[Patrick Turner]

I am editing my website again to include better info, more info, and
better formatting. I think the two most visited pages have been the PP
and SE OPT calculation pages where ppl have wanted to know how to wind
themselves an OPT. The revised SE OPT calc page is about done
including many more diagrams and oscilloscope pics of distortion and
satutuation ppl should see whaile testing their amps.

The PP calc page is also going well, but I wanted to include a portion
about calculating anode dissipation, and I searched the web and all my
old books for a formula to allow for the calculation of total Pda at
any sine wave level while a substantial amount of Pda exists at idle.
I already have formulas to predict class B amp Pda, all very neat, but
useless for class AB where we may want to plot the graph of Pda from
max Vo of 0dB, then at -3dB, -6dB, -9dB, -12dB.

The formula for tube class B I derived from general theory with solid
state amps is:-

Total Pda, 2 tubes = Power input from power supply - audio power
output
= ( 0.9 x Ea x Va / BRLa ) - ( Va squared / BRLa )

Where Ea is the idle Ea Vdc between a and k, Va is the Vrms at one
anode of the PP pair, and BRLa is the class B load for one tube, ie,
RLa-a / 4.

The formula may be simplified to :-

Total Pda of the 2 tubes in class B at any level = Vaa x ( [ 1.8 x
Ea ] - Vaa ) / RLa-a.
( Vaa is anode to anode signal in Vrms ).

Obviously, Pda will be zero at Vaa = 0V. But with class AB amps Pda
might be 50W for two 6550 at idle.

With an existing amp, its easy to plot a graph for Pda, just measure
power input and power output, and Pda = Pin - Pout, for any level you
wish, but a formula should cover all operation, and even RDH4 is very
timid about providing one, like my other stack of old books.

Patrick Turner.

[Patrick Turner]

Nobody has replied to my question below, and that's OK, because I
don't expect anyone who reads this group to know more than I do about
this particular subject.

I've finally completed work replacing all the resistors in a pair of
MingDa amps which have a pair of 845 tubes with Ea at 1,200V. I have
reduced the idle Iadc from about 70mA per tube to a more sensible
37mA. I have done some careful measurements of anode dissipation by
means of recording DC anode supply current into the OPT CT, and the B+
at this point, at various voltage levels up to clipping with loads
between 32 ohms and 3 ohms with the OPT ratio setting for 39:1.
This means the anode to anode load range is from about 49k to 6k,
allowing for the rather high winding losses of the chinese OPT which
has a tapped secondary winding. Maximum tube Pda occurred at clipping
for all loads.

I found that with a 3 ohm load, the maximum Pda per tube was just
under 100W at clipping and Idc input had trebled,
with a B+ sag of -50V to 1,150V.

I then drew up the anode voltage sine waves and the current waves at
the cathode.

The Pda in each half sine wave was calculated, summed, then divided by
2 to give the average Pda for a full wave cycle.

The formula I used is based on Pda = average anode voltage x average
anode current.

So, I applied this formula....

Pda per tube = 1/2 of
( Ea - [ 0.636 x { Ea - Ea min } ] ) x ( Ia + [ 0.636 x { Ia max -
Ia } ] ).

where Ea is at the working loaded condition, Ea min is the minimum
peak Ea negative going swing, Ia max is the maximum positive going
peak current in each tube, and Ia is the idle Iadc current.
The formula seems to be valid where the Idc anode supply current to
OPT CT has increased more than 50% of the idle value.

The large rise in anode supply dc current indicates that Pda
calculated for 1/2 the wave cycle where most of the power is generated
will be over 20 times the Pda in the part of the wave where the tube
is cut off for more than 0.9 of the 1/2 wave cycle, so negligible Pda
occurs during cut off.

Where the amp works in class A for low amounts of class A power with
AB loads, the Pda for each 1/2 cycle is more complex to work out. Its
also only necessary to calculate Pda for maximum clipping power, at
least with triodes.

