Scaling NFB resistor

[EFK]

Is there a specific formula one would use to scale the nfb resistor dependent upon transformer? I'm working on something using the brown deluxe circuit, which is 56K off a 8 ohm speaker and a 1.5K tail resistor. However, the transformer I'm using is 4 ohm only, so I want to scale the 56K down to compensate for the decreased nfb voltage. I don;t think I need to change the 1.5K tail resistor, correct? I went through Aiken's site and found some notes regarding proportionate voltages, and using those as ratios I think it worked out to something like about 38/39K for 4 ohm, but I have no idea whether or not that's accurate so looking for a little... feedback, no pun intended...

[Steve Conner]

To get the same amount of NFB in real terms, the ratio of the NFB divider has to be scaled according to the square root of the change in impedance.

So we have: 1.5/(56+1.5) * sqrt(8/4) = 1.5/(x + 1.5) where x is the new NFB resistor value.

Divide both sides by 1.5 then cross multiply: (x+1.5) = (56+1.5)/sqrt(8/4)

Subtract 1.5 from both sides: x = ((56+1.5)/sqrt(8/4))-1.5

so x= 39.28k - 39 will do

[EFK]

As usual, THANKS Steve!!!! I can't believe I actually was correct in an area involving math! That deserves a beer. Oh wait, it's only a little before 8 am here... it's got to be later somewhere....

BTW, I'm saving your post as that's a very clear and direct way of explaining it and a very useful formula to have for us math-challenged idiots.

[MWJB]

"You don't want to do it like that..."(in best Harry Enfield voice)

20W*8ohms = 160.
sqrt 160 = 12.65VAC at the speaker/OT secondary
12.65 * 1.5K/(1.5K+56K)
12.65*0.03 = 0.334v fed back
A ratio of 38:1

20W*4ohms = 80, so to get that same 0.334 volts fed back we just need to find the new NFB value, I set up a formula in XL, plug in a couple of common values and hey presto, "correct" value is...

sqrt80*1.5K(1.5K+xK)
8.94*1.5/(1.5+39) = 0.331v, new value is 39K! A NFB ratio of 27:1

Or, even simpler, when you halve speaker impedance (for same wattage), you get ~0.7 of the voltage at the secondary, multiply the NFB dropping resistor by 0.7 and you get 56*0.7 = 39.2...39K. Or, multiply the NFB ratio (38) by 0.7, 38:1 for the 8ohm becomes 26.6:1 for 4 ohms. 26.6*1.5K = 39.9K, nearest value 39K, a bit Heath Robbo, but gets the job done.

Er, hang on a minute...what was it Steve said again? ;-)

Doubling the speaker load then divide NFB dropper by 0.7, so a 16ohm speaker would require an 82K dropping resistor (nearest common value). Or 38/0.7 = 54.3:1. 1.5K*54= 81K, nearest value 82K.

Fender weren't typically that precise, in the larger BF amps 2 & 4 ohm outputs got the same loop, 8 ohm amps got a 50% reduction in load resistor, or a doubling of the feedback dropper, whichever way you want to see it.

[MWJB]

Or...

Divide dropping resistor by load resistor (56/1.5= 37.3), adding the value of the load resistor gives you your NFB ratio of 38.8:1. Now use the 0.7 factor to scale up and down...

4ohm wants 38.3*0.7= 27.16:1 ratio.
27.16*1.5 = 40.74
subtract load resistor value, 40.74-1.5 = 39.24K

16ohm wants 38.3/0.7= 54.71:1
54.71*1.5= 82.07
Subtract load resistor = 80.57K

[Gaz]

Here's a handy calculator if you're using a LTP:

Long Tailed Pair Feedback Calculator