, a dead short to ground via a large valued
capacitor.
<PREVIOUS
White
Cathode
Follower
with a
shorted
output
The top triode now functions as a Grounded
Cathode amplifier and does see the bottom triode at
all. The amount of current flowing from ground into
the capacitor then into the cathode of the top triode is
given by the formula:
Ip = VgGm´,
where
Gm´ = (mu + 1) / (Ra + rp).
Now as the bottom triode current flow is governed by
the top triode's current flow into the the plate resistor,
the amount of current flowing from the bottom triode's
plate into the capacitor is given by the formula:
Ip = VgGm
where Gm is the transconductance and
Gm = mu / rp.
By rearranging the formulas for current we get Vg = Ip
/ Gm´ for the top triode and Vg = Ip / Gm for the
bottom triode. Obviously, the only way that the two
grid voltages can match is if Gm´ = Gm. Expanding
this formula out yields:
(mu + 1) / (Ra + rp) = mu / rp,
which when we solve for Ra becomes
(Ra + rp) / rp = (mu + 1) / mu
Ra = rp(mu + 1) / mu - rp
Ra = (rpmu) / mu + rp / mu -rp
Ra = rp / mu
and as rp / mu = 1 / Gm
Ra = 1 / Gm.
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pg. 6
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Thus, the only way the Vg of the top triode can
equal Vg of the bottom triode is if the plate resistor
equals the inverse of the transconductance of the
triodes being used. (The test to put any tube circuit
equation through is to try the equation with a 6AS7
and then with a 12AX7 to check the equation for
absurdities.)
What happens if we chose to start with infinite ohms
as a load instead of 0 ohms. The answer is the same,
the optimal value for the plate resistor is the reciprocal
of the Gm of the triodes used, or what is the same
quantity, rp/mu.
White Cathode
Follower with
an infinite
impedance
output load
Now let us step back and look at what is happening
with this circuit in broad terms. Without an external
load the rp of the bottom triode will define the sole
load impedance for the top triode, remember we had
defined an infinitely high impedance load. Since the
gain of this circuit is less than unity, the cathode
voltage will slightly lag the grid's and this gap is the
change in the grid-to-cathode voltage that will prompt
a change in current flow through both the top triode
and plate resistor, which in turn will give rise to a
change in voltage across that resistor, which will then
be relayed to the bottom triode's grid. We need to
ensure that that bottom tube receives an identical gridto-cathode voltage signal as the top tube.
< PREVIOUS
pg. 7
The math can become quite thick here, but if we
think abstractly enough, it will not be too difficult to
follow. We know that if the top triode sees a +1 volt
pulse at its grid, its cathode will follow to some degree
less than +1 volt. Whatever this outcome may be, we
will refer to it as "Vg." Now Vg/rp equals the increase
current (Ip) flow through the entire circuit, as all
components are in current series with each other. Ip
times the plate resistor (Ra) equals the voltage pulse
that the bottom triode sees, which times the Gm of the
bottom triode will equal Ip, if the right value of Ra has
been chosen. Thus,
VgRa/rpmu/rp = Vg/rp,
which when we solve for Ra equals:
muVgRa/rp² = Vg/rp
muRa/rp = 1
muRa = rp
Ra = rp/mu.
Okay, what if we choose a load impedance somewhere
between zero and infinity, say, 10k. Same result, Ra =
rp/Gm. In this case, the load impedance is in parallel
with the rp of the bottom triode. So Vg/(rp||RL) equals
the increase current (Ip) flow through the top triode
and IpRa equals the pulse voltage to the bottom
triode. In this case, like the one with a shorted output,
we have true Class A output current swing capability,
so as the bottom tube approaches cutoff, the top tube's
current conduction will near twice its idle value. And,
of course, vice versa for negative input voltage swings.
Thus,
VgRa/(rp||RL)mu/rp = Vg/(rp||RL),
which when we solve for Ra equals:
VgRa/(rp||RL)mu/rp = Vg/(rp||RL)
VgmuRa/rp = Vg
muRa/rp = 1
muRa = rp
Ra = rp/mu.
