Re: Tank circuit L/C ratio

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <twftesla-at-uswest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:
> 
> Original poster: "Ed Phillips by way of Terry Fritz
<twftesla-at-uswest-dot-net>" <evp-at-pacbell-dot-net>

>         I learned the term "surge impedance" in college, almost 60 years ago.
> The definition was
> 
>         Zs = sqrt(L/C)
> 
> This is equal to the reactance of either L or C at the resonant
> frequency of the referenced circuit, whatever it may be.  (Work it
> out.)  Convenient for Q calculations and stuff like that.  Higher L/C
> ratios result in higher impedances, nothing more than that, and nothing
> magic at all.

I know this term from transmission lines. Quoting "The radio amateur's
handbook", 1947 edition (I love old books...):

"The characteristic impedance of a transmission line, also known as 
the surge impedance, is defined as that impedance which a long line
would present to an electrical impulse induced in the line. In an
ideal line having no resistance it is equal to the square root of the 
ratio of inductance to capacity per unit length of the line."

Although the interpretation is not the same in an LC tank, the 
expression is useful. If you take the maximum capacitor voltage in 
the primary, V1max, and divide by Zs1=sqrt(Lprimary/Cprimary) you 
obtain very closely the maximum current in the primary circuit.
If you compute the maximum secondary voltage as:
V2max=V1max*sqrt(C1/C2)
where C2 includes the terminal and the secondary self-capacitance, 
you can divide V2max by Zs2=sqrt(Lsecondary/C2) and obtain the maximum 
current in the secondary (approximately too).
Ex:
C1=10 nF
C2=10 pF
L1=0.1 mH
L2=100 mH
V1max=10000 V
Result in:
"Zs1"=100 Ohms
"Zs2"=100000 Ohms
I1max=10000/100=100 A
I2max=10000*31.62/100000=3.16 A
With k=0.105 (mode 9,10) these values are practically exact.

Antonio Carlos M. de Queiroz