The measurements showed that with a 16 ohm load connected to the
"8ohm" outlet, the RLa-a is about 24k, and Pda per tube became less
than idle right up to clipping at 54 Watts. With sec load = 32 ohms,
there was a nice 37Watts of almost totally pure class A available. No
need to worry tubes will overheat when RLa-a is high.

But loads below 4 ohms where RLa-a is about 7k2 including Rw can cause
Pda to rise to 77W, and any clipping soon has it going higher. But the
class B RLa for each tube is then only 1k8, and less than Ra. Ideally,
for 845, RLa-a should never be less than about 16k0 for where Ea =
1,200Vdc. This means the B RLa = 4k0, and about 2 x Ra, and the tubes
will never overheat.

Patrick Turner.

On Aug 18, 12:08*pm, Patrick Turner wrote:
I am editing my website again to include better info, more info, and
better formatting. I think the two most visited pages have been the PP
and SE OPT calculation pages where ppl have wanted to know how to wind
themselves an OPT. The revised SE OPT calc page is about done
including many more diagrams and oscilloscope pics of distortion and
satutuation ppl should see whaile testing their amps.

The PP calc page is also going well, but I wanted to include a portion
about calculating anode dissipation, and I searched the web and all my
old books for a formula to allow for the calculation of total Pda at
any sine wave level while a substantial amount of Pda exists at idle.
I already have formulas to predict class B amp Pda, all very neat, but
useless for class AB where we may want to plot the graph of Pda from
max Vo of 0dB, then at -3dB, -6dB, -9dB, -12dB.

The formula for tube class B I derived from general theory with solid
state amps is:-

Total Pda, 2 tubes = Power input from power supply - audio power
output
= ( 0.9 x Ea x Va / BRLa ) - ( Va squared / BRLa )

Where Ea is the idle Ea Vdc between a and k, Va is the Vrms at one
anode of the PP pair, and BRLa is the class B load for one tube, ie,
RLa-a / 4.

The formula may be simplified to :-

Total Pda of the 2 tubes in class B at any level = Vaa x ( [ 1.8 x
Ea ] - Vaa ) / RLa-a.
( Vaa is anode to anode signal in Vrms ).

Obviously, Pda will be zero at Vaa = 0V. But with class AB amps Pda
might be 50W for two 6550 at idle.

With an existing amp, its easy to plot a graph for Pda, just measure
power input and power output, and Pda = Pin - Pout, for any level you
wish, but a formula should cover all operation, and even RDH4 is very
timid about providing one, like my other stack of old books.

Patrick Turner.

[Patrick Turner]

Here I go again, I must be mad because I find myself talking to myself
on this subject and it seems nobody here has a clue about it, or they
find the subject or myself to be so boring that they'd rather refrain
from any input.

I have more to say merely "for the record" and to benefit anyone else
searching for an answer.

I have to move right along even when nobody is with me, and I write
for the record, because anyone searching with Google on how-to-
calculate anode dissipation in class AB amps accurately while taking
into account the idle bias dissipation plus signal caused dissipation
will be dissapointed to find nobody has posted very much at all online
- yet.

I've since read a few more pages from my precious old hard cover
textbooks from the 1930's. Some, like so much written in old books is
terribly written, and un-intentionally designed to bamboozle young
student radio engineers wanting a carreer with a radio station in the
Navy etc where they might find themselves surrounded by huge
enclosures chocka block with all sorts of glowing tube stuff which
kept them warm and alert and was less boring than alternative jobs if
you could ever get a job.
One was supposed to be very good at mathematics to score in radio
engineering, which meant only you knew what you were doing, and nobody
else did, which gave you power in the workplace as a "Boffin".
I started my interest intubes as a teenager, found the interest disn't
last, then had a carreer in Construction, which was also fulla
formulas and calculations, but they all seemed easy, and when I moved
back to vacuum tubes I had to understand more vague concepts and learn
a lot more formulas. Most are simple.

Where formulas are not simple, and perhaps unknown by the authors on
the subject, they end up skirting around the subject and ending with a
line like "Perfect calculations are not possible and may yeild
accuracy of +/- 10% and careful measurements must be undertaken to
appraise the design" In other words, after a few basic calcs, suck it
and see.
I have not managed to find any formula anywhere which accurately
allows for inclusion of the idle input power in a class AB amplifier.

