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antenna problem
- Thread starter mharriswy
- Start date
D
Deleted member 4993
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I need to solve for S. The formula I have is Z=276 log (2s/d). Z is the characteristic impedance of a feedline, d is conductor diameter and S is spacing between conductors. Can anyone help me transpose to find S?
Thanks
Use the definition of log function:
log (x) = y → x = 10y
Technically, you cannot solve for S from Z = 276 log(2s/d) - becuase you do not have an S (capital) in the equation!
typo
sorry my typo, it should read Z= 276 log(2S/d)
sorry my typo, it should read Z= 276 log(2S/d)
Use the definition of log function:
log (x) = y → x = 10y
Technically, you cannot solve for S from Z = 276 log(2s/d) - becuase you do not have an S (capital) in the equation!
You still need to follow Subhotash Kahn's suggestion. Whenever your unknown is a logarithm, you need to raise the base of the logarithm to that power (the inverse function of taking a logarithm). Get your equation into the formsorry my typo, it should read Z= 276 log(2S/d)
log(x) = y
and then raise 10 to the power of each side of the equation, giving
x = 10^y
HallsofIvy
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- Jan 27, 2012
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If I were being strict, I would say you can't solve for S because there is no "S" in the equation! But I will guess that you mean "transpose to find s".I need to solve for S. The formula I have is Z=276 log (2s/d). Z is the characteristic impedance of a feedline, d is conductor diameter and S is spacing between conductors. Can anyone help me transpose to find S?
Thanks
If the problem were to calculate Z, given s, we would do four things:
1) Multiply by 2
2) Divide by d
3) Take the logarithm
4) Multiply by 275.
To solve for s, we do the opposite of each step in the opposite order:
1) The opposite of "multiply by 275 is "divide by 275".
Of course, we have to do this to both sides of the equation. Z/276=(276 log (2s/d))/276 gives Z/276= log(2s/d).
2) The opposite of "take the logarith" is "take the exponential". Take 10 to the power of each side.
\(\displaystyle 10^{Z/276}= 10^{log(2s/2}= 2s/d\).
3) The opposite of "divide by d" is "multiply by d".
\(\displaystyle 10^{Z/276}d= (2s/d)d= 2s\)
4) The opposite of "multiply by 2" is "divide by 2".
\(\displaystyle \frac{10^{Z/276}d}{2}= s\)