Optimization and Zo
We can use the stock, long, complex equation for
output impedance for the White Cathode Follower or
we can realize that we have
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stipulated that Gm´ = Gm as a condition of
satisfaction in the quest for the optimally valued Ra,
and we found that Gm´ = (mu + 1)/(Ra + rp). In
effect, what we have actually done by specifying the
correct value for Ra is to balance the push-pull aspect
of the circuit, which includes each triode offering the
same output impedance to the load. Consequently,
Zo = 1 / 2Gm,
or
Zo = rp / 2mu.
Conclusion
We find once again that we cannot get something for
nothing: spectacularly low output impedance came at
the price of a disappointingly low input overload
voltage and a miniscule output current ability. But
what we did get, when we gave the White Cathode
Follower the optimal plate resistor value to work with,
was a buffer circuit twice as good as a textbook
Cathode Follower: half the output impedance and a
symmetrical output current swing with twice the
output current swing than a single triode Cathode
Follower.
<PREVIOUS
The Plate Follower
Also known as the Anode Follower, the Plate
Follower is in many ways the inverse of the Cathode
Follower. The Cathode Follower preserves the phase
of the input signal; the Plate Follower, inverts. The
Cathode Follower's output is taken at the cathode; the
Plate Follower's output, at the plate. The Cathode
Follower's input impedance is extremely high; the
Plate Follower's input impedance, relatively low, as it
is equal the value of resistor R1. And finally, where
the Cathode Follower can only aggressively pull the
output more positively; the Plate Follower, can only
aggressively pull the output more negatively.
Still, the Plate Follower makes a fine buffer and
boasts some very desirable features: a ground potential
input, adjustable gain, and low heater-to-cathode
differentials. The need for a coupling capacitor or a
connection to a high voltage input is eliminated in the
Plate Follower, as the grid is, in DC terms, at the
ground voltage. Unlike the Cathode Follower, whose
gain always falls short of unity, the Plate Follower can
achieve unity gain output, or if
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pg. 8
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desired, less than unity or more than unity gain. This is
a great help when cascading stages and just a bit more
gain is needed. Because the cathode is not floating at
some high voltage, the issue of maintaining a low
heater-to-cathode voltage difference does not arise.
The first step is to determine the open-loop gain (a)
of the Grounded Cathode amplifier and then the ratio
of resistors R1 and R2. Thus,
R = Ra||RL||R2
a = muR/(muR + rp + (mu + 1)Rk),
if Rk is bypassed, then
a = muR/(muR + rp)
Ratio = R2/R1
and finally,
Gain = aRatio/(a + Ratio + 1).
Now that we have the gain, we can determine the
output impedance.
Zo = (R||(rp + (mu +1)Rk))(Gain/a)
if Rk is bypassed, then
Zo = (R||rp)(Gain/a).
The Broskie Cathode Follower
Plate Follower circuit
The negatives for this buffer are that its bandwidth is
compromised by the low pass filter created by resistor
R1 working into the Miller Effect capacitance of the
triode and this same resistor defines the input
impedance of the circuit and serves to load down the
previous stage. Increasing the value of R1 unburdens
the previous stage, but worsens the high frequency
response. Additionally, the circuit requires three extra
resistors and, potentially, a bypass capacitor for
resistor Rk as well.
The Math
Since the Plate Follower is functionally equivalent
to the inverting Op-Amp circuit, the mistake that is
commonly made is to assume that the gain is given by
R2/R1. This formula works for Op-Amps as they have
near infinite open loop gain, whereas the Grounded
Cathode amplifier, which is at the core of this circuit,
has a very finite gain that can never exceed the mu of
the triode. Consequently, the formula for the gain of
the Plate Follower must include the relatively weak
gain of the triode used.
< PREVIOUS
pg. 9
Although this circuit was covered in the June Issue
in the article on converting a balanced signal into
single-ended one, it deserves to be reexamined as a
buffer circuit.
