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Old 9th Apr 2019, 11:15 am   #41
PJL
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Default Re: Maths help....Again...exp?

This is the simulation from PSU Designer. It is not created by a formula, it calculates the outcome in time steps so you can see the initial surge during the first cycle and the settling down towards a steady state. Each component in the circuit obeys simple rules but, as the circuit contains a rectifier and is non-linear, the overall circuit behaviour cannot be accurately calculated.

The formula you are using is assuming that the rectifier is instantaneously charging the reservoir capacitor up to the input voltage on each cycle. It makes no allowance for the transformer regulation but this would be the first place to look when designing a PSU.

Calculations on a linear LRC network can be done 100% accurately but anything with a non-linear component will require approximations.
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Old 9th Apr 2019, 11:27 am   #42
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Default Re: Maths help....Again...exp?

Quote:
Originally Posted by kalee20 View Post

What don't I agree with Dave about? If the load is a quick-responding switching regulator, then it will draw constant power so in this case, as voltage falls, current will increase so the ripple waveform, instead of ramping linearly down (constant current load) or curving with negative exponential (resistive load), it curves increasingly steeply downward according to a square-root law. And these days, this is becoming quite real-world too!
I quite agree!

I was talking in terms of simple three-terminal linear regulators, or of series-pass valve regs.

When switchers enter the scene, it gets a lot nastier. Their efficiency means they tend to take constant power, so to whatever is feeding them the don't look like a resistive load, they don't look like a constant-current load. they look like a negative resistance load1 These things can make systems go unstable. In an aeroplane more and more of the electrical load is going into 'smart' stuff with switch-mode internal regulators. At some point the generator controller isn't going to cope with the less stable loads. Quite worrying. Real resistive loads have nice stabilising effects on power systems, but they're fast going away.

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Old 9th Apr 2019, 11:32 am   #43
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Default Re: Maths help....Again...exp?

I know what exponential decay is in terms of CR and time, we did graphs etc of that at City & Guilds tech.....What I can't do yet is work out the answer using the formula that's under discussion, my own calculator has no e, exp or upward arrow function and if I times something by trying to put a minus in front of it the display just goes AWOL... so I searched the web for an online exp calculator, I couldn't make sense of them either except for one, the one in the link I posted earlier.

Next phase was to try a different approach using the mentioned exp calculator, I did the calc for T/CR on the calculator I have at home, that was no problem for me, I entered the result into that exp calculator and it spewed out a result.

Then with my home calculator I divided Vp-0.7 with that result, the result of that was then subtracted from Vp-0.7 and the result of that agreed with the result shown on the website in the link I posted earlier, the result was Vr=0.47volts.

I then used the same method for the other examples shown on that website and the results I obtained were in agreement.

But that hasn't solved the problem of me not solving the original equation, to that end GeoffK pointed me to a scientific calculator on Windows 10 which I now have.....

…..so now it would be nice if someone could talk me through the procedure to obtain the correct answer using the formula under discussion and the Windows 10 scientific calculator that I now have, the inputs are Vp-0.7=14.3 volts....T=0.01667 secs....R=5,000 ohms....C=100uF (I know how to do T/CR but that could be included again in the talk through procedure)

Anyone?

It would also be good if someone can explain to me the relationship between the method that I used and the mathematical goings on in the formula incase I've already missed it.

Formula to crack on the calculator is shown here again for convenience:

Vr=(Vp-0.7)(1-exp(-T/CR))

P.S. I haven't replied to all the posts but I appreciate everyone's input so far.

Lawrence.
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Old 9th Apr 2019, 12:09 pm   #44
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Default Re: Maths help....Again...exp?

Looking at the "exp" item, it's most likely another name for log, but as most logs work in base 10 , it's most likely that, but to add to the confusion, some older computers ( heading back to the old speccie days ) used the Naperian base of 2 and a bit.
Easiest way to find if calculator used base 10 is to enter 2 and get the log of that. If the answer is .3010 then it's base 10 .
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Old 9th Apr 2019, 12:15 pm   #45
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Default Re: Maths help....Again...exp?

What you calculated on your home calculator, which gave the correct answer, was to work out

(Vp-0.7) - (Vp-0.7)/exp(T/CR)

Do you agree ?

We can rewrite this expression by taking (Vp-0.7) out, since it's a factor of both the terms in the expression. That converts your home calculation to

(Vp-0.7)(1-1/exp(T/CR))

Does that make sense ?

Then all we have to do is to recognise that 1/exp(T/CR) is equal to exp(-T/CR). That was my point about exp of minus something being the reciprocal of exp of plus the same something, quite a few posts ago. Making that change gives us

(Vp-0.7)(1-exp(-T/CR))

Hey presto ! In just two steps we've shown that what you calculated on your home calculator turns out to be equal to the original formula, so it's no surprise that your home calculation gave the right answer .

