LC Series and Parallel circuit summary

This article is on some of the LC circuit information to summarize the results, please look at the dialectical, where there is the wrong place please criticize:

First, LC series parallel circuit qualitative understanding:

In LC circuits, the frequency values corresponding to the inductance and tolerance are called resonant frequencies, as shown in Figure 1 below. When receiving radio or television signals or wireless communication signals, the frequency of the receiving circuit is the same as the frequency of the signal emitted by the radio station or radio chosen.

Fig. 1 Inductance and capacitance curve

Characteristics of LC Series resonant circuit:
LC Series Resonant circuit refers to the inductor and capacitor formed in series, and the resonant state (the relationship curve has the same resonant point) circuit, as shown in Figure 2. In a series resonant circuit, when the signal is close to a certain frequency, the current in the circuit reaches the maximum, and this frequency is called the resonant frequency.

Figure 2 LC Series resonant circuit and the relationship between current and frequency curve

The conditions of the different frequency signals through the LC series circuit are shown in Figure 3. By the figure, when the input signal through the LC series circuit, according to the characteristics of inductors and capacitors, the higher the signal frequency inductance impedance, and capacitance impedance is smaller, the impedance is large attenuation of the signal, the higher the frequency of the signal through the inductance will decay very large, and the DC signal can not pass the capacitor. When the frequency of the input signal is equal to the frequency of the LC resonance, the impedance of the LC series circuit is minimized. This frequency signal is easily output through the capacitor and inductor. At this time the LC series resonant circuit plays the role of frequency selection.

Fig. 3 Signal flow through LC series circuit

Characteristics of LC parallel resonant circuit:

LC Parallel Resonant Circuit is the inductor and capacitor formed in parallel, as shown in Figure 4, in a parallel resonant circuit, if the current in the coil is equal to the current in the capacitor, then the circuit reached the parallel resonant state. In this circuit, in addition to the LC Parallel section, the impedance changes in other parts are almost no effect on energy consumption. Therefore, the stability of this circuit is better than the series resonant circuit to apply more.

Figure 4 LC Parallel resonant circuit and the relationship between current and frequency curve

Figure 5 shows the different frequency of the signal through the LC parallel resonant circuit State, when the input signal through the LC parallel resonant circuit, the same according to the inductor and capacitor impedance characteristics, the higher frequency signal is easy to reach the output by the capacitor, the lower frequency signal is easy to reach the output through the inductor. As the impedance of the LC circuit at the resonant frequency fo is the largest, the resonant frequency point signal cannot pass the LC parallel oscillation circuit.

Fig. 5 signal flow through LC parallel circuit

Second, LC parallel circuit Quantitative understanding:

the amplitude-frequency characteristic, passband and selectivity of LC Series frequency selection circuit.

LC Series Resonant circuit is widely used in the frequency-selective circuit of the Heterodyne radio, such as input circuit, frequency conversion circuit, intermediate frequency circuit and so on.

Above is an LC series resonant circuit, wherein R represents the loss resistance of the coil L. The AC impedance of the circuit is: when the circuit is resonant,

Therefore, the resonant frequency of the circuit is:. The resonant characteristic of the series circuit is that the impedance of the circuit is the smallest and z0=r, the current of the circuit is maximum and i0=vs/r when the signal voltage is certain, the voltage at both ends of the inductor or capacitor is the largest and the Q times of the signal voltage. Q is defined as:, q is called the quality factor of the loop.

1. amplitude-Frequency characteristics

Current of LC series resonant circuit:

For convenience, the amplitude-frequency characteristics of series loop currents are usually represented by the relative ratio of current (called normalization):

The amplitude-frequency characteristic curve (i.e. the resonant curve) can be drawn by using the above formula, which shows that the higher the Q value, the sharper the curve, and the better the selectivity of the circuit.

2. Pass band

Near the resonant frequency

, brought in:

The frequency of satisfying (ie 0.707) is thought to pass through the loop, the frequency range of the loop is called the pass band, the width of the pass band is represented by B

Thus: the lower the Q value, the wider the bandwidth, the higher the Q value, the narrower the pass band. 3, the selectivity of the selective circuit is usually expressed by the resonant curve of the rectangular coefficient of KR, KR defined as a down to 0.1 when the bandwidth B0.1 and a down to 0.7 time bandwidth B0.7 ratio, R, L, C Series loop rectangular coefficient is:

The ideal rectangular coefficient is kr=1, while the LC series loop resonant curve has a large rectangular coefficient, so the selection is poor.



LC Parallel Frequency selection circuit

The R in the figure shows the equivalent loss resistance of the circuit. It is shown that the equivalent impedance of the LC parallel resonant circuit is:
1, LC parallel resonant circuit has the following characteristics:
2, LC parallel circuit resonant frequency is: 3, LC parallel circuit resonant, the equivalent impedance of the circuit is a pure resistance, the maximum resistance: the signal source current and the circuit in the Oscillation loop current relationship:

The above-stated: LC Circuit resonant, the branch current is approximate to the total current of Q times, usually, q>>1, so, the resonant LC parallel circuit of the circuit current than the input current much larger. In other words, the influence of the outside in the resonant circuit can be neglected. This conclusion is very useful for the analysis of LC sine wave oscillation circuit.

4. Frequency response of LC parallel resonant circuit

LC Parallel circuits have frequency selection characteristics. In the resonant frequency FO, the circuit is pure resistance (V and I no difference) resistance maximum. At the F FO, the circuit is capacitive.

do not misunderstand, this figure is not the amplitude-frequency characteristic curve of LC parallel circuit, only the partial meaning

The larger the Q, the larger the resonant zo, the sharper the amplitude characteristic curve, and the faster the phase-frequency characteristic changes near the F=FO, the better the frequency-selection performance. For the same δφ, the greater the Q value, the smaller the corresponding δf, and the better the stability of the frequency.