However, any class AB amplifier will not overheat its tubes during the
first 25% of its power output unless the tube Pda at idle is close or
equal to the Pda rating for the tubes, and some idiot connects a load
value which is too low.

Where the maximum class AB power is more than twice the initial
amount of class A power, Pda should never be more than 60% of the Pda
rating for the tube.

For where a class AB amp has moved from class A into class AB
operation, and where the maximum peak Ia in each tube rises above 2.5
x Ia at idle while the other tube is cut off, the tube dissipation amp
may be considered to be substantially like a class B amp, and formulas
for Pda and efficiency begin to become valid enough for checking the
design to see if tubes will overheat or not.

Loadline analysis is important to gain a full picture of the intended
power amp design.
From the load line analysis the Ea swing for the class B load each
tube sees while working AB can be determined.
The Ea minimum should be found graphically. It may also be found by
calculations using estimations of the ohmic value of the "diode line"
or Ra at Eg1 = 0V curves, but should be confirmed by graphical
methods.

Consider the example of a 1996 MingDa monobloc amp
with pair of 845, Shuguang type B, Carbon anodes,
all made in China. After I completely rewired it to stop
smoke,
Ea = 1,220V at idle, Ia = 37mA, Pda at idle = 44Watts,
Grid bias = -191V, Maximum class AB1 signal
drive to each grid = 135Vrms.
RLa-a = 12k0, including 6% winding resistance.
Class B load for each tube = 3k0.

I found the power max at anodes at with 400Hz sine wave
at clipping = 85.6W, with 80.6W at the secondary output.

Ea had sagged from 1,220 to 1,166V, because of increased
Iadc drawn from PSU.
From all this I was able to establish a known Ea point along the
ClassB load line of 3k0 and where it intersects the Ra curve
for Eg1 = 0V.

Va-a = 1,013Vrms = 716Vpk swing at each anode.
Ea min = Ea - Ea swing = 1,166V - 716V = +450V.
Where Ea = +450V on load line is at 0.238Amps.
0.238A is the maximum peak Ia in the 845.
It is 6.4 times the value of the idle Ia, and the
tubes are definately working in class B with
only the first 8 watts in pure class A.

The Ra line could then be drawn and shown to be about 1,900 ohms in
slope value, about what I would expect because Ra for 845 well away
from the Ra curve for EG1 = 0V is about 2k2 in most cases, ie,
slightly higher.

The old books have the simple class B formulas :-

Power out = Ia max x ( Ea - Ea min ) / 2
= 0.238 x ( 1,166 - 450 ) / 2
= 85 watts, or very close to what I measured.

Now for ALL class B amps, Efficiency factor n = 0.785 x ( 1 - Ea min /
Ea ).

This formula reveals that if the Ea min swings down to 0V, then the
amp devices are perfect, and efficiency n = 0.785 thus giving
efficiency percentage = 78.5%.

The efficiency at any other voltages other than maximum Ea swing
levels may be calculated.

In this 845 case n = 0.785 x ( 1 - 450 / 1,166 ) = 0.482, so eff% =
48.2%.

Now Power from PSU = Audio PO + total Anode dissipation, Pda.

Also, P psu = Audio PO / n, where n is efficiency factor.
So Ppsu = 85W / 0.482 = 176W.

During my tests I monitored the input dc current to the OPT which
increased from 74mA to 151mA,
thus P psu = Ea x Idc = 1,166 x 0.151 = 176Watts.

So the calculated Ppsu = equals the measured Ppsu.

Now Pda = Ppsu - PO audio = 176 - 85 = 91 Watts.

Therefore each tube dissipates 45.2 W at maximum PO.

I measured the tubes at 5 levels above 8W and the plotted the graph
for Pda against output Vo and PO, with Pda measured by calculating
Ppsu - PO, thus obtaining a Real World graph, not something
theoretical.

