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In order to deepen the understanding of the conditions and characteristics of circuit resonance, and to master the physical meaning and measurement method of circuit quality factor (circuit Q value), technicians from Huatian Power have conducted a series of studies on series circuits and obtained the following experimental conclusions.  

Principle Explanation of Series Resonant Circuit

In the series circuit of R, L, and C shown in Figure 1, when the frequency f of the sinusoidal AC signal source changes, the inductive and capacitive reactance in the circuit also change, and the current in the circuit also changes with f. Taking the voltage uo on resistor R as the response, when the amplitude of the input voltage ui remains constant, the value of UO is measured under different frequency sine signal excitations. Then, with f as the horizontal axis and UO/UI as the vertical axis (since Ui remains constant, UO can also be directly used as the vertical axis), a smooth curve is drawn, which is the amplitude frequency characteristic curve, also known as the resonance curve, as shown in Figure 2.

Characteristics of series resonant circuit

(1) Because during series resonance, Xl=Xc， Therefore, the impedance of the circuit during resonance is

(2) When in series resonance, the impedance is the smallest, and when the voltage U is constant, the current is the largest, with a value of

Due to the pure resistance of the circuit, the current is in phase with the power supply voltage

(3) The voltage across the resistor is equal to the total voltage. The voltage of inductance and capacitance is equal, and their magnitude is Q times the total voltage, that is

approach

In the formula, Q is the crystal quality factor of the series resonant circuit, and its value is

The quality factor in resonant circuits can generally reach around 100. It can be seen that the voltage on the inductor and capacitor is many times higher than the power supply voltage, so series resonance is also called voltage resonance. The smaller the resistance of the coil, the less energy the circuit consumes, indicating good circuit quality and high quality factor; If the inductance L of the coil is larger, the more energy is stored, and when the loss is constant, it also indicates that the circuit quality is good and the quality factor is high. So in electronic technology, due to weak external signals, series resonance is often used to obtain a voltage that is the same frequency as the signal voltage but many times larger.  

(4) During resonance, electrical energy is only supplied to the consumption of circuit resistors, and there is no energy conversion between power circuits. Instead, magnetic energy and electrical energy are converted between inductors and capacitors.  

Selective series resonant circuit

The resonant circuit has the ability to select frequencies. 

The interference caused by adjacent unwanted frequencies is minimal, we say that this resonant circuit has good selectivity, which means it has a strong ability to select signals.

If the frequency w (or f) is taken as the independent variable and the loop current i is taken as its function, the resonance curve shown in Figure 3 can be plotted as a function curve. Obviously, the steeper the resonance curve, the better the selectivity. So what factors determine the selectivity of resonant circuits? In the R-L-C series circuit, assuming the terminal voltage is U and the impedance is | Z |, then

The above equation shows the functional relationship between the current I and angular frequency α in the R-L-C series circuit. For a given circuit, the resonant current 0I is a constant.  The relationship between current and frequency variation is related to the quality factor Q.We provide several different Q bits, such as taking Q as 10, 50, 100, etc., and rewrite the above equation into the following form.