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Old 22nd Feb 2019, 3:43 pm   #1
ms660
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Default Formula...?

Known...(antenna length) l = 24.4 metres, Lambda (wavelength) = 300 metres.

Formula in book: 2*pi*l/Lambda.

My calc: = 0.511.

In the book it shows....2*pi*l/Lambda = 29.3 degrees.

I can figure out 29.3 degrees by another route, but not by the above formula.

Maths not to good with me but can someone explain?

Lawrence.
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Old 22nd Feb 2019, 3:53 pm   #2
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Default Re: Formula...?

The formula θ = 2 * π * λ / L gives you an angle in radians.

Since there are 2 * π radians in a full circle, we can convert radians to degrees by multiplying by 180 / π.

0.511 radians * 180 / π = 29.3°.

EDIT: If you want θ in degrees, just use θ = 360 * λ / L.
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Old 22nd Feb 2019, 4:02 pm   #3
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Default Re: Formula...?

Quote:
Originally Posted by julie_m View Post
The formula θ = 2 * π * λ / L gives you an angle in radians.

Since there are 2 * π radians in a full circle, we can convert radians to degrees by multiplying by 180 / π.

0.511 radians * 180 / π = 29.3°.

EDIT: If you want θ in degrees, just use θ = 360 * λ / L.
Yes but that doesn't explain the formula in the book.

My alternative route mentioned in Post1 to arrive at 29.3 degrees was

l(360/Lambda)

Lawrence.
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Old 22nd Feb 2019, 4:11 pm   #4
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Default Re: Formula...?

What is the UNKNOWN, ie 0.511 you're calculating?
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Old 22nd Feb 2019, 4:34 pm   #5
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Default Re: Formula...?

29.3 degrees and 0.511 radians are the same thing.
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Old 22nd Feb 2019, 4:34 pm   #6
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Default Re: Formula...?

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Originally Posted by Station X View Post
What is the UNKNOWN, ie 0.511 you're calculating?
Good question Graham, it's part of an example calculation to do with an antenna, I should have included a link Link below to RDH4, starts near the bottom of book page 903, to be fair I've also posted the question on GVR.

Also to me there seems to be a mix up with Zo and Zi in that same example, see formula (29) and the formula given in part (a) in the calculations?:

http://frank.yueksel.org/other/RCA/R...sion-Lines.pdf

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Old 22nd Feb 2019, 5:36 pm   #7
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Default Re: Formula...?

Quote:
Originally Posted by ms660 View Post
... Yes but that doesn't explain the formula in the book ...
You're right, it doesn't. The problem is that the author isn't really interested in the angle's units. He's trying to work out Xi and for that he needs to know its cotangent. Back in the 1950's when RDH4 was written he'd have looked the cotangent up in a book of trig tables (or he'd have looked the tangent up and worked out the inverse with his slide rule). As long as he knew the angle, in whichever units the tables were in, he'd be OK. My guess is that his original text was in radians but some subeditor decided that they would standardise on degrees instead. They converted the right hand side of the equation but failed to put the 180/pi factor into the left hand side. People who work with this stuff all the time just know that 2.pi.l/lambda is really an angle and swap between degrees and radians without thinking about it.

EDIT I think you're also right about the Zo and Zi mixup. In part (a) where he works out Zi as 603 ohms he should have said that that's Zo. Just a few lines further down he says Zi is 21 - j.1070 ohms and that's correct.

Cheers,

GJ
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Last edited by GrimJosef; 22nd Feb 2019 at 6:05 pm.
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Old 22nd Feb 2019, 5:53 pm   #8
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Default Re: Formula...?

Quote:
Originally Posted by GrimJosef View Post
Quote:
Originally Posted by ms660 View Post
... Yes but that doesn't explain the formula in the book ...
You're right, it doesn't. The problem is that the author isn't really interested in the angle. He's trying to work out Xi and for that he needs to know the cotangent of the angle. Back in the 1950's when RDH4 was written he'd have looked the cotangent up in a book of trig tables (or he'd have looked the tangent up and worked out the inverse with his slide rule). As long as he knew the angle, in whichever units the tables were in, he'd be OK. My guess is that his original text was in radians but some subeditor decided that they would standardise on degrees instead. They converted the right hand side of the equation but failed to put the 180/pi factor into the left hand side. People who work with this stuff all the time just know that 2.pi.l/lambda is really an angle and swap between degrees and radians without thinking about it.

Cheers,

GJ
Cheers for that but should the Zo (formula (29)) be the same as Zi (4th line of (a) or is Zi in the 4th line of (a) a mistake?

Lawrence.
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Old 22nd Feb 2019, 6:10 pm   #9
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Default Re: Formula...?

Sorry, my EDIT to my previous post may have crossed with your last query. Zo is not the same as Zi - there is a mistake in the 4th line of (a).

I have a 6th impression (1963) of RDH4 up in the loft and I've just been up to check it. This part hasn't been corrected in the main text there and there's nothing about it in the Addenda at the back.

Cheers,

GJ
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Old 22nd Feb 2019, 6:14 pm   #10
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Default Re: Formula...?

Quote:
Originally Posted by GrimJosef View Post
Sorry, my EDIT to my previous post may have crossed with your last query. Zo is not the same as Zi - there is a mistake in the 4th line of (a).

I have a 6th impression (1963) of RDH4 up in the loft and I've just been up to check it. This part hasn't been corrected in the main text there and there's nothing about it in the Addenda at the back.

Cheers,

GJ
Cheers for that, it's easy to see where the seeds of my confusion have crept in.

Lawrence.
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