Transformer, Oscillator & transposing fomulae

You'll need to use the admittance units (Siemens) to convert to resistance in your calculation for R'L. Based on the given equations, it can be estimated that the turn ratio (n) would be approximately 2.
  • #1
cjm181
69
1
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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  • #2
##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.
 
  • #3
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!
 

1. What is a transformer?

A transformer is an electrical device that transfers electrical energy from one circuit to another through electromagnetic induction. It consists of two or more coils of insulated wire wound around a core made of magnetic material.

2. How does a transformer work?

A transformer works on the principle of electromagnetic induction. When an alternating current flows through the primary coil, it creates a changing magnetic field which induces a current in the secondary coil. This allows for the transfer of energy from the primary circuit to the secondary circuit.

3. What is an oscillator?

An oscillator is an electronic circuit that generates a continuous periodic waveform, such as a sine wave or a square wave. It is commonly used in electronic devices such as radios, computers, and clocks.

4. How does an oscillator work?

An oscillator works by converting direct current (DC) into an alternating current (AC) at a specific frequency. This is achieved by using a feedback loop that amplifies and feeds a portion of the output signal back into the input, creating a continuous oscillation.

5. What is the transposing formula?

The transposing formula is a mathematical formula used to rearrange equations in order to solve for a different variable. It involves isolating the variable of interest on one side of the equation by performing inverse operations on both sides. This is commonly used in physics and engineering to solve for unknown quantities in complex equations.

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