How to Calculate LRC Transfer Function

LRC filters are electronic components that use inductance "L," resistance "R" and capacitance "C" to filter certain unwanted frequencies out of electronic circuitry. "Highpass" filters remove frequencies below a design-determined cutoff frequency. "Lowpass" filters remove frequencies above the cutoff. "Passband" filters only allow frequencies between two cutoff frequencies to pass. Filtering frequencies remove some energy from the system. Without amplification, the output voltage of the circuit is therefore necessarily less than the input. The LRC transfer function is the ratio of the output voltage to the input voltage for the filter.

• 1

  Square the angular frequency then multiply it by the inductance and the capacitance. For example, 366 radians per second squared is 133,956. That value multiplied by 2 henrys and 1 micro-farad yields 0.268.

• 2

  Subtract the previous result from 1. For example, 1 minus 0.268 yields 0.732.

• 3

  Multiply the angular frequency by inductance and the imaginary number j, then divide by the resistance. For example, 366 radians per second times 2 henrys and j, divided by 50,000 ohms, yields j2.68.

• 4

  Divide 1 by the sum of the results of step 2 and step 3. In our example, the result is the fraction 1 divided by 0.732 plus j2.68. This is the LRC transfer function for our case. The answer is necessarily complex, because AC voltage is complex.