As a balanced to SE converter, the circuit function
is the subtract signal B for signal A. Because balanced
signals consist of two phases, the function effectively
becomes A + B. A signal common to both A and B, let
us call it C, is canceled, as the function C - C obtains.
Noise is usually equally shared between two balanced
signals and is thus eliminated in the single-ended
output. So far, the circuit mimics a transformer in
function, which was the goal.
But this circuit, which I have been testing and I have
found to work so very well that I have named it the
"Broskie Cathode Follower," differs from a
transformer in that it does not reflect impedances, but
rather provides a low output impedance and a
symmetrical current swing, i.e. it can aggressively
pull up or down like a White Cathode Follower.
The Broskie Cathode Follower is like a Cathode
Follower wedded to a Plate Follower, but not quite.
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A normal Cathode Follower does not have a pair of
resistors wrapped around its input and output.
Resistors R3, R4 were added to better balanced the
circuit's output impedance.
Broskie Cathode Follower
Once again, the easiest path to understanding what
the output impedance of a circuit is to imagine
connecting a 1 volt battery to the output (or any
portion of the circuit to determine the impedance at
that point) and then to calculate the resulting current
flow into or out of the battery and then taking the
inverse of the current as the output impedance. If we
calculate the output for the bottom half of this circuit
and then do the same for the top half, we will have,
once we parallel the two results, the output impedance
for the entire circuit. Starting with the bottom half
first, the 1 volt pulse at the output will be relayed
through the resistor string of R2 and R1 to the grid of
the bottom triode. As resistor R1 and R2 define a
voltage divider, only 0.5 volts of the original 1 volt
will present itself to the grid. This 0.5 volt signal is
then multiplied against the transconductance (Gm) of
the triode, which, if its cathode resistor is not
bypassed, equals
mu/(rp + (mu + 1)Rk),
otherwise just
mu/rp.
<PREVIOUS
For a 6DJ8, the result would be 5 mA greater
conduction, as 0.5 V x 0.01 A/V = 5 mA.
Moving to the top triode, the 1 volt pulse at the
output will be relayed through the resistor string of R4
and R3 to the grid of the top triode. As resistors R1
and R2 also define a voltage divider, once again only
0.5 volts of the original 1 volt will present itself to the
grid. But the cathode has not remained at a fixed
voltage as was the case in the previous example, but
instead has moved up +1 volt with the connection of
the battery. Thus the cathode voltage must be
subtracted from the change in grid voltage, in this case
0.5 V - 1 V = -0.5 V. Then this negative going signal
is multiplied against the transconductance (Gm) of the
triode, which much as in the previous case, if its
cathode resistor is not bypassed, equals
(mu +1)/(rp + (mu + 1)Rk),
otherwise just
(mu +1)/rp.
For a 6DJ8, the result would be 5.15 mA less
conduction, as -0.5 V x 0.0103 A/V = -5.15 mA. If the
mu of the triode is large, we can ignore the difference,
as it will be less than the variation between triodes
anyway. But if the mu is small, say 2, as it is for the
6AS7, then resistor R4 should be made (mu +1)/mu
times larger in value.
Why the difference in Gm from the top section to
bottom? When a signal is applied to the cathode rather
than the grid, we have more than just a change in the
grid-to-cathode voltage, we have a change in cathodeto-plate voltage as well. Do not forget that the triode,
unlike the transistor or MOSFET, has rp, a change in
cathode-to-plate voltage will mean a change in the
flow of current through the triode. So, effectively, the
cathode has an amplification factor of mu + 1 and a
transconductance figure of (mu + 1)/rp, while the plate
has an amplification factor of 1/mu and a
transconductance figure of 1/rp.
