How do I evaluate this equation? (dB to THD)

How do I evaluate this equation? (dB to THD)

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TonyRPH

Original Poster:

12,963 posts

167 months

Thursday 22nd April 2021
quotequote all
There are two equations given on this page

One converts % THD to dB and I understand this one and have a working example in Excel.

THD to dB = 20*LOG(0.0000178/100) = -134.99 dB

But the dB to THD calculation (top one in the attached image) I just cannot get my head around.

(a) is "Distortion attenuation" in dB and (k) is "Distortion factor THD" in %

I'm reading it as 10*(-134/20)*100 - however I'm somewhat confused by what looks like 10*ak over 2D? (ak) is the distortion attenuation in dB.

But if that's 2D in the equation (as against 20) then I'm stumped!

Thanks in advance!






jeremyc

23,335 posts

283 months

Thursday 22nd April 2021
quotequote all
TonyRPH said:
I'm reading it as 10*(-134/20)*100 - however I'm somewhat confused by what looks like 10*ak over 2D? (ak) is the distortion attenuation in dB.

There's your problem. You should read it as:
10 to the power of (-134/20) all multiplied by 100.

It's a simple re-arrangement of the other equation to solve for k in the following steps:
1. Divide both sides by 20.
2. Take the antilog of both sides.
3. Multiply both sides by 100

TonyRPH

Original Poster:

12,963 posts

167 months

Thursday 22nd April 2021
quotequote all
jeremyc said:
here's your problem. You should read it as:
10 to the power of (-134/20) all multiplied by 100.

It's a simple re-arrangement of the other equation to solve for k in the following steps:
1. Divide both sides by 20.
2. Take the antilog of both sides.
3. Multiply both sides by 100
Thanks! But you make it seem so simple.

Now I just need to establish how I raise 10 to a power in Excel lol...

You can tell I didn't do very well in maths at school...!

otolith

55,899 posts

203 months

Thursday 22nd April 2021
quotequote all
=10^(B2/20)*100

jeremyc

23,335 posts

283 months

Thursday 22nd April 2021
quotequote all
TonyRPH said:
Now I just need to establish how I raise 10 to a power in Excel lol...

You can tell I didn't do very well in maths at school...!
=POWER(number,power)

smilenerd

otolith

55,899 posts

203 months

Thursday 22nd April 2021
quotequote all


Excel also uses the ^ operator.

=number^power

TonyRPH

Original Poster:

12,963 posts

167 months

Thursday 22nd April 2021
quotequote all
Thank you all for bearing with this numbskull.

In Excel I put: =POWER(-134/20,10)*100 - and instead of getting 0.0000178 - I get 18228378046?

If I do it this way: =10^(-134/20)*100 - I get something closer - 0.00001995 - but it should be 0.0000178 ?

Even if I calculate -134/20 separately (-6.7) and then put 10^(-6.7)*100 it's still the wrong answer so can't be the order of calculation?

What am I doing wrong?

Mr Pointy

11,148 posts

158 months

Thursday 22nd April 2021
quotequote all
Haven't you got the number & the power the wrong way round?

=POWER(10,(-134/20))*100

=0.000019952623


Edited by Mr Pointy on Thursday 22 April 15:29

TonyRPH

Original Poster:

12,963 posts

167 months

Thursday 22nd April 2021
quotequote all
Mr Pointy said:
Haven't you got the number & the power the wrong way round?

=POWER(10,(-134/20))*100

=0.000019952623


Edited by Mr Pointy on Thursday 22 April 15:29
I did yes - but the answer should be 0.0000178 ?


TonyRPH

Original Poster:

12,963 posts

167 months

Thursday 22nd April 2021
quotequote all
DOH!

I've just demonstrated what an idiot I really am....

Working it back, 0.00001995 = -134dB

It's all about the decimal places and rounding lol.

Thanks all.