Re: TC quesions (sic)

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

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

Ralph Zekelman wrote:

> > The ideal voltage gain
> >  is given by V2max/V1max = sqrt(L2/L1).
> 
> Hi Antonio,
> 
> Would you please go thru a derivation of this?
> Begin at the beguine.

By the usual lumped model:
L1=primary inductance
L2=secondary inductance
C1=primary capacitance
C2=secondary capacitance (self-capacitance of L2 and terminal
capacitance)
V1=voltage in C1 (input voltage) 
V2=voltage in C2 (output voltage)

Energy initially stored in the primary capacitor:
E1=0.5*C1*V1max^2
Maximum energy at the secondary capacitance:
E2=0.5*C2*V2max^2
By energy conservation, assuming low losses in the energy transfer:
E2=E1
And so:
V2max=V1max*sqrt(C1/C2)
But the two LC circuits are tuned to the same frequency:
L1*C1=L2*C2
and so:
C1/C2=L2/L1
and finally:
V2max=V1max*sqrt(L2/L1)

Antonio Carlos M. de Queiroz