[Eeyore]

In the recent thread about west's preamp his final CF stage was discussed.

Several ppl criticised my analysis of the cathode follower stage suggesting that
I had to draw a load line to establish it's 'gain'.

Those critics has now gone silent.

What happened ?

Graham

[Patrick Turner]

Eeyore wrote:

In the recent thread about west's preamp his final CF stage was discussed.

Several ppl criticised my analysis of the cathode follower stage suggesting that
I had to draw a load line to establish it's 'gain'.

Those critics has now gone silent.

What happened ?

Graham

Maybe they got distracted by all your wisest, hummour filled and
information rich posts
elsewhere.

But to work out the gain of a CF, you do need to draw the load lines
first for
common cathode gain using the cathode load in the anode circuit,
as per usual practice, including both dc and ac coupled loadings.
Say you find gain = 16. It means 1Vg in gives 16Va out.
When the load is moved to the cathode, the 1V is in series with the 16Vk
out,
so you need 17Vgin for 16Vkout, and gain = 16 / 17 = 0.941.
The term gain is misleading, because there is no actual voltage gain,
and insertion loss would be more appropriate, but ppl say gain with CF,
and its just convention.

So for a CF, closed loop gain for CF, A', = A / ( A + 1 ) where A is
open loop gain
or the anode circuit gain if the load was in ther anode circuit.

Obviously where A is high, A' is close to A, and most ppl don't bother
doing the load lines
as long as the load is more than 2 x Ra, and sufficient idle current
exists
to get the desired Vswing without cut off in the loads.
Ie, the CF is designed in the mind over a coffee break.

Patrick Turner.

[Eeyore]

Patrick Turner wrote:

Eeyore wrote:

In the recent thread about west's preamp his final CF stage was discussed.

Several ppl criticised my analysis of the cathode follower stage suggesting that
I had to draw a load line to establish it's 'gain'.

Those critics has now gone silent.

What happened ?


Maybe they got distracted by all your wisest, hummour filled and
information rich posts elsewhere.

:~)


But to work out the gain of a CF, you do need to draw the load lines
first for common cathode gain using the cathode load in the anode circuit,
as per usual practice, including both dc and ac coupled loadings.
Say you find gain = 16. It means 1Vg in gives 16Va out.
When the load is moved to the cathode, the 1V is in series with the 16Vk
out,
so you need 17Vgin for 16Vkout, and gain = 16 / 17 = 0.941.
The term gain is misleading, because there is no actual voltage gain,
and insertion loss would be more appropriate, but ppl say gain with CF,
and its just convention.

I'm well familiar with that convention. No problem. I see no reason to distinguish
loss or gain when a number suffices.


So for a CF, closed loop gain for CF, A', = A / ( A + 1 ) where A is
open loop gain or the anode circuit gain if the load was in ther anode circuit.

Obviously where A is high, A' is close to A, and most ppl don't bother
doing the load lines as long as the load is more than 2 x Ra, and sufficient idle
current
exists to get the desired Vswing without cut off in the loads.

Naturally.


Ie, the CF is designed in the mind over a coffee break.

That was my thinking too.

I came across a document btw which gave a quick approximation to the output Z of a CF
as 1/mu. My presumtion was that the gain was Rl/(Rl+output_Z) too.

Are you familiar with that method ?

Graham

[Patrick Turner]

Eeyore wrote:

Patrick Turner wrote:

Eeyore wrote:

In the recent thread about west's preamp his final CF stage was discussed.

Several ppl criticised my analysis of the cathode follower stage suggesting that
I had to draw a load line to establish it's 'gain'.

Those critics has now gone silent.

What happened ?


Maybe they got distracted by all your wisest, hummour filled and
information rich posts elsewhere.

:~)

But to work out the gain of a CF, you do need to draw the load lines
first for common cathode gain using the cathode load in the anode circuit,
as per usual practice, including both dc and ac coupled loadings.
Say you find gain = 16. It means 1Vg in gives 16Va out.
When the load is moved to the cathode, the 1V is in series with the 16Vk
out,
so you need 17Vgin for 16Vkout, and gain = 16 / 17 = 0.941.
The term gain is misleading, because there is no actual voltage gain,
and insertion loss would be more appropriate, but ppl say gain with CF,
and its just convention.

