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Hoffman Amps Forum image Author Topic: Understanding the math behind a Single Ended amplifier  (Read 3100 times)

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Offline Tomahawk

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Understanding the math behind a Single Ended amplifier
« on: January 25, 2022, 10:56:59 pm »
I am working on a single ended design to learn the basics and math behind tube amplifiers.
The design is largely based off a Champ and a Princeton. I want to use a 5Y3 rectifier. The preamp is planned to contain 3 12AX7 tubes and a single EF86.

Power Transformer assumed as an Edcor XPWR2855: 315-0-315v CT @ 100ma, 6.3V@2.25A CT, & 5V@3A

19V drop accrmross the choke was calculated using this LC filter calculator and an Edcor XC75-15H-75mA choke (15 Henry @ 75mA; 21.13 Ohms per henry)

https://edcorusa.com/collections/power-chokes/products/xc75-15h-75ma-15h-75ma-choke
https://www.ampbooks.com/mobile/amplifier-calculators/LC-ripple-filter/calculator/
https://edcorusa.com/collections/tube-power-transformers/products/xpwr285-630v-315-0-315-100ma-ct-6-3v-2-25a-5v-3a

Is there any glaring issues in my math or any values I have chosen?
« Last Edit: January 25, 2022, 11:03:28 pm by Tomahawk »

Offline tubeswell

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Re: Understanding the math behind a Single Ended amplifier
« Reply #1 on: January 26, 2022, 12:14:27 am »
The preamp is planned to contain 3 12AX7 tubes and a single EF86.


Assume 1mA per 12AX7 triode and 1mA for the EF86 and assuming each tube stage is used, that's 7mA for the preamp. Add another 2mA for the 6V6 screen grid, and that's 9mA at the screen filter cap node (if you have a separate screen supply node, which the 5E1 doesn't', but the 5F2A does - YMMV). Add another 36-38mA for the 6V6 plate and you've got 45-47mA total draw at idle, maybe a smidgeon above 50ish mA under full signal. Work off those numbers for the PS dropping string/nodes. YMMV
A bus stops at a bus station. A train stops at a train station. On my desk, I have a work station.

Offline Tomahawk

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Re: Understanding the math behind a Single Ended amplifier
« Reply #2 on: January 26, 2022, 10:04:54 pm »
I did some more math with your suggestions and came up with the attached.
Plate current mathed out to 37mA
A bias voltage of -21.9v

Offline HotBluePlates

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Re: Understanding the math behind a Single Ended amplifier
« Reply #3 on: January 26, 2022, 11:37:03 pm »
... Plate current mathed out to 37mA
A bias voltage of -21.9v

About 340v on the plate, about 20v at the cathode.  That leaves 320v plate-to-cathode.  Times 37mA is 11.84 watts, a fine number for a single-ended 6V6.

But how do you know about -22v bias leads to 37mA at the plate (and ~39mA plate + screen)?  Yes that's what you calculated with the assumed 560Ω cathode resistor, but when you plug in a tube will it really pull 39mA total current?

You need to refer to the 6V6 data sheet.  What matters is our screen voltage (about 340v) and the bias voltage.  But there is no graph for a screen voltage of 340v.  So look at the triode curves on the bottom of Page 4.

     -  Draw a vertical line at 340v (your screen voltage).
     -  Draw a horizontal line at 37mA.
     -  Notice these intersect mighty close to -25v.

You would need to raise the cathode resistor to 25v / 39mA = ~640Ω.  680Ω is the most-common standard value, but 649Ω is available at similar price.  Throughout, we're assuming about 2mA of idle screen current.

But "higher resistance" is one path.  Another path is to add a filter cap for the screen, and insert a dropping resistor to get a lower screen voltage.

     -  Move left along your "37mA" horizontal line to the -20v gridline.  That seems to intersect at around 295v on the screen.
     -  NOTE: The X-axis is "plate voltage" but triode curves assume plate & screen are connected, so we really see the impact on plate current of screen voltage vs bias voltage.
     -  20v / 39mA = ~513Ω, an odd value.
     

Let's say we happen to notice old Fender amps showed around 18v of bias for the 6V6.  18v / 39mA = ~462Ω, which looks an awful lot like the typical "470Ω" resistor available everywhere.

     -  What screen voltage do we need for 37mA plate and 18v of bias?
     -  Keep moving left on that 37mA horizontal line you draw on the triode curves.  Seems to land a little below "280v" like maybe 275v?

340v on the plate - 18v at the cathode leaves 322v plate-to-cathode.  Times 37mA, that's 11.91 watts, still golden for our SE 6V6.  Now we're looking for ~275v on the screen.

     -  Tubeswell already outlined that 7mA is drawn by the preamp, and 2mA by the 6V6 screen.  9mA total.
     -  We need to drop from 340v to 275v, or 65v across the dropping resistor.
     -  65v / 9mA = ~7.2kΩ.  That's an odd value; 6.8kΩ is very common, though 7kΩ is also available in a 3w part.

A side-benefit of lowering screen voltage and using a smaller bias voltage (and cathode resistor) is that your preamp will drive the 6V6 easier.  Before adding any feedback, the 6V6 will move from distorting with a peak drive signal of 25v to a peak drive signal of 18v.  You will not need as much preamp-gain to push the output tube.

Lower screen voltage also means the widely-varying individual 6V6s will tend to run cooler in your amp, so you're less likely to encounter tubes that try to burn themselves up.  (I think this is a common failing of modern amps; we do not need every last milliwatt of power, and modern tubes can use all the help they can get for cooler operation.)
« Last Edit: January 27, 2022, 06:13:46 am by HotBluePlates »

Offline Grees01

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Re: Understanding the math behind a Single Ended amplifier
« Reply #4 on: January 27, 2022, 01:05:37 am »
Man, what a stellar and informative and educational reply HBP!!!!!. I didn't ask the question, but I sure like your answers. Thank you for sharing that information.
G.

 


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