Pda starts at idle = 44W, then fell a few watts before rising to about
44W at class A to AB threshold at 8 Watts. Then Pda slowly rose to 46W
in anear straight line. Therefore the 845 were never going to be
stressed in their conditions of use unless the amp was pushed well
into clipping or if the load value was reduced. Pda max was never
above 1/2 the Pda rating of 100W for the 845.

I repeated all the above with a 4 ohm load, and found that the
formulas were accurate once above the class A-AB threshold. However,
with a 4 ohm load, although 89W of audio PO was available at clipping,
Pda was found to rise to a maximum of 74W per each 845 with a near
straight line increase above about 3 watts of class A PO.

The original un-reformed MingDa had a very ill-concieved tapped
secondary winding for either Com-4 or Com-8 ohms, and where an 8 ohm
load was used at Com-8 the turn ratio is only 22.4, giving RLa-a =
4k0, and winding Rw total about 700 ohms, thus the class B load per
tube = 1,175 ohms, and this load is WAY TOO LOW for any kind of
acceptable hi-fi performance and may definately lead to overheatig
tubes at high power, which was not more than I have already obtained
because of the original appallingly set up driver amp using RC coupled
300B with the same low Ia as one might use in 1/2 a 6SN7.
The Com-4 outlet was found to offer a 37.6 TR, and thus give the RLa-a
= 12k0 including Rw, and this is just acceptable.
Using the turns between the "4" and "8" terminals gave a reasonable
match for 4 ohms. I've changed the amp labelling to direct the owner
to use the available terminals to get the best hi-fi.

Conclusions. Class B RLa should not be less than Ra for most power
triodes, but some power triodes like 805 operate with grid input
current in class AB2, and Ra is quite a high value. And with any beam
tetrodes the Ra is quite high. So when designing class AB amps one
must be careful about Pda. and carefully check the Pda with above
formulas and reasoning.
In pure class A PP and all SE amps, Pda usually aways reduces as PO
increases above idle unless the RLa is way too low, as it could be
with a shorted speaker load.
I once worked on a Cambridge Audio ( Woodham 5050 mode) amp from the
UK which had KT88 biased up way too hot. Ea = 600V, and RLa-a = 3k2
with 8 ohms used at the Com-8 terminals. This dog of an amp soon gave
more smoke than music and it is a monument to modern stupidity. I
gutted the whole horrid mess of a circuit to the bin, beefed up the
metal work, and installed a choke input PSU thus getting Ea down to
about 450V, converted the absurd unity gain OP stage to 50% UL taps
and banned the owner from ever using the Com-8 OP termnals, and
finally he got 40W of hi-fi instead of smoke.

My efforts to construct a formula to calculate Pda for any two PP
devices and which include substantial idle bias currents is a
continuing work, but so far un-successful.
Formulas I have seen online and articles fail dismally to offer any
useful other than I have so far worked out, which isn't all that
accurate at low levels of audio PO.

I'm now working on incorporating the above with some wave form graphs
into a website page separate from the page at
http://www.turneraudio.com.au/output-trans-pp-calc.htm where I have
tried to place it, but where it is too large and distracting, because
the page is meant to be about OPT design, not load matching. One
cannot design OPTs without first deciding on the load matching. Bit of
a catch 22.
Anyway, now back to work....

Patrick Turner.


On Aug 21, 12:37*am, Patrick Turner wrote:
Nobody has replied to my question below, and that's OK, because I
don't expect anyone who reads this group to know more than I do about
this particular subject.

I've finally completed work replacing all the resistors in a pair of
MingDa amps which have a pair of 845 tubes with Ea at 1,200V. I have
reduced the idle Iadc from about 70mA per tube to a more sensible
37mA. I have done some careful measurements of anode dissipation by
means of recording DC anode supply current into the OPT CT, and the B+
at this point, at various voltage levels up to clipping with loads
between 32 ohms and 3 ohms with the OPT ratio setting for 39:1.
This means the anode to anode load range is from about 49k to 6k,
allowing for the rather high winding losses of the chinese OPT which
has a tapped secondary winding. Maximum tube Pda occurred at clipping
for all loads.

