LC Resonance Frequency Calculator

Capacitance:
Inductance:
Resonant Frequency:



LC Resonant Frequency Formula

When a coil and capacitor are placed in parallel they will resonate at a certain frequency, a frequency that can be determined by this formula:

f (kHz) = 159,155 / √( LC )  or   f (MHz) = 159.155 / √( LC )

  f  is Frequency

L is Inductance in micro Henries

C is Capacitance in pico Farads

Although to understand why a certain value of inductor and capacitor resonate at a certain frequency you must understand REACTANCE. Furthermore once reactance is understood it will be much easier to understand the formula above and why 159,155 is a constant.

Inductive Reactance

Inductance is the characteristic of an electrical conductor that opposes change in current. As Lenz's law states "The induced emf in any circuit is always in a direction to oppose the effect that produced it." This opposition to change in current is called Counter Electromotive Force (cemf). Inductance can be compared to Inertia. A physical analogy to Inductance would be moving a heavy load. It takes more work to start the load moving that it does to keep the load moving, as in reverse it takes more work to stop that load moving than it does to keep it moving. This is because that load possesses Inertia, just as current possesses Inductance in an electrical circuit.

As an alternating current flows through an inductor, it is continuously reversing itself.  This causes the same inertial cemf effect discussed above, only now it is constantly reversing. This opposing force to the flow of alternating current is called Inductive Reactance because it is the reaction an inductor presents to alternating current.

The greater the inductance and the greater the frequency of the alternating current, the greater the Inductive Reactance. Inductive Reactance can be found using this formula:


XL = 2π fL

XL  is Inductive Reactance

  f  is frequency in Hertz

is Inductance in Henrys


Capacitive Reactance

Capacitors also present an opposition to a.c. When an alternating current flows through a capacitor each plate changes polarity according to the frequency.  As electrons move from plate to plate they are limited to that plates storage ability (capacitance). Therefore at a higher frequency the maximum number of electrons stored will change plate more often, which means more current will flow. Also, as the capacitance increases, more electrons change plate every cycle, and more current will flow.

As you can see, an increase in frequency will cause a decrease in the capacitor's opposition and allow more current to flow, and an increase in capacitance will cause a decrease in the capacitors opposition and thus allowing more current to flow. This opposition a capacitor presents to alternating current is called Capacitive Reactance. Capacitive Reactance can be found using this formula:

X=  1 / 2π fC

Xc  is Capacitive Reactance

  f  is Frequency in hertz

C  is Capacitance in farads
    

LC Frequency Property Table

Component
Symbol
Frequency
Lower
Higher

Broken
Circuit
Unbroken
Circuit

Unbroken
Circuit
Broken
Circuit


This table should help you understand an inductor's and capacitor's properties in an ac circuit. As you can see, a frequency too low will cause a capacitor to appear as a "Broken Circuit" since it will have a higher capacitive reactance, while it will cause an inductor to appear as an "Unbroken Circuit" since it will have a lower inductive reactance.

Memorize this simple table, becuase it will come in handy when building LC filters in which you must place either the inductor or capacitor first. For example:

In the low pass filter below, all of the higher frequencies will pass through the capacitor (Unbroken Circuit) instead of the inductor (Broken Circuit) and go to zero, while the lower frequencies will not pass through the capacitor (Broken Circuit) although will pass through the Inductor (Unbroken Circuit).

Low Pass Filter
                              


LC Resonance


Now that you understand the characteristics of an inductor and capacitor in an ac circuit, you may see their characteristics when placed together either in series or parallel. In both, series and parallel, an inductor and capacitor will resonate at a given frequency. I will start by explaining series resonance.

More To Come...