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LC Circuits Basic and Application Overview

Author: Apogeeweb Date: 9 Jul 2021  143

lc resonant circuit

Introduction

LC circuit, also called passive filtering circuit, is commonly used for harmonic compensation, which does not require additional power supply. It is generally composed of capacitors, inductors and resistors. This kind of filtering circuit is easy to design, but its pass-band magnification and cut-off frequency vary with the load, which is not suitable for occasions with high signal processing requirements. Passive filtering circuits are usually used in power circuits, like DC power rectification, or large current loads.

LC (Inductor-Capacitor) Circuits

Catalog

Introduction

Ⅰ LC Circuit Types

Ⅱ LC Circuit Characteristics

Ⅲ LC Circuit Working Features

Ⅳ LC Circuit Functions

Ⅴ LC Circuit Calculation


Ⅰ LC Circuit Types

Commonly used filter circuits include passive filter and active filter. If the circuit are only composed of passive components (resistors, capacitors, inductors), it is called a passive filter circuit. The main forms of passive filtering are capacitive filtering, inductive filtering and compound filtering (including inverted L-type, LC-type , LC-π type and RC-π type, etc.). The filter circuit is not only composed of passive components, but also composed of active components (bipolar tubes, unipolar tubes, integrated operational amplifiers), which is called an active filter circuit, and its main form is active RC(resistor-capacitor) circuit.
The LC circuit has advantages of simple structure, high reliability, and wide range of applications. Its main feature is that the resistance of the inductor is small, and the DC loss is small. What’s more, the inductance in LC circuit to alternating current is large, so that the filtering effect is good.
LC circuits are divided into LC low-pass filters, LC band-pass filters, high-pass filters, LC all-pass filters, and LC band-stop filters according to their functions. According to tuning, they are further divided into single-tuned filters, double-tuned filters and three-tuned filters and so on. 
The LC filter design process mainly considers its resonant frequency, capacitor withstand voltage, and inductor withstand current. In addition, it is necessary to pay attention to that passive LC circuits are not easy to integrate. 

 

Ⅱ LC Circuit Characteristics

The LC circuit is generally formed by a proper combination of inductors, capacitors and resistors, and parallel with the harmonic source. It not only for filtering, but also takes into account the role of compensation.

LC circuits

LC circuits

Figure 1. LC Circuit Types


The following are the characteristics of several LC circuits:
1) The load impedance of the L-type filter is high, and the source impedance is low.
2) The load impedance of the inverted L filter is low, and the source impedance is high.
3) The load impedance of the T-type filter is low, and the source impedance is low.
4) The load impedance of the Π filter is high, and the source impedance is high.
In actual use, these features are generally followed. In practice, impedance is difficult to estimate, especially in high frequency bands. Due to parasitic parameters, the circuit impedance changes greatly, and the circuit impedance is also related to the working state of the circuit, so the debugging shall prevail in practice.

 

Ⅲ LC Circuit Working Features

According to the different impedance of reactive components to AC and DC, the basic form of the LC circuit composed of capacitor C and inductance L is shown in the figure. Because the capacitor C is open to DC and has a small impedance to AC, C is connected in parallel at both ends of the load, while the inductor L has a small impedance to DC and a large impedance to AC, so L should be connected in series with the load.

In electronic circuits, the inductor coil acts on the finite current of the alternating current. From the inductance formula XL=2πfL, it can be known that the larger the inductance L, the higher the frequency f, and the larger the inductive reactance. We already know that capacitors have the ability to "block DC and pass AC", while inductors have the function of "pass DC, block AC, pass low frequencies, and block high frequencies". If the direct current accompanied by many interference signals is passed through the LC filter circuit, most of the AC interference signals will be prevented by the inductance from being absorbed and turned into magnetic induction and thermal energy, and most of the rest will be bypassed to the ground by the capacitor, which can suppress the interference. So a relatively pure DC current at the output is getting.

The inductance of the power supply on PCB is generally made of a very thick enameled wire wrapped around a round magnetic core coated with various colors. In addition, there are usually several tall filter aluminum electrolytic capacitors nearby, which is a classic LC filter circuit. In addition, PCB also uses a large number of snake-type lines and chip tantalum capacitors to form an LC circuit. Few people notice, when design LC circuit, the snake line folds back and forth on the circuit board, which can also be regarded as a small inductance.

