P-P load lines, I must be getting something wrong (includes useful spreadsheet)

[Hardtailed]

So I've read and reread Merlin's article on load lines for power amps.

It all looked fine, until I tried to run the math for my main amp: a 50W Marshall clone.
It has roughly 485V on the plates, a 3400 primary Z, and runs a pair of EL34 which have a max dissipation of 24W.

According to Merlin, while both valves are operating, the Z seen by each one is half the total plate-to-plate impedance, so 1700 in this case.
Once one valve goes into cutoff, the remaining one sees 1/4th the total Z, so a mere 850 ohms.

To make playing around with values I made a little spreadsheet (see in attachment).

Just to help you understand:
Vp = Plate voltage
Zp = Primary (plate to plate) impedance
Bias current = the quiescent current per tube (not including screen current)
Pmax = maximum dissipation for the tube you're using
These are the only values you can modify

The rest is as follow:
Idle dissip: calculates for you the dissipation at idle based on Vp and Bias current
70% P Max: Since we often bias to 70% dissip, this is just a reference.
The chart then calculates current (I) and dissipation (P) from 0 to 500V. Zpp/2 is with 2 valves running (aka "class A"), Zpp/4 is with 1 valve running (aka "Class B"). Zpp/2 is also provided with bias added on top. I(Pmax) maps the max dissipation curve for the tube.

This does not take into account the characteristic curves of the tube, it's just for the fun of checking load lines against various Zs, voltage and tube types.

So anyway, if I plug my amp's values in there, with the bias at 70%, you can see that each valve spends most of its time way above 24W. It goes as high as 60W!!! The average dissipation is obviously over 24W.

Also, if I map an EL34 curves on top of that, at 0 grid volts, the current is way high, like over 300mA, yet my PT only gives around 2=400mA. I know the reservoir cap will jump in at that point, but still...

What am I getting wrong here?

Obviously, my tubes don't red plate so whatever the spreadsheet says, in the end it works. Anyone can help me understand this?

[Steve Conner]

Well, the math looks fine.

The B+ will sag, so the load line should start lower than 500V. Maybe it sags to 400 at full power.

Tube drop means you never see plate voltages below 50-100.

The plates don't immediately light up red as soon as you exceed 25W.

Because of resonance, speakers are higher than their rated impedance over much of the bass and low mid register.

EL34 Marshalls never had a too good reputation for reliability anyway.

[Hardtailed]

Well, the math looks fine.

The B+ will sag, so the load line should start lower than 500V. Maybe it sags to 400 at full power.

Tube drop means you never see plate voltages below 50-100.

The plates don't immediately light up red as soon as you exceed 25W.

Because of resonance, speakers are higher than their rated impedance over much of the bass and low mid register.

EL34 Marshalls never had a too good reputation for reliability anyway.

So I guess what you're saying is... don't fret it if the load lines goes over the max dissipation curve!

Although, the 60W figure really surprised me.
485V is what I measure at idle with tubes in (so, under "some" load). I guess it must sag at full tilt, although it does have a gigantic power transformer and a hefty 100uF main reservoir cap.
It is the loudest amp I've ever heard.

If I plug the numbers of the AC30 clone I did recently (335V, 8K per pair, 44mA bias), despite the overdissipation at idle, it looks way more conservative! (It wasn't nearly as loud as the "50W" clone too)

[Wilder Amplification]

This is exactly the problem with some of MetroAmp's plexi clones.

Marshall took the load spec for EL34s at 425V B+ and assumed that that load would be fine for all voltages. Throw in the fact that most transformers from that era were wound for 110VAC operation and we now run 120V here, this would cause a 9% increase in AC voltage at the HT winding. Since most 100W trannies were spec'ed at 350VAC, add 9% to that and you end up with 380VAC, which rectified and filtered goes up to over 500V (537VDC no load).

Luckily, as a byproduct of transformers that were available at the time, the B+ would sag enough at full power, which allowed the amp to run safely at max power out without over dissipating.

MetroAmp cloned the Dagnall 1203-80 power transformer, but theirs are WAY stiffer so they don't sag as much at full power out. As such, some have reported red plating at full clip because the load is obviously too low for that B+.

Assuming a 500V supply that is 100% regulated, a 2.5K Zpl-pl would be the proper load for that voltage with 4 x EL34s. 1.7K would be the load for a 425V B+ in this scenario. 2.5K @ 500V would only allow the instantaneous dissipation to exceed the max by double, which would put the average a little less than the max 25W since the tube is below dissipation for a little more than 1/2 the swing.

Here's an ideal load line for KT88s @ 600V with a 5K Zpl-pl biased at 70%. You can see that it crosses the grid curves right where it should and the instantaneous dissipation does not exceed the max by more than double.

[Hardtailed]

This is exactly the problem with some of MetroAmp's plexi clones.

Marshall took the load spec for EL34s at 425V B+ and assumed that that load would be fine for all voltages. Throw in the fact that most transformers from that era were wound for 110VAC operation and we now run 120V here, this would cause a 9% increase in AC voltage at the HT winding. Since most 100W trannies were spec'ed at 350VAC, add 9% to that and you end up with 380VAC, which rectified and filtered goes up to over 500V (537VDC no load).

Interesting stuff, and other proofs that the classic designs are often happy accidents.

I'm using a Hammond replacement set in mine, don't know how stiffer than the original they are. I've never seen the tubes red plate, but then... I can't really crank this thing, the volume is just completely stupid.

So if I get your drift, the rule of thumb is to no exceed twice the max dissip as we go up the load line. If I go by this and load my numbers, and considering I currently have KT77s which are 30W max, I'm ok!
But the EL34s are being pushed over their limit, unless we account for sag.