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LW1DSE > TUBES 13.01.18 23:12l 240 Lines 11183 Bytes #999 (0) @ WW
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Subj: The æ (mu) Follower
Path: IW8PGT<IZ3LSV<I0OJJ<LU4ECL<LU4ADN<LU1DBQ<LU7DQP
Sent: 180113/2045Z @:LU7DQP.#LAN.BA.ARG.SOAM #:27256 [Lanus Oeste] FBB7.00i
From: LW1DSE@LU7DQP.#LAN.BA.ARG.SOAM
To : TUBES@WW
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The æ-follower is a high gain, low output impedance inverting stage
with excellent PSRR and very low non-linear distortion; making it enormously
popular for hifi.
The æ-follower will clip hard when overdriven, producing a rich
spectrum of both odd and even harmonics. However, because the two triodes are
AC coupled together the stage can suffer from blocking distortion, although a
simple DC coupled version appeared in the unusual Juergen-Simon 'Advanced
Bass Preamp' in the early 1990s.
o +B
³
³
³
³ V2
ßßß
ÚÄÄÄÄÄÂÄÄÄ-----
³ ³ ÚÄÄÄ¿
³ ³ ³ C4 ³³
³ ³ ÃÄÄÄÄÄÄÄÄÄ´ÃÄÄÄÂÄo Vo1 (Low Zo)
³ ³ ³ ³³ ³
³ ³ ³ ³
³ C3 ± ± ³
ÄÁÄ ± ± Rk2 ³
ÄÂÄ ± ± ±
³ Rg2³ ³ ± Rl
³ ÀÄÄÄ´ ±
³ ³ ³
³ ± ³
³ ± Ra ÄÁÄ
³ ± ///
³ ³ ³³
ÀÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄ´ÃÄÄÄÂÄo Vo2 (High Zo)
C1 ³ ³³ ³
Vi ³ C5 ³
³³ ßßß ³
oÄÄÄ´ÃÄÂÄÄÄÄÄÄÄ----- ³
³³ ³ ÚÄÄÄ¿ V1 ³
³ ³ ±
³ ÃÄÄÄ¿ ± Rl'
³ ³ ³ ±
± ± ÄÁÄ ³
± Rg1 Rk1 ± ÄÂÄ C2 ³
± ± ³ ³
³ ³ ³ ³
ÄÁÄ ÄÁÄ ÄÁÄ ÄÁÄ
/// /// /// ///
Figure 1:ÿSchematic of a æ follower.
Operation of the circuit is simple: The lower triode (V1) is a
normal grounded cathode gain stage, except that it has an active load formed
by the upper triode and load resistors. The upper triode (V2) is an ordinary
cathode follower. The signal at the anode of the lower triode is fed to the
grid of the cathode follower. Because the cathode follower has close to unity
gain, the signal voltage at the top of the load resistance will be almost the
same as that at the bottom, so almost no signal current is wasted through
it;- they have been "bootstrapped" and the cathode follower acts as a
constant current source (CCS). Thus the AC impedance of the load resistors is
greatly magnified thanks to the cathode follower, so that the gain of the
lower triode become equal to the æ of the valve- hence the name æ-follower.
There are also two possible outputs from the circuit:
* The upper output, from the cathode of the cathode follower, has a very low
output impedance capable of driving a very heavy load such as a tone stack or
power valve, and this is the output normally used.
* The lower output, from the anode of the lower triode (shown in faint), has
a higher output impedance and (slightly) higher gain. Unfortunately, any load
we attach to this output appears in parallel with the load formed by the
cathode follower. Unless the load impedance we attach to this second output
is very large (e.g., greater than 5Meg, which would probably mean a cathode
follower, cathodyne or long tailed pair), it will reduce effectiveness of the
cathode follower as a CCS, dragging the gain of the whole stage down. However,
the lower output is usually set at a fairly low DC voltage making it
particularly suitable for DC coupling to a following stage (such as a long
tailed pair). Usually, a DC coupled stage presents an almost infinite load,
so the gain of the æ-follower would not be compromised.
For simplicity, the two triodes are usually the same type, but they
don't have to be. High gm valves are well suited to cathode follower part of
the circuit (such as an ECC82 / 12AU7). High æ valves tend to be less suited
to the lower section since they tend not to operate reliably at low anode
voltages. Design of the stage is quite straight forward. The following
example uses an ECC81 (12AT7) because it has a respectable gm and high æ,
but actually works well at low anode voltages. The HT is 285V.
The lower triode: The quiescent anode voltage of the lower triode
(Va1) isn't critical, and is usually made to be in the region of 70V to 100V,
or one third of the HT voltage. This means that the voltage across the upper
triode is equal to HT - Va1. In this case we will set the lower triode's
anode voltage at 85V. This leaves 285 - 85 = 200V for the upper triode.
Because the upper triode forms a CCS, it forces the AC load line of the lower
triode to become almost horizontal. Since we have just chosen the anode
voltage, we can draw a vertical line at Va = 85V and choose any bias point on
it we like.