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pg. 10
NEXT >
Uses for this circuit are more numerous than just the
one of converting balanced into single-ended. For
example it could be used to buffer the output of a
Cascode amplifier. The Cascode suffers from a
virtually nonexistent PSRR, whatever is on the power
supply connection, will appear at the output. Now if
we connected the non-inverting input of the Broskie
Cathode Follower to the power supply connection and
the inverting input to the plate of the top triode in the
Cascode circuit, we will have scrubbed the power
supply noise from the signal. Like a transformer, if
only one half of the input signal is used, the gain will
fall by half as well. Of course, the inputs could be
switched if the inverted output of the Cascode was
desired. Another example would be to use two Broskie
Cathode Followers for the output of a balanced
preamplifier. This way we could achieve a clean, low
output impedance, balanced output.
The topology of the Broskie Cathode Follower can
be easily transposed to FETs for they are depletion
mode devices like the vacuum tube. With the addition
of appropriate biasing circuitry the topology can be
implemented with transistors or MOSFETs.
microphone preamplifier. To a rough sketch of two
directions he could travel is found in this month's
Design Idea.
The Circular/Bridge Amplifier
This circuit counts as a buffer in that offers a low
output impedance and no voltage gain. As the last few
issues of this journal have dealt with this circuit, we
will not go over the how's and why's, but rather what
to expect from this circuit as a buffer.
Circular/Bridge
Amplifier
The easy mistake to make is to assume that this
circuit is just two Cathode Followers in series with
each other and that as a consequence the output
impedance would equal twice that of one Cathode
Follower. Do not forgets that the power supplies are
effectively dead shorts to AC signals. It helps to
redraw the circuit so that the two power supplies are
shown shorted.
=
A sweet microphone preamplifier or phono headamp could easily be made from four FET's and a few
resistors. On the other hand, one of our readers,
Rowan, has asked for some direction in building a tube
and only tube based
< PREVIOUS
pg. 11
Connecting a 1 volt battery across the output
terminals will shift one terminal +0.5 volts higher and
the other -0.5 volts lower than at idle. The grids of
both triodes have not moved and remain fixed at the
negative bias voltage. Consequently, the tube whose
cathode was forced 0.5 volts negative sees a +0.5 volt
increase in its grid-to-cathode voltage and conducts
more current.
www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved
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Conversely, the tube whose cathode was forced 0.5
volts positive sees a -0.5 volt decrease in its grid-tocathode voltage and conducts less current. You can
readily see that the mid-point ground halves the
voltage presented to each triode, effective halving the
Gm of the triodes. But as the triodes are effectively in
parallel with each other, the total Gm sums to unity.
"But wait, there's more!" Remember what you just
read in the section on the Broskie Cathode Follower,
"When a signal is applied to the cathode rather than
the grid, we have more than just a change in the gridto-cathode voltage, we have a change in cathode-toplate voltage as well. Do not forget that the triode,
unlike the transistor or MOSFET, has rp, a change in
cathode-to-plate voltage will mean a change in the
flow of current through the triode."
So it would seem that the Gm of the triodes in this
circuit is effectively increased by (mu + 1)/mu because
of the signal is being applied to the cathode rather than
the grid. But this is not quite right. For right now, let
us forget the addition of the plate transconductance
and move our attention to the grid-to-cathode voltage
relationship.
We do not receive the full transconductance from
both triodes, as the grid's voltage is fixed and the
applied voltage is split between cathodes. In other
words, only half the Gm per tube is available to buck
the applied voltage, so we would expect the Gm to be
halved to
Gm = mu/2rp.
"But wait, there's more!" The power supplies are
floating in this circuit and represent (ideally) zero
ohms impedance to AC signals and they are attached
to the cathodes and move with the cathodes. Thus,
while one triode's cathode was being forced 0.5 volts
positive by the addition of the battery, its plate was
being forced 0.5 volts negative by the relayed signal
through the power supply connected the other tube's
cathode.
<PREVIOUS
Thus, the total plate transconductance (Gp) of the
triodes must be added to the half the effective Gm of
the tube:
Gm´ = mu/2rp + 1/rp.
While this circuit is still being run in strict Class A,
the triodes are effectively in parallel, as the power
supplies represent zero impedance to AC signals.
Consequently, the Gm is doubled to:
Gm´ = 2( mu/2rp + 1/rp)
which reduces to
Gm´ = (mu+2)/rp.
