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Calculate Required Impedance of Output Transformer

I'm trying to learn how to select the correct output transformers to match the load impedance of my 23 ohm headphones.

So the output transformers are matching "line matchers".
The turns ratio is 5.1 with 15K ohms/600.
I'll use a matched pair (left/right) in my tube amp build.

Please correct me but my understanding is that
5.1 squared = 26.01
so then i multiply
26.01 x 23 ohms = 598.23
so then 598.23 is close enough to 600 ohms which means the above output transformers are perfectly matched to the 23 ohm load of my headphones.
Right?
 
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kodabmx

Member
Paid Member
2011-10-31 1:00 am
Toronto
Nope.

Assuming you meant 15k:600R (your math show this to be true), You will connect a 23R load to the secondary designed for 600R (headphones) to the transformer which will reflect ~575R to the tube as the load on a winding designed to be 15K. This effectively makes the coil act like a 575R:23R transformer.

575R is too low for almost all tube outputs, and the audio quality will be basically garbage IMHO.

Best to start with the schematic of the amplifier and we can go from there. If you haven't built an amplifier yet, you can just build a design that doesn't require a transformer output.
 
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Nope.

Assuming you meant 15k:600R (your math show this to be true), You will connect a 23R load to the secondary designed for 600R (headphones) to the transformer which will reflect ~575R to the tube as the load on a winding designed to be 15K. This effectively makes the coil act like a 575R:23R transformer.

575R is too low for almost all tube outputs, and the audio quality will be basically garbage IMHO.

Best to start with the schematic of the amplifier and we can go from there. If you haven't built an amplifier yet, you can just build a design that doesn't require a transformer output.

the schematic (see below) calls for 10K ohms/150 ohms with 8.2 turns ratio.
The designer of the schematic posted a few years ago the following cut/paste

....snip
Hi, An alternative is any small push-pull output transformer with the right value for the primary and something that will match your phones on the secondary. You can also play the impedance game with them. Find one with the right number of turns ratios and use it. The precise number is not all that important, but the ratio in the ones used is 8.2 to 1. Remember that the actual impedance is the square of the turns ratio times the load impedance. (of if you rather ...divide the primary impedance by the square of the turns ratio). A 600 ohm to 8 ohm would be a pretty good match (ratio of 8.6).
snip....

DIY 6DJ8 (ECC88) Tube Hi-Fi Headphone Amplifier Project
 
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Sorento

Member
2008-03-12 9:59 pm
the schematic (see below) calls for 10K ohms/150 ohms with 8.2 turns ratio.
The designer of the schematic posted a few years ago the following cut/paste

....snip
snip....

DIY 6DJ8 (ECC88) Tube Hi-Fi Headphone Amplifier Project

Not true ... The designer called for a turns ratio of at least 11.5 : 1 for hp 32 ohms on a 10k : 75R tap.
quote
While there is some loss of efficiency in using headphones below 32 ohms on the 75 ohm tap there was minimal effect on the quality of the sound. For use with higher impedance headphones you can use the Edcor XSM10K/600. The primary impedance of the Edcor XSM10K/600 is 10k with a 600 ohm center tapped secondary that is ideal for use with 300 ohm and 600 ohm headphones.
unquote
 
I'm trying to learn how to select the correct output transformers to match the load impedance of my 23 ohm headphones.

So the output transformers are matching "line matchers".
The turns ratio is 5.1 with 15K ohms/600.
I'll use a matched pair (left/right) in my tube amp build.

Please correct me but my understanding is that
5.1 squared = 26.01
so then i multiply
26.01 x 23 ohms = 598.23
so then 598.23 is close enough to 600 ohms which means the above output transformers are perfectly matched to the 23 ohm load of my headphones.
Right?

Your tube sees 600 ohms primary load (instead the 15K) when you load the secondary with 23 ohms in place of 600 ohms.
 
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I would not recommend decreasing the step-down ratio for that project, as it will bring up the noise floor in trade for power you probably don't need.

To speak more generally regarding the subject of your post, when you have 23 ohm headphones, I would tend to assume that they are very sensitive headphones and that power won't be an issue (unless they are power hungry planars, but that seems somewhat unlikely).

For really sensitive 23 ohm headphones, I would use a 10K:16 transformer or something close to those specs. There are plenty of 8K-10K guitar amp transformers that will perform really nicely at headphone levels; that's where I'd start. Using your 23 ohm headphones on the 75 ohm tap of that Edcor transformer will decrease the reflected impedance sufficiently to drive up distortion and you don't have to make that sacrifice since you're scratch building this.

If you happen to have power hungry planar headphones that are 23 ohms, then you will need to select a different amplifier design capable of far greater power output.