RF toolkit capacitance calculation
显示 更早的评论
In RF toolkit/transmission line objects, the capacitance per unit length is calculated using the acosh function:
C=πε/acosh(D/2a)
Most texts use this equation:
C=πε/ln(D/a)
Are these expressions equal? If so, how are they equal?
采纳的回答
David Goodmanson
2020-10-3
编辑：David Goodmanson
2020-10-3
Hi Derek,
The exact expression is indeed the acosh expression used in Matlab, and we would expect no less. The log expression is an approximation, and it's a bit of a holdover from the times when scientific software was not readily available. acosh was not so easy to calculate, but log tables were common. Leaving out the factor of pi*epsilon, the approximation goes as follows. Using the variable Cinv for 1/C, then
Cinv = acosh(D/2a)
so
cosh(Cinv) = D/2a
(exp(Cinv) + exp(-Cinv))/2 = D/2a
Now if D/2a is large, then Cinv is large and you can drop the exp(-Cinv) term compared to the exp(Cinv) term. Then
exp(Cinv) = D/a
Cinv = log(D/a)
The natural question is, how large is large?
Da = 2:.001:20; % D over a
Cinv1 = acosh(Da/2);
Cinv2 = log(Da);
plot(Da,Cinv1,Da,Cinv2)
legend('acosh(d/2a)','log(D/a)','location','northwest')
The plot shows a pretty good approximation for D/a greater than about 5.
2 个评论
Derek Neal
2020-11-12
David Goodmanson
2020-11-12
编辑：David Goodmanson
2020-11-17
Hi Derek,
It's good to check these things out as you are doing. Looks like they are using radius instead of diameter because that doubles the resistance, and in this situation you have two wires carrying equal current, not just one wire.
更多回答（0 个）
类别
在 帮助中心 和 File Exchange 中查找有关 Other Formats 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
