# [TCML] Calculate Output Voltage

Antonio Carlos M. de Queiroz acmdq at uol.com.br
Fri Nov 16 11:38:04 MST 2007

```Mddeming at aol.com wrote:
> You're right. It's Wrong. That formula is correct for non-resonant,
> iron-core transformers with coupling coefficient close to 1.00. A better  theoretical
> value is Vs=Vp x sqrt(Ls/Lp), where L is the inductance, and  this is an upper
> limit. Hitting 80% of this value requires a very well  designed and tuned
> coil.
Not completely wrong, as inductance is always proportional to the square
of the number of turns.
If it were possible to wrap a primary coil along all the length of the
secondary coil, the voltage
gain would be close to the turns ratio, as both coils would have almost
the same geometry.
But as the coils don't have the same geometry, the voltage gain is the
turns ratio multiplied
by a constant, smaller than 1, that depends on the exact geometry. The
voltage gain can also
be written as sqrt(Cs/Cp), where Cs is the total secondary capacitance
and Cp the primary
capacitance. As LsCs=LpCp for a correctly tuned coil, the result is the
same.

Antonio Carlos M. de Queiroz

```