What is the formula for calculating output impedances?

[garrettendi]

So say I have two headphones, one is 32 ohms and the other is 100 ohms and I decide to connect them to a headphone output using a Y-cable.

How do I calculate the total load? I know if both were 32 ohms it'd be a 16 ohms load but what is the formula for mis-matched impedances?

[James Perrett]

I always remember it as 1/R1 + 1/R2 = 1/Rtotal

[garrettendi]

So in this example:

1/32 =0.03125
1/100 = 0.01

0.03125 + 0.01 = 0.04125

And then to convert that back to ohms:

1/0.04125 = 24.24 ohms?

[garrettendi]

Further question:

I have 32 ohm headphones as described, as well as a wireless transmitter for my cochlear implant. The transmitter is a line in device, and the manufacturers state it can go up to 100 ohm without significant distortion. So I figure calling it a 100 ohm headphone would be apt. So the calculated impedance would be 24 ohms.

The wireless transmitter works great connected on its own to my Behringer UMC204HD, no problems at all... I have an Art HeadAmp4 that I could connect to the Berry, but given I only need to use two headphones for a very short period of time, it would be much more convenient to use a Y splitter if possible.

The really annoying thing is NOWHERE in the manuals, specs, or the online forum do Berry mention the headphone output impedance.

Do you guys suspect that using a Y-splitter for this instance is ok, or would I be forced to use my HeadAmp 4?

[Hugh Robjohns]

How do I calculate the total load? I know if both were 32 ohms it'd be a 16 ohms load but what is the formula for mis-matched impedances?

The lowest value dominates the calculation, so intuitively I'd guesstimate it's going to be a bit less than 32 Ohms -- say 25 Ohms -ish.

The actual formula for parallel resistances is R-parallel = 1/(1/R1+1/R2+1/R3...etc) which works out to 24 Ohms in this case.

However a few points to note:

1. this is not output impedance! This is the total load impedance.

2. In situations like this, the mismatched load impedances will cause mismatched loudnesses and it's never a good idea to connect dissimilar headphones to the same headphone amp because one listener will complain it's too quiet and the other that it's too loud.

Use your four-way headphone amp!

H

[garrettendi]

So it wouldn't damage anything, it would just potentially sound awful through one headphones?

I actually have a volume control on my implant, so I can set that as desired and the second listener can set the level of the output to whatever is comfortable.

[garrettendi]

Use your four-way headphone amp!

My apologies Hugh, I missed this last comment.

I think it'd be more "convenient" to use the Y-splitter, but given I already have the HeadAmp 4 there is a big difference between "convenience" and being downright "lazy".

I'll use the HeadAmp!

But for future use, at least now I can calculate impedance

[James Perrett]

The transmitter is a line in device, and the manufacturers state it can go up to 100 ohm without significant distortion. So I figure calling it a 100 ohm headphone would be apt.

I think you've got the wrong end of the stick here! What EXACTLY does it say?

[garrettendi]

It doesn't say anything! I had to phone the manufacturers (Cochlear) and after being sent around a bit I got the following:

"It can connect to all my headphone sockets safely and can go up to 100 ohms, even then - no damage to mini mic (this is the name of the transmitter) just a bit of a distortion."

And:

"The mini mic uses a line input"

Details can be found here: http://www.cochlear.com/wps/wcm/connect ... microphone

It has a 3.5mm jack for connecting to headphone outputs. This is the best way to listen to headphones with the Cochlear Implant, and they recommend it to be used with headphone outputs.

EDIT: The quick guide PDF demonstrates it perfectly.

[Hugh Robjohns]

Oh yes, I missed that -- good spot James.

A line-input device is only interested in the signal voltage. Impedance is almost entirely irrelevant provided that the unit's input impedance is significantly higher (usually x10) than the source's output impedance.

So I suspect what your implant specs are stating is that the source impedance should be less than 100 Ohms -- which is a perfectly reasonable request and most line output stages will meet that requirement easily, as will most headphone amps, in fact.

In contrast, real headphones need power -- they are just mini-loudspeakers and need energy to make them move about. Power is the product of voltage and current, so for a given amplifier voltage the received power will be dependent on the headphone's load impedance since it is that which impedes the flow of current.

Hence low-impedance headphones tend to sound louder than high-impedance headphones because greater current can flow and thus more power reaches the voice coils (although the sensitivity of the headphone's magnetic motor design also plays a role in the perceived volume).

H

[garrettendi]

Thanks Hugh. Forgive me for being dense but there's a bit about what you said I didn't fully understand... What's the "bottom line" if I may ask?

I've used headphones and the "mini mic" with my HeadAmp 4 with never a problem, and a Y-splitter with 32 ohm headphones and the "mini mic" on my e-drum kit, again with no issues.

EDIT: I know from the hospital and the Cochlear company that using the "mini mic" with headphone outputs is safe AND 100% recommended. So all that's left to know is the whole mixing things up.

[Hugh Robjohns]

The situation you're describing is completely different to the situation or wiring dissimilar headphones together.

In wiring dissimilar headphones to the same headphone output you're trying to share power between the two sets of headphones, but because one has a very different impedance to the other, that power won't be shared equally and the two headphones will have very different volumes as a result.

In your situation, you're only sending power to one pair of headphones. The cochlear implant's electronics are essentially 'eavesdropping' across the headphone amp's output, but they are not drawing any significant power from it. Moreover, because the implant's electronics has its own volume control you can set the volume for the headphones as required, and then adjust the cochlear implant box to suit your own demands -- but do take care to set the headphones first. I don't think you'd enjoy it if you set your implant level and then the headphone user cranks their level up, raising yours at the same time!!

For that reason, I still think using the headphone box with four independent outputs would be safer, wiser and more versatile...

H

[garrettendi]

Thanks Hugh!

I'll try to use the HeadAmp to give that extra bit of control, but content in the knowledge that the Y-splitter is an option - albeit with the caveat of setting the headphone volume FIRST.

One of the perks of having an implant though, is that while loud sounds fed directly in will not be comfortable, it is safe. They did tests with rats where they fed in very very loud sounds into implanted rats and there were no effects on the implant and hearing.

So the manufacturers and the hospital have both confirmed that loud music is completely safe for me when fed directly into the implant.

Having said that, while I enjoy the freedom of not having to obsess about volumes, I would MUCH rather not need an implant and have perfect hearing. Life with an implant is not particularly pleasant. Learning to hear music after the operation takes months, with no guarantee that the patient will EVER hear music again.

But that's a story for a SoS Meet! (HINT!)

EDIT: So remember people.... Turn down your headphones! You don't want to suffer like I and my loving fiancee have because of my situation!

Also, I do keep my volumes to a comfortable level anyway. Loud music, even though it won't damage the implanted ear, DOES have an impact on my tinnitus.