Designing Inductor Value for Coupled RLC Circuit

[abhierao]

hello,

i am deriving an equation for designing an inductor in a coupled RLC circuit. is there an equation for calculating inductor value by knowing the input and output voltages & output current of the RLC circuit ?
i have tried KVL and KCL equations but in vain.
please help

thank you

 

[Runei]

Using KVL and KCL you end up with a 2nd Order Differential Equation. This equation has to be solved in order to find the time behavior of the system.

Have you learned about Laplace Transforms yet? Or do you know how to solve differential equations?

 

[abhierao]

i am running a steady state solution so i do not have to worry about transient solution & differential equations. but if you suggest me to run through differential equation then that's not a problem, yes i do know laplace transforms & i have solved differential equation for current in a coupled rlc circuit

 

[abhierao]

http://www.ee.bgu.ac.il/~intrlab/lab_number_7/Two inductively coupled RLC circuits.pdf
this is one link that i can link to my work. the circuit is similar but with a load resistance at output where i am measuring my voltage. he has some equations by assumptions but i have made use of KVL to get without those assumptions.
i know input voltage 20volts, output power 15v , 1A or 10v 1.5A. k i can choose anywhere close to 1 or lesser values, i want to design inductor with these values. i have frequency of 100 hz.
please help

 

[alphysicist]

for your question. Designing an inductor value for a coupled RLC circuit can be a complex task, as it involves considering various factors such as the input and output voltages, output current, and the coupling coefficient between the inductor and the rest of the circuit. While there is no single equation that can be used to calculate the inductor value in all cases, there are a few approaches that can be taken to determine the appropriate value for your specific circuit.

One method is to use the resonance frequency of the circuit, which is the frequency at which the inductive and capacitive reactances are equal. This can be calculated using the equation f = 1/(2π√(LC)), where L is the inductance and C is the capacitance. By knowing the desired resonance frequency and the capacitance value, you can solve for the required inductance value.

Another approach is to use the voltage transfer function of the circuit, which relates the input and output voltages. By considering the desired output voltage and the input voltage, you can calculate the inductance value using the equation L = Vout/(ωIout), where ω is the angular frequency and Iout is the output current.

It is also important to consider the quality factor (Q) of the circuit, which is a measure of the circuit's ability to store and release energy. A higher Q value typically results in a sharper resonance peak and better selectivity. The Q value can be calculated using the equation Q = ωL/R, where R is the resistance in the circuit.

In summary, there is no one equation that can be used to calculate the inductor value for a coupled RLC circuit, but by considering factors such as the resonance frequency, voltage transfer function, and quality factor, you can determine the appropriate value for your specific circuit. I hope this helps in your design process. Best of luck!