Cheers,

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Old 9th Apr 2019, 1:26 pm   #46
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Default Re: Maths help....Again...exp?

My bold:

Quote:
Originally Posted by GrimJosef View Post
What you calculated on your home calculator, which gave the correct answer, was to work out

(Vp-0.7) - (Vp-0.7)/exp(T/CR)

Do you agree ?

Thanks for that, yes, got that, cheers.

We can rewrite this expression by taking (Vp-0.7) out, since it's a factor of both the terms in the expression. That converts your home calculation to

(Vp-0.7)(1-1/exp(T/CR))

Does that make sense ?

No, but that's because I know zilch about taking out terms from a formula, on the other hand yes I can accept that because you know what you're doing with maths and I don't in this particular case.

Then all we have to do is to recognise that 1/exp(T/CR) is equal to exp(-T/CR). That was my point about exp of minus something being the reciprocal of exp of plus the same something, quite a few posts ago. Making that change gives us

(Vp-0.7)(1-exp(-T/CR))

Hey presto ! In just two steps we've shown that what you calculated on your home calculator turns out to be equal to the original formula, so it's no surprise that your home calculation gave the right answer .

It's all the - sign stuff that confuses me, the method I used in which you derived and showed an actual formula...(Vp-0.7) - (Vp-0.7)/exp(T/CR)…. makes sense to me insofar that if the problem was all new to me from scratch I could easily solve that formula, no silly minus sign in front of something that needs to be multiplied but I would still like someone to talk me through the procedure of solving the original equation using a Windows 10 scientific calculator.

Cheers,

GJ
Lawrence.

Update, I calculated T/RC where T=.01667 secs...R=5,000 ohms....C=100uF....the answer came to 0.03334, I then did the following with the scientific calculator, I entered 1 then - then pressed the exp button then - then entered 0.03334 then hit the equals button, this is what I got...
...0.9666....multiplying 14.3 (Vp-0.7) by that number doesn't give Vr, the ripple voltage, where did I go wrong?

Lawrence.
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Old 9th Apr 2019, 1:29 pm   #47
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Default Re: Maths help....Again...exp?

The microsoft scientific calculator is rubbish and won't allow you to do this. Alternatives are:

* Microsoft Excel
* Microsoft Mathematics - download here https://www.microsoft.com/en-gb/down....aspx?id=15702

Image of calculation on Microsoft Mathematics below and you enter it like a formula using 'e^' for 'exp'. The '^' symbol does not display correctly in the app.
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Old 9th Apr 2019, 1:40 pm   #48
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Default Re: Maths help....Again...exp?

Quote:
Originally Posted by Oldcodger
Looking at the "exp" item, it's most likely another name for log
Exp is antilog, for a base 'e' log.
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Old 9th Apr 2019, 1:44 pm   #49
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Default Re: Maths help....Again...exp?

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Originally Posted by PJL View Post
The microsoft scientific calculator is rubbish and won't allow you to do this.
In a way I'm kind of glad my alternative method works, I had no idea that things could become so unclear and complicated....for me at least.

Is there a suitable live online calculator I can use instead of a download? I've got enough download clutter on my PC as it is.

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Old 9th Apr 2019, 1:52 pm   #50
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Default Re: Maths help....Again...exp?

Quote:
Originally Posted by ms660 View Post
My bold:

Quote:
Originally Posted by GrimJosef View Post
We can rewrite this expression by taking (Vp-0.7) out, since it's a factor of both the terms in the expression. That converts your home calculation to

(Vp-0.7)(1-1/exp(T/CR))

Does that make sense ?

No, but that's because I know zilch about taking out terms from a formula, on the other hand yes I can accept that because you know what you're doing with maths and I don't in this particular case.
If something is equivalent to a load of other things multiplied together then all of those other things are called factors of the first thing. So 21 is 7 multiplied by 3, and 7 and 3 are therefore factors of 21. Likewise 13 and 3 are factors of 39. If I wanted to know what 21 + 39 was then I could simply do the addition and get the answer 60. But I could also write that as 7x3 + 13x3 and now, since 3 is a common factor (i.e. it occurs in both terms), I could 'take the factor 3 outside' and rewrite the expression as (7 + 13) x 3 which is 20 x 3 which is also 60. Adding 21 to 39 isn't hard, so doing the same sum by taking the common factor out doesn't save us much effort. But when the expressions get complicated, say because they contain variables like Vp, then taking out common factors can be a useful thing to do.

Cheers,

GJ
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Old 9th Apr 2019, 1:55 pm   #51
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Default Re: Maths help....Again...exp?

Microsoft Mathematics looks like a useful free app from Microsoft, far better than the standard Microsoft Calculator that does not even support a sign or a decimal point on exponents on my PC.
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Old 9th Apr 2019, 3:05 pm   #52
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Default Re: Maths help....Again...exp?