In this case a bias of -1V looks good. Any less and we would be
entering grid current territory, any more and we would be operating in the
region of low æ, as well as restricting the anode current to a pathetic
trickle. At our chosen bias point the anode current is 2.5mA. Use Ohm's law
to calculate the value of bias resistor:
Rk1 = 1V / 0.0025A = 400ê .
The nearest standard is 390ê.
It is usual to add a cathode bypass capacitor to the cathode of V1.
Leaving it unbypassed would hardly affect the gain in this case, but it would
increase the anode impedance which reduces the PSRR factor and increases the
output impedance of the lower output. The bypass capacitor's value can be
found assuming a 1Hz crossover point as:
C2 = 1 / (2ã * f * Xc)
C2 = 1 / (2ã * 1Hz * 390ê)
= 410 æF
The nearest standard is 470æF, at 16 VDC.
The grid-leak resistoris chosen in the normal way, and 1Mê is usual.
The upper triode: We already know that we have 200V of HT available
for the upper triode and we can mark this point on the x-axis, and we now
also know that the anode current is 2.5mA (current through the triodes is the
same because they are in series). We can therefore choose any bias point that
lies on the 2.5mA line, and it is usual to bias to half HT (200 / 2 = 100V)
for maximum headroom in the cathode follower. This ensures the cathode
follower acts as a CCS for a long as possible before cutting off or
saturating.
In this case at half HT (Va = 100V) and an anode current of 2.5mA,
the bias is about -1.3V. We can now draw a load line through the two points
and use it to find the total value of load resistance (Rl + Rk2). In this
case the load line tells us (Va = 200V / Ia = 5.2mA) that we need a total
load of 38Kê. Use Ohm's law to calculate the value of bias resistor
Rk2 = 1.3V / 0.002A = 520ê.
The nearest standard is 560ê.
The bias resistor is subtracted from the total load we need, making
38000ê - 560ê = 37440ê. The nearest standard is 39Kê and this is what we'll
use for Ra.
The quiescent anode voltage on the graph is 100V. This is actually
the anode to cathode voltage, so the true cathode voltage will be:
285V - 100V = 185V.
Bootstrapping, grid-leak and input capacitor: Now we have set the
upper triodes conditions we can work out what AC load it present to the lower
triode.
The gain of the cathode follower can be approximated using:
æ / (æ + 1). Or, a more accurate figure can be found using the open-loop gain
read off the load line, which is about 40 in this case.
Av = Ao / (Ao + 1)
Av = 40 / (40 + 1)
= 0.98
Due to bootstrapping, the AC load presented to the lower valve will
be:
r(ccs) = (Ra + Rk) / (1 - Av)
r(ccs) = (39000ê + 560ê) / (1 - 0.98)
= 1.98 Mê.
This is an extremely high value load, and will indeed make the AC
load line of the lower triode almost horizontal.
As usual the grid-leak resistor on the cathode follower is also
bootstrapped and can be made smaller in value than we might normally use,
which will reduce resistor noise and blocking distortion. If we use a value
for Rg2 of 220Kê, the effective input impedance of the cathode follower will
be:
Zin = Rg2 / (1 - Av * (Ra / Ra + Rk2))
Zin = 220000ê / (1 - 0.98 * (39000ê / 39000ê + 560ê))
= 6.5 Mê.
Since the input impedance of the cathode follower is so high, the
input coupling capacitor (Cg2) can be chosen based solely on a desired
reactance at a low frequency. For a reactance of equal to Rg2 (at 45ø) at
10Hz:
C3 = 1 / (2ã * f * Xc)
C3 = 1 / (2ã * 10Hz * 220000ê)
= 72nF
The nearest common value is 68nF, although anything from 47nF to
0.1æF would also be fine.
Gain: The gain to the lower output is equal to æ, assuming the
output has a load greater than 5Meg attached. The data sheet quotes æ for
the ECC81 as 70, although looking at our horizontal load line it looks to be
more like 60 because we are operating at such a low anode current.
When using the upper output, the gain of the cathode follower needs
to be taken into account, so the gain to this output is 60 * 0.98 = 58.8
(the difference between the two is so small that there is little point in
using the lower output, except for DC coupling).
Output impedance: The output impedance from the upper output is
simply that of the cathode follower, which can be closely approximated as:
Zout = ra/æ = 1/gm
Using ra and æ from the graph, this yields:
16000ê / 60 = 267ê
which is very low indeed!
Heater elevation: Because the upper cathode is at a high voltage it
is usually necessary to elevate the heater supply to avoid exceeding the
maximum rated heater-cathode voltage (Vhk). For the ECC81 this is 90V, so we
would need to elevate the heater by at least 100V.
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º Compilled from various sources in Internet. Translatted to ASCII by LW1DSE º
º Osvaldo F. Zappacosta. Barrio Garay, Almte. Brown, Buenos Aires, Argentina.º
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