Warning, do not be fooled into believing that the
Circular/Bridge amplifier has in some respect departed
from the more conventional totem pole configuration.
It hasn't. In a properly designed Totem Pole amplifier,
the same effective transconductance obtains:
Gm´ = (mu+2)/rp.
=
Totem Pole vs. Circular/Bridge
In the case of the 6DJ8, the increase in Gm´ will be
slight as the mu (33) will predominate, but in the case
of a 6AS7 or a 12B4 or 6C33, the increase will be
dramatic as the these tubes have very low mu's.
In spite of the complexity of the circuit, the math for
the output impedance is simple:
Zo = 1/Gm´
or what is equivalent,
Zo = rp/(mu +2).
If multiple pairs of output tubes are used, then
Zo = rp/[n(mu +2)],
where n = the number of pairs used.
For example, if one 6AS7 is used to supply both
triodes for this circuit, the output impedance would be
280/(2 + 2) or 70 ohms.
www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved
pg. 12
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And if eight 6AS7's are used, the output impedance
would be 280/[8(2 + 2)] or 8.75 ohms. Not nearly as
low as we had hoped.
"But wait, there's more!" the assumption being
made here is that the rp is constant; alas, it is not. Nor
is the mu. Both vary with plate voltage and current.
(Of the two the mu is closer to being an actual
constant.) The RCA Receiving Tube Manual lists the
mu as 2 and the rp as 280 at 135 volts of plate voltage
and 125 mA of plate current. If we reexamine the tube
at 100 volts and 340 mA, with a grid voltage of -10
volts, we find that the mu has climbed to 2.5 and the rp
fell to 148 ohms.
Now, if we redo our calculation, the output
impedance is 148/[8(2.5 + 2)] or 4.1 ohms, which,
when placed in parallel with the 8 ohm load, becomes
2.7 ohms. (Yes, using the load to lower the advertised
Zo is cheating, but common.) Not bad, but then not
great. Once again, these formulas assume true Class
A operation. This makes sense, for if a triode stops
conducting, its Gm falls to zero and it offers no
resistance to applied voltage.
8
0
8
0
-32v
0
+32v
Here is where we can see that amplifier
classification is more than just pedantic taxonomy. If
we desire a flat, i.e. a consistent output impedance
from 1 watt to full output, then this amplifier output
stage or the rearranged version, the standard Totem
Pole, must either be run in strict Class A, strict Class
A2, or optimized Class AB. Optimized Class AB
means that the bias point has been carefully set so that
the overlap of the two output devices occurs where
each device has half its normal transconductance so
that when paralleled, a constant transconductance is
realized. This means that the optimized Class AB
amplifier will have twice the output impedance of the
same amplifier run in pure Class A.
//JRB
Audio Gadgets is software for the technically
minded audiophile. The quickest way to
understanding what Audio Gadgets is all about is to
imagine a programmable calculator designed for
the audio enthusiast. Audio Gadgets does far too
much to fit in even a 21" monitor; consequently, the
notebook metaphor is used to hold ten pages of
audio topics. Stepped attenuators to tube circuits.
Windows 3.1/ 95/98/NT
Shown above is the stepped attenuator page, which is only one
of ten audio pages.
< PREVIOUS
pg. 13
www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved
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Design Idea:
Tube Microphone Preamplifier
Will a differential input plate follower configuration
create a low Z in, low enough to work as a
transformerless input pre? Also instead of using a split
rail I want to use a JFET in a grounded gate setup
with something like 500 ohms on the drain. So far it
sounds terrific. Tube CAD helps a lot but some things
need the attention of the algorithmic genius himself.
Your response will be appreciated. By the way I made
the February Circuit of the Month regulator and all I
can say is it's a serious thing indeed.
Rowan
Thanks for the new title. I like it, but it will not fit on
a personalized license plate.
In spite of the title, I have to admit that I know very
little about the requirements for a microphone
preamplifier. How much gain is needed? Balanced
outputs or a single-ended output? So those in the know
do please E-mail the required specifications.
