Circuits with L and C elements have special characteristics due to their frequency characteristics (such as frequency Vs, current, voltage, and impedance), which may have significant minimum or maximum values at specific frequencies. The applications of these circuits mainly involve transmitters, radio receivers, and television receivers. Consider an LC circuit in which capacitors and inductors are connected in series on the power supply, and the connection of the circuit has a unique characteristic of resonance at a precise frequency called the resonant frequency. This article discusses what an LC circuit is, and the harmonic operation of simple series and parallel LC circuits.
What is an LC circuit?
LC circuit, also known as energy storage circuit, tuning circuit or resonant circuit, is a circuit consisting of an inductor embedded in a capacitor represented by the letter "C" and connected together by the letter "L". These circuits are used to generate signals of specific frequencies or receive signals from composite signals of specific frequencies. LC circuit is a basic electronic component in various electronic devices, especially in wireless devices such as tuners, filters, mixers and oscillators. The main function of LC circuit is usually to oscillate with minimal damping.
Series LC circuit resonance
In a series resonant LC circuit configuration, capacitor "C" and inductor "L" are both connected in series, as shown in the following circuit. The sum of the voltages across the capacitor and inductor is the sum of the total voltages across the open circuit terminals. The current in the LC circuit+Ve terminal is equal to the current through the inductor (L) and capacitor (C) v=v L+v C, i=i L=i C
When the amplitude of the "XL" induced reactance increases, the frequency also increases. Similarly, when the reactance value of the "X C" capacitor decreases, the frequency also decreases.
Series LC circuit resonance
At a specific frequency, two reactances XL and XC have the same magnitude but opposite signs, therefore, this frequency is called the resonant frequency, represented by an LC circuit.
Therefore, in resonance
X L = -X C
ωL= 1 /ωC
ω=ω0= 1 /√LC
This is called the resonant angular frequency of the circuit. Convert angular frequency to frequency using the following formula
f0 =ω0/2π√LC
In a series resonant LC circuit configuration, the two resonances X C and X L cancel each other out. In practical rather than ideal components, the flow of current is usually opposite to the resistance of the coil winding. Therefore, the current provided to the circuit is maximum during resonance.
The definition of a receiving circuit is that when In Lt f and f0 are maximum, the impedance of the circuit is minimum.
For f<f0, X L<<(- X C), therefore, the circuit is capacitive
For f<f0, X L>>(- X C), therefore, this circuit is inductive
Parallel LC circuit resonance
In a parallel LC circuit configuration, capacitor "C" and inductor "L" are connected in parallel, as shown in the following figure. The sum of the voltages across the capacitor and inductor is the sum of the total voltages across the open circuit terminals. The current in the LC circuit+Ve terminal is equal to the current passing through the inductor (L) and capacitor (C)
v = v L = v C
I=IL +IC
Let the internal resistance of the coil be "R". When two resonances X C and X L occur, the reactive branch currents are the same and opposite, so they cancel each other out to provide the minimum current on the key wire. When the total current is minimized in this state, the total impedance is maximized, and the resonant frequency is given by the following equation
f0 =ω0/2π= 1 /2π√LC
Note that during resonance, the current of any reactive branch is not the minimum. But the current of each reactive branch is given separately by separating the reactive voltage "V" from the reactive voltage "Z".
Parallel LC circuit resonance
Therefore, according to Ohm's law, I=V/Z
The suppressor circuit can be defined as: when the line current is at its minimum and the total impedance is at its maximum at f0, the circuit is inductive below f0, and capacitive above f0.