Transformer, Oscillator & transposing fomulae

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SUMMARY

The discussion focuses on the calculation of loop gain in an oscillator circuit, specifically addressing the equations for gain and resistance. The relevant equations provided are Gvloopgain = 1/n ((hfe/hie)R'L) and R'L = RL || hoe || (n^2(R1 || R2)). The user expresses confusion regarding the quadratic formula's application in this context, indicating a potential misunderstanding of the resistance calculations involving h_{oe}. Key values include R1 = 4700, R2 = 24000, RL = 2700, Hie = 250, and Hoe = 10^-5.

PREREQUISITES
  • Understanding of oscillator circuit design
  • Familiarity with electrical engineering concepts such as admittance and resistance
  • Knowledge of algebraic manipulation and quadratic equations
  • Proficiency in using circuit analysis techniques
NEXT STEPS
  • Study the principles of oscillator design and stability analysis
  • Learn about the implications of using h_{oe} in resistance calculations
  • Explore the application of quadratic equations in electrical engineering problems
  • Investigate the significance of turn ratios in transformer circuits
USEFUL FOR

Electrical engineers, circuit designers, and students studying oscillator circuits and their mathematical foundations will benefit from this discussion.

cjm181
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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
242437

242438


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

Thanks

C
 
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##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.
 
cjm181 said:
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!
 

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