cathode follower design resource?

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floid
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cathode follower design resource?

Post by floid » Thu Sep 04, 2014 12:46 pm

can someone point me to a good discussion of cathode follower design? it's a pretty straight forward topic i know, but there are a couple fine points on which i can't find a definite answer in my resource collection.
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Post by themagicmanmdt » Thu Sep 04, 2014 10:39 pm

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Post by floid » Fri Sep 05, 2014 3:51 am

i have a pretty comprehensive but very dense discussion in an old design handbook that spits out ridiculous numbers when i try to work their output impedance calculation - it's almost like entering a recursive loop. the other resources i have don't give me enough to figure out what what i'm missing, and example schematics vary enough in their fine points (12au7 vs 12at7, different plate voltages, single vs parallel triodes, etc) that i can't systematically work backward from them. so i spent an hour online at the library and got tangled up in white and akido and white akidos... sigh, i think i'm overthinking this. all i want is to use the oscillator socket in an old reel to reel for two followers with Rk values that will play nice with my junkbox trannies.
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Post by floid » Sat Sep 06, 2014 1:39 pm

more intelligent use of google led me straight to a calculator that gives the same numbers i got by hand. so here's a better question: why terminate a 420 ohm output with a transformer in the range of 10-15k:600, as in some examples i've seen? shouldn't a 1:1 be fine?
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Post by The Scum » Sun Sep 07, 2014 12:12 pm

Can you post a link to said calculator, and the parameters you're feeding it? Picture worth a dozen words, and all that...

You need to look to the next stage to answer the question. What is it's input impedance? What voltage/current is it expecting? And what's the output voltage?

The 10K:600 will step the voltage down, and give you more current drive.

Remember that a 600:600 transformer will only have an input impedance of 600 Ohms if it's terminated with 600 Ohms. But true 600 Ohm inputs are pretty anachronistic these days, so we'll just slug them with a 620 Ohm termination resistor, and feed them to the modern standard of 10K (or 22K, or 47K) inputs.

A 600:600, feeding a 600 Ohm load will look like 600 Ohms to your circuit. But 420 Zout into 600 Zin looks like a pretty significant divider - you'll lose voltage, and if you've just built out the Zout with a 420 resistor, do the math to see what sort of power it's dissipating.

600 Ohms stuff is also the basis of the ol' dBm standard - referenced to 1 milliWatt into a 600 Ohm load. Impedance matching is done to maximize power transfer...but these days we're transferring voltage, at very low currents.

Again, what are you feeding? You might be able to connect directly to a 10K or higher load...within limits of it's input voltage abilities. Loaded with 10K, the 420 is more or less insignificant.
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Post by floid » Mon Sep 08, 2014 2:26 pm

here is the calculator I found:
http://www.ampbooks.com/home/amplifier- ... -follower/
From Electronic Circuits and Tubes, by the Electronics Training Staff of the Cruft Laboratory, Harvard University (1947), here are a couple of equations I was using:
1) Z= Rp*Rk/(Rp+(1+mu)*Rk)
2) Z=Rk/(1+gmho*Rk)
where Rp= plate resistance
Rk= cathode resistor
gmho= transconductance

So for instance a single section of 12au7a with 250V at plate and a 47k cathode resistor gives 423 ohms, reducing the plate voltage to 100V gives 320 ohms.
What was throwing me was that I was expecting something in the 10-15k range, since that seems a typical transformer in this position. But you called it, I wasn't thinking in terms of reflected loads - using the 1:10 Zout:Zin rule of thumb, 423 ohms wants to see no less than 4.2K reflected to it, right? We would actually term it a 4.2K ohms out if using a 1:1 here?
What are the practical limits to cathode resistor size?
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Post by The Scum » Tue Sep 09, 2014 5:16 pm

using the 1:10 Zout:Zin rule of thumb, 423 ohms wants to see no less than 4.2K reflected to it, right?
Yup.

But ~5K is a somewhat uncommon transformer value, so 10K or 15K are called for.
We would actually term it a 4.2K ohms out if using a 1:1 here?
If you were to load the secondary with 4.2K, then sure.

The ratio scales the impedances accordingly. Audio transformers are designed for some optimum application, where they'll be the most linear (in frequency response) when loaded as anticipated. But the ratio still applies (more or less) even when the loading is incorrect. That "more or less" starts to fall apart when the secondary if shorted or open, and the parasitics of the winding capacitance and inductance start to take over.
What are the practical limits to cathode resistor size?
Probably the current in the tube...but don't quote me on that. As it gets smaller, you get more current, running things hotter, and heat is a concern.

If you scale the resistor in the calculator, you'll notice that the impedance doesn't change much over a really wide range of resistance. 10M, 100K and 10K are all pretty similar...it's as you get below 10K that you finally start lowering the Z more quickly...

At this point, why not build one and see what happens?
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Post by themagicmanmdt » Fri Sep 12, 2014 10:01 am

you're there.
that's the way to calculate the output impedance of the tube in a standard CF.

the impedance bridging rule-o-thumb is for the output impedance to do into ('should be driving into) an input impedance 10x it's size.

it doesn't need to be. this is something you can voice to taste. driving only, say, a 3x output impedance will still sound good, mayhaps a little slower, thicker.

the bigger problem is the size of the cap on the output of your CF so it can get down to 20hz flat.

if you want to drive a 600 ohm load with a 1:1 transformer (or just direct, unbalanced), that'za big cap, gonna be pricey, and not sound as good as a smaller cap.


most inputs aren't 600 ohms. most line inputs are going to be >10k.
with that said, the step-down 10k:600 (or so) transformer isn't really necessary.

honestly, if you want to expect to drive a 600 ohm load with a 1:1, get the giant cap necessary (it'll probably be an electrolytic, or a very big film), and, even then, it'll sound a bit squishy due to the lack of current drive. but, it'll still work and sound good. but, not really really good.

if you really plug into 600 ohm gear, embrace the facts, get a 10k:600. it's not that much voltage loss.

other follower designs (white, etc) help with the current drive, but you sacrifice output voltage swing. i'm sure the tone changes a bit. never messed with them. (yet). i enjoy the mojo of the regular CF. at first, i didn't. but, it was the tube type to blame.

not a 12au7. eww. no bueno.

use a 6FQ7. or 6DJ8. or 6SN7.
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Post by floid » Sat Sep 13, 2014 8:29 pm

very informative guys!
i'm still not sure i have my head wrapped around the concept of 'we used to match impedances, but now we bridge.' i've done some interesting reading in Yamaha's Sound Reinforcement Manual and others...
Interesting to hear the 1:10 rule isn't really one. i don't mind this project sounding a little 'sluggish' or not being flat to 20. it's a silvertone suitcase with enough circuit to be more than just an amp, but that depends on using what i have on hand - which is no 10k or 15k:600 output i'd want to live here permanently. 4k and smaller, or 25k and bigger.
magicman, why do larger cap sizes hurt? the load becoming more capacitive? or the switch to electros/ inefficiencies in large films?
12a*7s i have plenty, but few other dual triodes. worth getting some i think.
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