Could someone confirm the answer to exp0.03334 on their scientific calculator, the online exp calculator I'm using says 1.0339 the Windows 10 calculator just returns 0.e+3334 which doesn't compute with me.

Lawrence.
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Old 9th Apr 2019, 3:19 pm   #53
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Default Re: Maths help....Again...exp?

The Microsoft calculator has In and pressing Inv at the top row gives e^x
Exp is the exponent i.e. 1^Exp2=100

It is a perfectly good inbuilt calculator, not rubbish at all.
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Old 9th Apr 2019, 3:24 pm   #54
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Default Re: Maths help....Again...exp?

When x is much less then 1, exp(x) is approximately equal to 1+x.

So exp(0.03334) is approximately 1.03334. The online exp calculator's answer is 1.0339 and that's correct (and very close to the approximate answer).

Cheers,

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Old 9th Apr 2019, 3:38 pm   #55
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Default Re: Maths help....Again...exp?

Quote:
Originally Posted by GeoffK View Post
The Microsoft calculator has In and pressing Inv at the top row gives e^x
Exp is the exponent i.e. 1^Exp2=100

It is a perfectly good inbuilt calculator, not rubbish at all.
The windows 10 scientific calc that I now have on my PC doesn't have an In or Inv button....unless I've missed it.

Lawrence.
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Old 9th Apr 2019, 3:48 pm   #56
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Default Re: Maths help....Again...exp?

Quote:
Originally Posted by GrimJosef View Post
When x is much less then 1, exp(x) is approximately equal to 1+x.

So exp(0.03334) is approximately 1.03334. The online exp calculator's answer is 1.0339 and that's correct (and very close to the approximate answer).

Cheers,

GJ
Cheers, I've saved the link for the online exp calc that gave me the answer of 1.0339 for exp0.03334:

https://www.medcalc.org/manual/exp_function.php

It's the only one I could find that I could make sense of.

Lawrence.
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Old 9th Apr 2019, 3:49 pm   #57
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Default Re: Maths help....Again...exp?

Quote:
Originally Posted by GeoffK View Post
The Microsoft calculator has In and pressing Inv at the top row gives e^x
Exp is the exponent i.e. 1^Exp2=100

It is a perfectly good inbuilt calculator, not rubbish at all.
You are right, I always uses Excel and hate calculators!

So instructions for Lawrence are:
1. Press [C]
2. Enter 0.03334
3. Press [Inv]
4. Press [ex]
5. Result = 1.033902...

Microsoft Mathematics accepts complex expressions and is far more intuitive.
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Old 9th Apr 2019, 3:56 pm   #58
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Default Re: Maths help....Again...exp?

Quote:
Originally Posted by PJL View Post
Quote:
Originally Posted by GeoffK View Post
The Microsoft calculator has In and pressing Inv at the top row gives e^x
Exp is the exponent i.e. 1^Exp2=100

It is a perfectly good inbuilt calculator, not rubbish at all.
You are right, I always uses Excel and hate calculators!

So instructions for Lawrence are:
1. Press [C]
2. Enter 0.03334
3. Press [Inv]
4. Press [ex]
5. Result = 1.033902...

Microsoft Mathematics accepts complex expressions and is far more intuitive.
There's no Inv button on my Windows 10 calculator.....

I don't want to download a separate Microsoft app because when ever I download apps the pop up box rate, the spam junk rate and the general PC slowness and annoyance rate increases, that's just the way it is.

Lawrence.
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Old 9th Apr 2019, 4:14 pm   #59
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Default Re: Maths help....Again...exp?

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Originally Posted by ms660 View Post
Could someone confirm the answer to exp0.03334 on their scientific calculator, the online exp calculator I'm using says 1.0339 the Windows 10 calculator just returns 0.e+3334 which doesn't compute with me.

Lawrence.
I checked this on my ancient CASIO COLLEGE fx-80 Scientific Calculator and got the answer 1.0338606 which of course rounds to 1.0339.
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Old 9th Apr 2019, 4:32 pm   #60
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Quote:
Originally Posted by ms660 View Post
Could someone confirm the answer to exp0.03334 on their scientific calculator, the online exp calculator I'm using says 1.0339 the Windows 10 calculator just returns 0.e+3334 which doesn't compute with me.

Lawrence.
I checked this on my ancient CASIO COLLEGE fx-80 Scientific Calculator and got the answer 1.0338606 which of course rounds to 1.0339.
Cheers for that, that's three sources that say the same so I'll stick with that and the alternative formula as that seems to work out ok for me. Maths was always hard for me at school, most of what I learned came from a teacher who actually took the time to explain things to me at school, as fate would have it one of the first calls I had as an outside engineer in the R&TV trade was to her house, we had a natter.

Lawrence.
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