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Patrick Turner
 
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Default old stability equation



Piotr Wyrostek wrote:

Hello world,

In an old tube book I found an equation or rather inequality
- upper limit for the amplification factor allowing to work
without oscillations caused by C(ag) in a triode (CC) amp:

k=sqrt(0,25*S/(2*pi*f*C(ag)))

k is the amplification factor (mi)
S is the conductance
C(ag) is the anode-grid capacitance

f is the frequency.

If the equation were correct, almost every ECC83 stage would oscillate on
high audio frequences, for example, when we have 220k on anode,
1mA anode current, ~ 200V on anode and 680 ohm on catode
we get mi = ~76 (Mullard data).

Then, for 20kHz, we get (S = ~1.5 mA/V, C(ag)=1.7pF):

(0.25*(1.5/1000))
k = sqrt( -----------------------) ~ 41
6.28*20000*(1.7/10^12)

From the equation, the gain should be no more than 41 when the frequency
is 20kHz, but is much more - 76. (we may assume several hundred pF
of the next stage Miller capacitance, and even than the gain will be above 41)

Is the equation correct and is the above really the case,
or am I taking something wrong?

Piotr Wyrostek


Well, you got me this time.
I just build it and test it, and if it don't oscillate, all is well.

Its hard to get a 12AX7 to oscillate from a miller effect,
but two or three cascaded might oscillate if there is NFB,
because, say, after 3 identical stages, the phase shift at each stage's
-3dB cut off is -45 degrees, and at soon after -3dB, its -60degrees,
so 3 stages makes 180 degrees, and the open loop gain is still well above 1.0,
to the NFB will make it oscillate becaue the NFB has become POSITIVE FB,
an essential thing required for oscillation.
The miller effect in just one triode stage can't produce a phase shift of more
than
-90 degrees, so how could it oscillate?
There would have to be extra phase shift generated some place.

Tubes with high Gm might oscillate parasitically, at some HF,
because the miller effect and stray inductances and other stray C might cause
it to become an oscillator at somre HF.

What can oscillate, will oscillate, and part of the art of building good
AF or RF amplifiers is to stop any possibility of oscillations at frequencies
outside the
audio, or RF amp bandwidth from occuring.

Patrick Turner.


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Tom Schlangen
 
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Hi Piotr,

In an old tube book I found an equation or
rather inequality - upper limit for the
amplification factor allowing to work
without oscillations caused by C(ag) in a
triode (CC) amp:


[...]

Is the equation correct and is the above
really the case, or am I taking something wrong?


I doubt that this formula given is correct for
a single gain stage under consideration and I am
quite sure that when you breadboard your example
(simulating estimated Miller capacitance somehow)
you will find so. Just try it :-)

Tom

--
The large print giveth, the small print taketh away.
- Tom Waits
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