Still, a microphone preamplifier cannot differ too
radically from an MC pre-preamplifier. Low noise is
the requirement.
A Plate Follower feedback arrangement would
provide a low impedance input, but one triode would
not provide sufficient gain to both sustain the feedback
and provide a high gain output. This means we must
cascade two triodes to increase the total gain from the
preamp.
<PREVIOUS
Your disdain for negative power supplies is
understandable, particularly, if you wish to use tube
rectifiers. Nonetheless, I do not see the FET working.
You see FETs have a resistive region where the drain
impedance is significant. This occurs up to a few volts
and then the FET enters its saturation region, with its
nearly infinite drain impedance. The 6DJ8 requires
about a 2 volt cathode bias to draw 10 mA of current.
In other words, the point at which the FET becomes a
current source is too high to bias up a 6DJ8. Even a
small negative power supply voltage (-5 volts) would
greatly help.
Finding the right FET can also be
problematic, as a high IDSS will be needed
so that the idle current can be cut back by
using a source resistor. The only FET I can
think of that would prove quiet and beefy
enough is the 2N4391. (Look for the metal
can version: TO-18.)
On the other hand, using a negative power supply
has some real advantages. The most important of
which is that the ground is freed up from having to
support both the signal and amplifier circuit currents.
This is a much better arrangement, as all the active
circuitry is maintained by the plus and minus legs of
the power supplies and the input and output signals
have the ground bus to themselves. Add to this
advantage the fact that active current sources really are
not needed, as large valued cathode resistors are easy
to implement.
One advantage to split-rail power supplies is never
mentioned, but should be. A split-rail power supply is
1/4 as dangerous as the same total voltage single rail
power supply. How so? Let us say that you are
fiddling with a chassis with a +/1 200 volts power
supply. Your left hand is turning the metal volume
knob, while your right hand is attaching a scope probe
to a resistor. But back of your right hand also hits a
part charged to +200 volts. A shocking experience.
www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved
pg. 14
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Now if the same thing happened with a single rail +400 volt power supply, the shock would be four time worse,
as the danger is equal to the voltage squared.
The last advantage to a split rail power supply is that it allow for some of the noise canceling tricks that I am so
fond of in this journal and in the GlassWare website's Circuit of the Month articles. Look carefully at the two
resistors and one capacitor network that serves as the common cathode resistor for the Differential amplifier at the
input of the circuit below. It is required to inject more negative power supply noise current into the Differential
amplifier so that the noise at the plate will be cancelled.
Plate Follower based microphone preamplifier
Plate Follower based microphone preamplifier in AC terms
< PREVIOUS
pg. 15
www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved
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A vacuum tube
microphone preamp
that uses multiple
tubes in parallel to
lower the noise level
and Broskie
Cathode Follower to
both buffer the
output and convert
the balanced signal
into an unbalanced
output.
Differential amplifier based microphone preamplifier
An Alternative
Tube Noise
Now, if a single rail power supply must be used and
FET current sourcing is not an option, the alternative
might be something less fancy, such as the above
circuit.
This circuit is quite simple: a Differential amplifier
handles the balanced inputs and the parallel triodes
lower the noise. The buffer output stage, the Broskie
Cathode Follower, is described both in this issue and
in June's article on Unbalancing Acts. Basically, it
mimics a transformer by converting the balanced input
signal into an unbalanced output. It also provides a
low output impedance of about 450 ohms, which if too
high for your application, can be lowered to about 130
ohms by capacitor bypassing the two 287 ohm cathode
resistors.
Unfortunately, ultra low noise and tubes seldom go
together. Two issue arise with using tubes in low noise
applications: electrical noise from within the tube and
microphonic noise generated from outside the tube. A
floating sub chassis can make an otherwise unlistenable amplifier quiet. I like to use L channel
extruded aluminum, which is easy to punch and drill.
Sorbathane sheeting works well at isolating the
vibrations, as do eyeglass rubber bands.
Assuming that the mechanical design is adequate,
we still have the problem of noise intrinsic to the tube.
