Law of Thermodynamics

The 1st Law of Thermodynamics tells us that energy is neither created nor destroyed, thus the energy of the universe is a constant. However, energy can certainly be transferred from one part of the universe to another. To work out thermodynamic problems we will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.
The energy transfer between different systems can be expressed as:

E₁ = E₂         (1)
where
E₁ = initial energy
E₂ = final energy

The internal energy encompasses:

• The kinetic energy associated with the motions of the atoms
• The potential energy stored in the chemical bonds of the molecules
• The gravitational energy of the system

Band Pass Filter with LC

LC Band pass filters are usually LC filters containing resonator combinations of inductance and capacitance which are designed mathematically to respond to design frequencies while rejecting all other out of band frequencies. Because LC bandpass filters have inherent limitations these statements should not be taken too literally.

Now we move from the simple to the complicated. By this stage you should be able to understand:

unloaded Q ( Q_U )
loaded Q ( Q_L )
reactance.
LC circuit combination for any given frequency.

LC Band pass filters are derived from tables named after the mathematicians who did the original calculations.

The main filters considered are:

Butterworth
Chebyschev
Bessel
Gaussian

Harmonic Trap of Filter

With the addition of one small component, a capacitor, we can transform a low pass filter into a filter with near infinite attenuation at a designed trap frequency. I call this an "harmonic trap filter".
Let's look at the old low pass filter in figure 1 below.

                                                             schematic of low pass filter


I presume you have already completed the tutorial on low pass filter and understand them fully. Now to construct an harmonic trap filter all I need to do is insert a capacitor C3 as in figure 2 below.

                                                           harmonic trap filter schematic