I'm well familiar with that convention. No problem. I see no reason to distinguish
loss or gain when a number suffices.

So for a CF, closed loop gain for CF, A', = A / ( A + 1 ) where A is
open loop gain or the anode circuit gain if the load was in ther anode circuit.

Obviously where A is high, A' is close to A, and most ppl don't bother
doing the load lines as long as the load is more than 2 x Ra, and sufficient idle
current
exists to get the desired Vswing without cut off in the loads.

Naturally.

Ie, the CF is designed in the mind over a coffee break.

That was my thinking too.

I came across a document btw which gave a quick approximation to the output Z of a CF
as 1/mu. My presumtion was that the gain was Rl/(Rl+output_Z) too.

Are you familiar with that method ?

Output Z could never be 1 / µ .
This is because µ is just an amplification factor, and in fact µ = Gm x
Ra.
For all tubes, this equation is the fundemental gain equation and it
also works
for all devices regardless of whether current is required at the
controlling input
terminal. But with devices controlled by non current inputs, fets and
tubes, it is certainly the key
equation, and for a power mosfet, 2SK134, Rd = 220ohms, Gm = 0.9A/V, so
µ = 198.
Because solid fet devices have such huge variations of Gm and Rd,
engineers never
use tube derived ways of describing mosfet output stage functions.
And certainly they deny a BJT has a µ.
Its usually a very high figure when you do measure it.
But I digress.
Convention for tubes is what we are considering. Screen driven tube
inputs also exhibit a µ and gm,
and can be measured if need be.
Things get a lot more complicated about gain when you have an
ultralinear output circuit
with input to the screens 1/2 way between triode and fixed voltage for
pentode,
and you also have cathode FB applied. The equations are much
bigger/longer, and I have the UL
formulas here from the 1955 Radiotronics technical publications, but no
calculations for
pure cathode feedback or combined CFB + UL.
I digress yet again, but in considering output R at cathode and anode
there can be a lot to consider; a CF is very simple and easy.
Anode Rout is also easy, simply Ra in parallel with RL, including DC
load // AC coupled load.

Rout is very close = 1 / gm, and gm is amps/volt

But that isn't really true either; Rout really is 1 / gm in parallel
with whatever RL is present.
So if you have a 1/2 6SN7, gm = 2mA/V, cathode RL = 50k, the Rout = 500
ohms // 50k.
Since 50k is so much larger than 1/gm, it is neglected.

If the open loop gain was 16, RL = 50k, then closed gain of CF by your
formula = 50,000 / 50,500 = 0.990099009

Clearly this is quite wrong, so the formula isn't right at all.

For a 6SN7 where 1V applied between grid and cathode is required to make
a 16V change in load voltage,
CF gain will be A / ( A + 1 ), always, where A is the open loop gain
calculated as A = µ x RL / ( Ra + RL )

So gain should be 16 / ( 16 + 1 ) = 16 / 17 = 0.941.

With a typical signal bjt, voltage gain into say 7k might be 700, so if
Rc is very high,
open loop gain is simply gm x RL, in this case A = 700 = gm x 7,000, so
gm must be 0.1A/V.
Just what Rc is becomes unimportant, a lot higher than the load usually.
Emitter follower Rout = 1/gm = 1/ 0.1 = 10 ohms, typical little bjt
results.

Same for a pentode. A = gm RL very approximately, because Ra is so
large.
Typical signal pentode Ra = 500k, and if the gm = 0.005A/V, then µ =
2,500.
So if there is a CCS load on a CF with a pentode, gain = 2,500 / 2,501 =
0.9995.
In practice you never see this, and a CF load would be 50k
where pentode gain roughly is 0.005 x 100,000 = 500, so CF
gain = 500 / 501 = 0.998, and the gain reduction due to NFB
is 500 times, or 54dB, and if the THD with plate loading was 5% at
50Vrms,
it would be 0.01% at 50vrms from the cathode, and at 0.5Vrms, maybe
0.0001%,
and impossible to measure easily.