In short, the principle of the LC filter circuit is actually a combination of the basic characteristics of the L and C components. Because the capacitive reactance of the capacitor xc=2nfc will decrease as the signal frequency increases, and the inductance of the inductor xl=2f will increase as the signal frequency increases. If the capacitors and inductors are connected in series, parallel or mixed together, the impedance of their combination will also vary greatly depending on the frequency of the signal. This shows that different filter circuits will present a small or large reactance to a certain frequency signal, so that it can pass or block the frequency signal. Thereby filter circuit plays a role in selecting a certain frequency signal and filtering out a certain frequency signal.

LC Inductor-Capacitor Resonating Circuits

Figure 2. LC Resonating Circuits

Ⅳ LC Circuit Functions

1) LC circuit can be used as a filter circuit used in some power supplies. If the DC power with many interference signals is passed through the LC filter circuit, most of the AC interference signals will be blocked by the inductance and become magnetic induction and thermal energy. Most of them are bypassed to ground by capacitors, which can suppress the effect of interference signals and obtain relatively pure DC current output.
2) Have oscillation effect, or sometimes generate a clock signal for the single-chip microcomputer (some have an external clock signal). 
3) It can also be used as a frequency selection circuit, or a transmitting oscillation circuit (but it must be a circuit that can send and receive signals), and it also serves for the generation of input signals from other circuits.
4) Since the output voltage of the rectifier circuit is not all pure DC, the output of the rectifier circuit observed from an oscilloscope is very different from the DC, and the waveform contains a large pulsating component, which is called ripple. In order to obtain the ideal DC voltage, it is necessary to use an LC circuit composed of reactive components (such as capacitors and inductors) with energy storage function to filter out the pulsating elements of output voltage.

LC circuit GIF

Ⅴ LC Circuit Calculation

1) The voltage of the RC tank capacitor is:
Voltage=U*exp(-t/rc)
U represents the initial value of the voltage, rc represents the resistance and capacitance, t is the elapsed time, and exp (-t/rc) represents the -t/rc power of e.
Time constant τ=rc
Namely the product of capacitance and resistance, voltage = U*exp(-t/τ) after introducing the time constant
Therefore, the voltage change with zero input response is an exponential decay process, theoretically infinite time, but generally it is considered that the decay is over after 3 to 5 time constants.
Therefore, the discharge time depends on the time constant τ=rc

2) For the LC oscillating circuit, it is related to the product of the LC circuit.
Specifically, for the general LRC loop,
R>2*sqr (L/R)
R=2*sqr(L/R)
R>2*sqr (L/R)
sqr (X) represents the root sign (X)
Divided into three situations, roughly speaking, the discharge time depends on the value of R, L, C in the circuit, U is not equal to 0 and I = 0, the capacitor discharges through L, R
Two eigenvalues can be obtained by solving second-order partial differential equations such as:
p1=-(R/2L)+spr[(R/2L)*(R/2L)-1/LC]
p1=-(R/2L)-spr[(R/2L)*(R/2L)-1/LC]
Capacitor voltage=[U/(p2-p1)]*[p2exp(p1*t)-p1exp(p2*t)]
Based on this, the relationship between capacitor discharge time and LRC can be analyzed.

 

Frequently Asked Questions about LC Circuit

1. What is meant by LC circuit?
An LC circuit is a circuit that uses the elements inductor (L) and capacitor ( C). This circuit is also referred as resonating circuit, tank circuit, or tuned circuit.

 

2. What does an LC circuit do?
LC circuits are used either for generating signals at a particular frequency, or picking out a signal at a particular frequency from a more complex signal; this function is called a bandpass filter.

 

3. Where are LC circuits used?
The LC circuit is used to select or generate a specific frequency signal. The application of LC circuits is reflected in many electronic devices, especially radio devices, such as transmitters, radio receivers and television receivers, amplifiers, oscillators, filters, tuners and frequency mixers.

 

4. What are the properties of LC circuit?
An LC circuit is a closed loop with just two elements: a capacitor and an inductor. It has a resonance property like mechanical systems such as a pendulum or a mass on a spring: there is a special frequency that it likes to oscillate at, and therefore responds strongly to.

 

5. What is LC in LC oscillation?
LC oscillations- The electric current and the charge on the capacitor in the circuit undergo electrical LC oscillations when a charged capacitor is connected to an inductor. The electrical energy stored in the capacitor is its initial charge which is named as q_m.

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