High transconductance helps as it reduces the thermal
resistor noise of the tube, but other issue are evolved
in the generation of tube noise. The only answer is to
hand pick quiet tubes. I have used a small testing jig to
test 6DJ8 type tubes. It consisted of a small chassis
with one socket and two BNC connecters for mating
with an oscilloscope. The circuit within consisted of a
FET current source load for each triode section and a
regulated heater power supply. The grid was grounded
and the cathode returned to ground via a bypassed 200
ohm resistor. The trick was to look at the shape of
noise as well as the amplitude.
Extruded aluminum drilled
and punched to accept
tube sockets makes an
excellent platform for a
tube based project.
<PREVIOUS
www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved
pg. 16
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Click image to see enlargement
Sharp, chaotic, jagged mountain ranges were much
worse sounding than foggy fuzz. A wood pencil was
used to ring the tube to its susceptibility to
microphonics.
Phantom Power Supply
Condenser microphones often require a 48 volt
power supply to charge up their elements. Many solidstate microphone preamps use electrolytic capacitors
to isolate this voltage from the preamp's delicate
transistors. Tubes, on the other hand do not fear high
voltage and 48 volts is almost laughably wimpy. Still,
be careful. I once looked the lowest voltage capable
of killing someone under normal conditions and I
was shocked to find it to be an amazingly low 42
volts!
Since tubes do not fear 48 volts, even if we do, why
not dispense with the cheap capacitors altogether.
A two-pole switch can be used to connect the
junction of the two 6.8k input resistors to either
ground or 48 volts and change the value of the cathode
resistor of the first stage to match the shift in grid DC
voltage. (Actually, I would use a three pole, four
position rotary switch to cover the two aforesaid tasks
and to mute the output while switching from one mode
to another.)
The power supply should be very clean and probably
regulated. The heaters definitely should be fed a
regulated voltage that is floated at + 48 volts; yes, you
can use the same 48 volts used to bias the condenser
microphone. One danger with 3 pin regulators,
whether they be fixed or adjustable, is that the internal
gain falls with frequency, so the declining effective
feedback ratio defines an inductive element, which
when in series with the wrong capacitance value
produces oscillation. The easy workaround is to place
a high wattage resistor in series with the regulator's
output before connecting the output to the heaters.
This means something like a 10 volt regulator should
be used to make up for the loss through the resistor.
Besides keeping the regulator from oscillating, a series
resistor will extend the tube's heater life, as the resistor
will absorb the inrush current that flows into a cold,
i.e. low resistance heater element. A large valued
capacitor can still be used and probably should be used
to shunt the heaters themselves.
Rowan, good luck with whichever direction you
choose to follow and keep us posted.
//JRB
Condenser microphone preamplifier
< PREVIOUS
pg. 17
www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved
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E-mail
Part 2 to last month's Ian's E-mail
Subject: SE / PUSH-PULL
First of all kudos to you and to your fine magazine. At first, I
only understood a third of Issue 1, but now that I just reread it,
I understand about 90% of it. I don't know if I will ever hit
100%, but I'll try.
So here is my question. I love the idea you have of converting
a ST-70 into a para feed, SE amplifier using tubes instead of
chokes. I have a pair of MK 3's that I would like to convert to
style of amplifier. So my question is: Would it be possible to
make the amplifier work like the Nelson Pass solid-state SE, the
Aleph, which is SE up to a certain amount of wattage and then
switches to push-pull Class A. amplification for the rest of
output power? I know the solid-stage guys have a huge
advantage in that they are willing to use IC's in the signal path,
which we tube purist aren't, but at the cost of less design
flexibility. So is this worth pursuing? Thanks in advance.
Ian
until the desired break voltage was reached and
the amplifier switched over to being a Class AB
push-pull one. This time we will look into using a
current source made out of discrete parts. The
advantage this approach holds over the first is
that high quality chokes are both hard to find and
expensive, not to mention physically large. A
further advantage is that active current source
can made to track the current flow in the other
tube so as to ensure a better balanced idle
current. Additionally, this arrangement works a
little more easily with a mono-polar power supply,
i.e. one without a negative voltage for biasing the
output tubes.