I found that with a 3 ohm load, the maximum Pda per tube was just
under 100W at clipping and Idc input had trebled,
with a B+ sag of -50V to 1,150V.

I then drew up the anode voltage sine waves and the current waves at
the cathode.

The Pda in each half sine wave was calculated, summed, then divided by
2 to give the average Pda for a full wave cycle.

The formula I used is based on Pda = average anode voltage x average
anode current.

So, I applied this formula....

Pda per tube = 1/2 of
( Ea - [ 0.636 x { Ea - Ea min } ] ) x ( Ia + [ 0.636 x { Ia max -
Ia } ] ).

where Ea is at the working loaded condition, Ea min is the minimum
peak Ea negative going swing, Ia max is the maximum positive going
peak current in each tube, and Ia is the idle Iadc current.
The formula seems to be valid where the Idc anode supply current to
OPT CT has increased more than 50% of the idle value.

The large rise in anode supply dc current indicates that Pda
calculated for 1/2 the wave cycle where most of the power is generated
will be over 20 times the Pda in the part of the wave where the tube
is cut off for more than 0.9 of the 1/2 wave cycle, so negligible Pda
occurs during cut off.

Where the amp works in class A for low amounts of class A power with
AB loads, the Pda for each 1/2 cycle is more complex to work out. *Its
also only necessary to calculate Pda for maximum clipping power, at
least with triodes.

The measurements showed that with a 16 ohm load connected to the
"8ohm" outlet, the RLa-a is about 24k, and Pda per tube became less
than idle right up to clipping at 54 Watts. With sec load = 32 ohms,
there was a nice 37Watts of almost totally pure class A available. No
need to worry tubes will overheat when RLa-a is high.

But loads below 4 ohms where RLa-a is about 7k2 including Rw can cause
Pda to rise to 77W, and any clipping soon has it going higher. But the
class B RLa for each tube is then only 1k8, and less than Ra. Ideally,
for 845, RLa-a should never be less than about 16k0 for where Ea =
1,200Vdc. This means the B RLa = 4k0, and about 2 x Ra, and the tubes
will never overheat.

Patrick Turner.

On Aug 18, 12:08*pm, Patrick Turner wrote:



I am editing my website again to include better info, more info, and
better formatting. I think the two most visited pages have been the PP
and SE OPT calculation pages where ppl have wanted to know how to wind
themselves an OPT. The revised SE OPT calc page is about done
including many more diagrams and oscilloscope pics of distortion and
satutuation ppl should see whaile testing their amps.

The PP calc page is also going well, but I wanted to include a portion
about calculating anode dissipation, and I searched the web and all my
old books for a formula to allow for the calculation of total Pda at
any sine wave level while a substantial amount of Pda exists at idle.
I already have formulas to predict class B amp Pda, all very neat, but
useless for class AB where we may want to plot the graph of Pda from
max Vo of 0dB, then at -3dB, -6dB, -9dB, -12dB.

The formula for tube class B I derived from general theory with solid
state amps is:-

Total Pda, 2 tubes = Power input from power supply - audio power
output
= ( 0.9 x Ea x Va / BRLa ) - ( Va squared / BRLa )

Where Ea is the idle Ea Vdc between a and k, Va is the Vrms at one
anode of the PP pair, and BRLa is the class B load for one tube, ie,
RLa-a / 4.

The formula may be simplified to :-

Total Pda of the 2 tubes in class B at any level = Vaa x ( [ 1.8 x
Ea ] - Vaa ) / RLa-a.
( Vaa is anode to anode signal in Vrms ).

Obviously, Pda will be zero at Vaa = 0V. But with class AB amps Pda
might be 50W for two 6550 at idle.

With an existing amp, its easy to plot a graph for Pda, just measure
power input and power output, and Pda = Pin - Pout, for any level you
wish, but a formula should cover all operation, and even RDH4 is very
timid about providing one, like my other stack of old books.

Patrick Turner.- Hide quoted text -

- Show quoted text -