Describe the operation of an LC parallel resonant circuit.

Reactance and Impedance: Both the inductor and the capacitor in the circuit provide reactance, which is the opposition that these components offer to the flow of alternating current (AC) at different frequencies. The reactance of an inductor increases with frequency, while the reactance of a capacitor decreases with frequency. At the resonant frequency, the reactances of the inductor and capacitor are equal in magnitude but opposite in nature.

Resonant Frequency: The resonant frequency (f) of the LC parallel circuit can be calculated using the formula:

f = 1 / (2 * π * √(L * C))

Where:

f is the resonant frequency in Hertz (Hz)

π is a mathematical constant (approximately 3.14159)

L is the inductance of the inductor in Henrys (H)

C is the capacitance of the capacitor in Farads (F)

Impedance at Resonance: At the resonant frequency, the reactance of the inductor (XL) and the reactance of the capacitor (XC) are equal in magnitude but opposite in nature. As a result, they cancel each other out. This leads to a minimum total impedance (Z) in the circuit at resonance. The impedance of the LC parallel circuit at resonance is dominated by the resistance (R) in the circuit, which could be the internal resistance of the components or any external resistance connected.

Z = R

Current Response: With the impedance being minimized at the resonant frequency, the circuit allows maximum AC current to flow through it. This phenomenon is referred to as resonance. At frequencies significantly above or below the resonant frequency, the impedance increases due to the mismatch between the reactances of the inductor and the capacitor. Consequently, the current flow decreases.

Voltage Distribution: The voltage across the inductor and the capacitor can be significantly different. The capacitor tends to have a higher voltage across it due to its decreasing reactance with increasing frequency, while the inductor tends to have a lower voltage across it due to its increasing reactance.

Applications: LC parallel resonant circuits find applications in various fields, such as radio frequency (RF) circuits, filters, oscillators, and tuning circuits. They are used in RF applications to select a specific frequency range and reject others. In oscillators, they can help generate stable oscillations at the resonant frequency. In tuning circuits, they assist in selecting a particular frequency for resonance, allowing for precise tuning.

In summary, an LC parallel resonant circuit operates by exploiting the balance between the reactance of the inductor and the reactance of the capacitor to achieve a condition of maximum current flow at the resonant frequency. This makes it a fundamental component in various electronic applications requiring frequency selection and signal processing.