An Op-Amp based current source could be
used and it would yield the tightest current
balance, but at increased complexity and
expense. The simplest circuit would be made out
of a few resistors and capacitors and two
MOSFETs.
Last month we covered a modification to the
Dynaco MK 3 that resulted in an SE/AB amplifier.
That modification required the addition of placing
a choke in series with the cathode of one of the
output tubes. The choke made a constant current
source out of the tube, as its cathode would
follow its grid's voltage movement so well that no
variation grid-to-cathode voltage occurred,
The output stage
of a Dynaco MK
3 converted into
an SE / PUSHPULL amplifier.
Editor
<PREVIOUS
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pg. 18
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Click to move to previous page
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Moving about in the Tube CAD Journal
Tube CAD Journal Publishing
Publisher
GlassWare, creators of Audio Design Software
Our Purpose
The Tube CAD Journal is a monthly online magazine
devoted to tube audio circuit design. Each month we will
present some fresh looks at some old tube circuits and some
altogether fresh tube circuits as well (yes, new tube circuits are
possible). Circuits and more circuits. While we plan on
covering complex tube circuits, like phono preamps or power
amplifiers, our focus will be primarily on elemental circuits.
Elemental circuits are the primary topologies, or part
configurations, arrangements that can stand on their own as
recognizable functional circuits although they may be part of a
larger circuit. A power amplifier circuit, such as the famous
Williamson, comprises several sub-circuits: the Grounded
Cathode amplifier, the Split-Load phase splitter, the
Differential amplifier and finally a push-pull output stage. Just
as we must understand how a resistor or a capacitor functions in
a simple circuit, we must understand the function and logic of
these elemental circuits before we can understand more
complex compound circuits.
Why a Webzine?
The original intent was to print a conventional magazine. We
knew there was a need. A query on our Tube CAD registration
cards that a magazine devoted to tube circuit design drew an
overwhelmingly loud "YES." Still, we knew the difficulty and
impracticality of starting yet another underground tube audio
magazine.
The Web offers the publisher some great advantages over the
traditional approach: worldwide distribution, free subscriptions,
no paper (for those who must own a paper version, the size of
the journal has been left small enough to be printed on A4 or
8.5" by 11" three-hole punched paper for compilation in a threering binder), live forums, no Post Office, color, motion, a
glossary.
Schematics can now evolve, as the web allows for the easy
display of animated GIF's, which display color and motion.
Schematics can now show more than just part connections, they
can reveal voltage potentials, current flow directions, and
possibly, relative impedances.
Math errors and typos will not live indefinitely on a paper
page; once spotted, the Web page can be corrected quickly.
We look forward to your letters, suggestions and
contributions.
Editorial Staff
Editor: John E. R. Broskie
Copy Editor: Anna Russomano Broskie
Mailing Address
P.O. Box 67271
Scotts Valley, CA 95067-7271
E-Mail Address
[email protected]
Letters to the Editor
The Tube CAD Journal welcomes letters from its
readers. Please share your views, opinions, design
ideas, and critiques with us. Letters should be brief and
accompanied by your name, e-mail address (please
indicate if we can publish your e-mail address), city and
country. All letters become the property of Tube
CAD Journal and will be edited for length and clarity.
Please send letters to the POB or our e-mail address.
Article Submission
A self addressed, stamped envelope must accompany
all mailed editorial submissions. We are not responsible
for unsolicited materials.
Advertising
Please contact us if you are interested in placing an ad
in the Tube CAD Journal.
Printing
While no portion of Tube CAD Journal can be
reproduced for profit without the written permission of
the publisher, we encourage the reader to print one
copy of each Web page for easier reading and personal
archiving. First, click "File" and then "Page Setup"
on your browser menu bar and set the left page margin
to ½ inch.
Tube CAD Journal is published monthly by
GlassWare. ©1999 All Rights Reserved.
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