Help with a mathematics formula please anyone?

[TonyRPH]

My maths is not very strong - and I'm trying to perform a complex (to me!) calculation, but I cannot seem to master it.

I am using this equation as an example: (ignore the leading ":" it's just a bit of text I captured by mistake)



So as I read that, it's SQRT(3.374e-6)squared / (1.228)squared * 100 = 0.000275%

But no matter how many variations I enter into my calculator(s!), I cannot arrive at the given answer.

I have tried breaking the calculations down into individual chunks - and also enclosing everything inside parenthesis i.e. SQRT((xyze-6)SQ/(abc)SQ)*100

Can anybody help please?

I'm hoping the sample equation I have is correct!

Thanks in advance.

[TonyRPH]

Fugazi said:

100* sqrt((3.374*mu*Vrms)^2/(1.228*Vrms)^2)

Should work? What are the values of Vrms and Mu?

What is "mu"?

The value of Vrms is 3.374uV

3.374uV is 3.374e-6v or 0.000003374v - correct?

Can you explain what the "mu" is please?

[TonyRPH]

Trying your suggested method (discarding the "mu" confusion) I get 0.68105129

Gor the avoidance of any doubt on my 'old skool' calculator...

[TonyRPH]

Aha - I think I have fallen foul of the order in which the calculator performs the calculations.

[TonyRPH]

Very nice - I'll try that on my tablet (phone is a Microsoft Lumia and given the lack of apps...)

My calculators were getting screwed up with the scientific notation I think.

Thanks for the help everyone.

Chester draws said:

A most appropriate username!! (draws) :P

[TonyRPH]

As it happens, I was using the wrong button on my calculator to raise the number to -6

I was using Ex instead of 10x !

Solved!

[TonyRPH]

EliseNick said:

You can cancel the square root and the powers of two.

So you can...

Or at least I got the same result using this method.

So why add the additional complication in the first place?

[TonyRPH]

EliseNick said:

No idea! What's the context?

Apologies for the delay in replying.

The context is calculating THD+N (distortion + noise) for an audio preamplifier.

The article reads as follows (extract):

However, the THD+N ratio of a circuit can be predicted from the total noise by using Equation 10, where V is the total voltage noise in Vrms over a specified bandwidth and VF is the fundamental signal amplitude in Vrms



The result of the simulated total noise analysis at unity gain is shown in Figure 14. The audio analyzer
which will be used for real-world measurements will be set to a maximum bandwidth of 80 kHz, so this
simulated analysis is performed to 80 kHz.



The total noise at 80 kHz was found to be 3.374 µV RMS. Given our input signal amplitude of 1.228 V,the predicted THD+N ratio was calculated using Equation 11.



The simulated THD+N ratio was found to be 0.000275%, which meets the design requirement of 0.0005%.

[TonyRPH]

EliseNick said:

OK. Well, it's a bit wierd, but consider the first equation in this;

https://en.wikipedia.org/wiki/Total_harmonic_disto...

Along the top line are the sum of voltages squared, because you're adding noise (or distortion) power, which is proportional to V^2. Then the V_F on the bottom could be squared and inside the root. So your normalising the sum of powers by dividing by another power. So far so good. Then to get a voltage ratio you take the square root.

In your text, they appear to have left the V^2 in for no great reason, because they've scooped up everything in the V_N as far as I can see. I guess it acts as a reminder that you are in some sense adding powers rather than voltages.

All of the maths on the Wiki page went completely over my head!