Measure the Q factor of the series resonant circuit

The series resonant circuit is an important circuit structure in electronic engineering. The accurate measurement of the quality factor (Q factor) of this circuit is of great significance for evaluating and optimizing the circuit performance. This article will provide a detailed introduction to the measurement principle, methods, and practical applications of the Q factor of the series resonant circuit.
I. Basic Characteristics of Series Resonance Circuit
The series resonant circuit is composed of an inductor L, a capacitor C and a resistor R connected in series. When the signal frequency reaches the resonant frequency f 0, the circuit exhibits pure resistive characteristics. At this point, the impedance is the minimum and the current is relatively large. The formula for calculating the resonant frequency is f0 = 1/(2π√LC). The Q factor is an important parameter for measuring the selectivity of the resonant circuit. It is defined as the ratio of the reactance at resonance to the resistance, that is, Q = ω0L/R = 1/(ω0CR), where ω0 = 2πf0.

II. Measurement Principle of Q Factor
The basic principle of measuring the Q factor is based on the characteristics of the resonance curve. When the frequency deviates from the resonant frequency, the circuit impedance increases rapidly and the current decreases. The higher the Q factor, the sharper the resonance curve and the better the selectivity. Common measurement methods include the voltage method, bandwidth method and impedance method.

III. Measurement of Q Factor Using Voltage Method
The voltage method is the most direct measurement method. At the resonant frequency, measure the voltage UL or UC across the inductor or capacitor, as well as the input voltage Uin. Since at resonance UL = UC = Q * Uin, therefore Q = UL / Uin = UC / Uin. This method is simple and intuitive, but it requires relatively precise voltage measurement instruments.

4. Measuring Q Factor Using Bandwidth Method
The bandwidth method calculates the Q factor by measuring the 3dB bandwidth of the resonance curve. The specific steps are as follows: 1) Determine the resonant frequency f0; 2) Measure the two frequencies f1 and f2 when the current drops to 0.707 times its maximum value; 3) Calculate Q = f0 / (f2 – f1). This method is applicable to circuits with high Q values. The measurement accuracy depends on the accuracy of the frequency measurement.

V. Measurement of Q Factor Using Impedance Method
The impedance method calculates the Q factor by measuring the impedance characteristics during resonance. The resistance R at the resonant frequency is measured using an impedance analyzer, and then the Q value is calculated based on the formula Q = ω0L/R. This method requires relatively precise measurement of the inductance value L and the resistance value R.

VI. Measurement Precautions
1. The output impedance of the signal source should be as low as possible to avoid affecting the measurement results.
2. The input impedance of the measuring instrument should be large enough to reduce measurement errors.
3. The connection lines should be as short as possible to minimize the influence of distributed parameters.
4. The environmental temperature should be kept stable to avoid changes in component parameters.
5. Take the average of multiple measurements to improve measurement accuracy.

VII. The Practical Significance of the Q Factor
High-Q circuits have better frequency selectivity and are often used in radio receivers, filters, and other applications. However, an excessively high Q value may result in a too narrow bandwidth, which can affect the quality of signal transmission. Therefore, in actual design, the Q value needs to be reasonably selected according to the application requirements.

VIII. Analysis of Measurement Examples
Take a series resonant circuit with L = 100 μH, C = 100 pF, and R = 5 Ω as an example: 1. Calculate the resonant frequency f0 = 1 / (2π√(100 × 10^-6 × 100 × 10^-12)) ≈ 1.59 MHz 2. Measure the voltage across the inductor UL = 50 mV, and the input voltage Uin = 5 mV 3. Calculate Q = UL / Uin = 50 / 5 = 10 4. Verification: Q = ω0L / R = 2π × 1.59 × 10^6 × 100 × 10^-6 / 5 ≈ 10

IX. Error Analysis of Measurements
The main sources of errors include: 1. Component parameter errors 2. Measurement instrument accuracy limitations 3. Environmental interference 4. Distribution parameters of connection lines 5. Reading errors. Methods to reduce errors include using more precise instruments, improving measurement methods, and optimizing the testing environment, etc.

X. Application Expansion of Q Factor
In addition to the basic measurement methods, the Q factor has important applications in the following fields: 1. Microwave resonator design 2. Antenna performance evaluation 3. Material dielectric property measurement 4. Biomedical sensors 5. Quantum computing systems

By conducting more precise measurements and optimizing the Q factor, the performance of various resonant systems can be significantly enhanced. With the advancement of measurement technologies, the measurement accuracy and application scope of the Q factor will continue to expand.