With a pentode CF, ppl can cheat their way and use a 1k load.
OLG = 1,000 x 0.005 = 5, and with CF, its 5 / 6 = 0.833, and if the idle
current was 5mA,
maximum Vout = idle current x 0.707 x RL = 3.53Vrms.
OLG THD might be 5%, but at 0.35V its 0.5%, and with the FB its reduced
to
0.1% at 0.35V so this might be acceptable depending on the application.
The bjt performance with 1k will be a lot better because the gm is so
much higher,
at 0.1A/V, a typical signal bjt has a gain of 100 into 1k,
and in EF this gives a reduction of THD of about 100 times, not just 5
times with the pentode.
So for a pentode, the load should be much higher, say 20k, and the the
amount of gain reduction with CF and EF become similar,
and proportional to their respective gms.
Which sounds better can always be argued....

Where Rout from CF becomes high with respect to a load is in a OTL amp
where
one might have a CF + CF drive to speakers, circlotron or some such
and if the tube gm = 120mA /V with several paralleled tubes, Rout = 8.3
ohms,
and considerable loop FB needs to be used to linerarize the deal.
I love it when OTL ppl say the sound of no OPT is so clear,
but its really because of the usual 40db of GNFB.
The load is plotted as a very near vertical
line on the anode curves, and THD is usually maximal with any load from
1 to 50 ohms.
Gain is really low, and to produce 20V change in an 8 ohm load, gm =
0.12A/V, you need
66V applied between grid and cathode, so a total 86V needs to be applied
to the grid,
and class AB2 class B is often employed.
Mosfets are so much easier and better IMHO.


Patrick Turner.







Graham

[Eeyore]

Patrick Turner wrote:

Eeyore wrote:

I came across a document btw which gave a quick approximation to the output Z of a CF
as 1/mu. My presumtion was that the gain was Rl/(Rl+output_Z) too.

Are you familiar with that method ?

Output Z could never be 1 / µ .
This is because µ is just an amplification factor, and in fact µ = Gm x Ra.

Sorry, I was being daft.

I meant 1/gm.

Graham

[Engineer]

On Apr 12, 11:42 am, Patrick Turner wrote:
Eeyore wrote:

In the recent thread about west's preamp his final CF stage was discussed.

Several ppl criticised my analysis of the cathode follower stage suggesting that
I had to draw a load line to establish it's 'gain'.

Those critics has now gone silent.

What happened ?

Graham

Patrick wrote:

(snip)

The term gain is misleading, because there is no actual voltage gain,
and insertion loss would be more appropriate, but ppl say gain with CF,
and its just convention.

(snip)

My background is control systems. In this discipline, "gain" is a
system parameter in the continuous range "minus a very large number"
to "plus a very large number", passing through zero on the way (with
or without phase vs. frequency information as the problem dictates.)
The phrase "a gain of zero" is perfectly logical, as is a gain of 0.1,
0.94, 1.75, etc. IMHO, this also applies to any branch of analog
electronics (where I also spent a lot of time...) I have also used
insertion loss (mostly in dB's) in RF design. Anyway, I'm very happy
with "a CF gain of 0.94". As a factor in the forward path gain or
loop gain, or in a transfer function (Laplace), all is well.
Hope this helps.
Cheers,
Roger.

[Chris Hornbeck]

On Thu, 12 Apr 2007 21:18:06 +0100, Eeyore
wrote:

I came across a document btw which gave a quick approximation to the output Z of a CF
as 1/mu. My presumtion was that the gain was Rl/(Rl+output_Z) too.

Sorry, I was being daft.

I meant 1/gm.

Of course. This is also a good approximation for all kinds of
gain and noise (!) calculations for all field effect devices.
The conventional temperature factor for electron valves is
2.5 above room temperature for noise work.

The interesting bits of output capability, linearity, etc.
still reside in the load lines. Ain't no gettin' around 'em.

Much thanks, as always,

Chris Hornbeck
"Second star to the right,
Then straight on 'til morning."