Transformer, Oscillator & transposing fomulae

[cjm181]

Homework Statement

It can be shown that the loop gain of the oscillator at resonance is given by equation 1, Where R'L is given by equation 2.

Estimate the turn ratio

Relevant Equations

Gvloopgain = 1/n ((hfe/hie)R'L) .......................1
R'L = RL || hoe || (n^2(R1 || R2)) ...................2

When:
R1 = 4700
R2 = 24000
RL = 2700
Hie = 250
Hoe = 10^-5
Hie = 4000

But the quadratic doesn't work. I can't see where i have gone wrong. Is my approach miles off?

Thanks

C

 

[gneill]

$h_{oe}$ is an admittance (units are Siemens). So I think you'll want to use $1/h_{oe}$ to convert it to a resistance in your $R'_L$ calculation.

 

[PeroK]

Problem Statement: It can be shown that the loop gain of the oscillator at resonance is given by equation 1, Where R'L is given by equation 2.

Estimate the turn ratio
Relevant Equations: Gvloopgain = 1/n ((hfe/hie)R'L) ......1
R'L = RL || hoe || (n^2(R1 || R2)) ......2

When:
R1 = 4700
R2 = 24000
RL = 2700
Hie = 250
Hoe = 10^-5
Hie = 4000

View attachment 242437
View attachment 242438

But the quadratic doesn't work. I can't see where i have gone wrong. Is my approach miles off?

Thanks

C

This is why algebra was invented!