1、6.3 Resonance 6.3.1 Series Resonance A series RLC circuit is shown in Fig. 1. sV R1jCjLI Figure 1: A series RLC circuit. The relationship between the current amplitude and the angular frequency is shown in Fig. 2. rIRsV Figure 2: Frequency characteristics of a series RLC circuit. From Fig. 2, the ma
2、ximum current amplitude appears at r , which means that the signal is strongest. We call the circuit state with the maximum current amplitude as series resonance. r is known as the series resonant frequency. From Fig. 1, the impedance of series RLC is 1Z R j LjC = + + (1) The current of the circuit
3、in Fig. 1 is 1R j LjC = +sVI (2) From (2), the magnitude of the current is 22 1RLC =+ sVI (3) From (3), if 1 0L C = , i.e.,LC , the current amplitude is largest and the largest current amplitude is max R= sVI (4) It is obvious that the series resonant angular frequency is r 1LC = (5) Substituting 1
4、0L C = into (2), we obtain R=sVI (6) From (6), the voltage and the current are in phase when the circuit is in series resonance. 6.3.2 Parallel Resonance A parallel RLC circuit is shown in Fig. 1. sI R1jCjL V Figure 3: A parallel RLC circuit. From Fig. 1, the voltage of the circuit in Fig. 1 is 111
5、jCj L R R LjC= + + = + s s ssV V VIV (7) From (7), the voltage is 11jCRL = +sIV (8) From (8), the magnitude of the voltage is 2211CRL = + sIV (9) The relationship between the voltage amplitude and the angular frequency is shown in Fig. 4. rVs RI Figure 4: Frequency characteristics of the parallel RL
6、C circuit. From Fig. 4, the maximum voltage amplitude appears at r , which means that the signal is strongest. We call the circuit state with the maximum voltage amplitude as parallel resonance. r is known as the parallel resonant frequency. From (9), if 1 0L C = , i.e.,LC , the voltage amplitude is
7、 largest and the largest voltage amplitude is max R= sVI (10) It is obvious that the parallel resonant angular frequency is r 1LC = (11) Substituting 1 0L C = into (8), we obtain s R=VI (12) From (12), the voltage and the current are also in phase when the circuit is in parallel resonance. Resonance
8、 is a very special and interesting phenomenon in circuits. Therefore, resonant circuits have wide applications such as radio, television, and mobile phones. Wireless energy transmission, a rapid developing technology, also use the principle of resonance. The concept of resonance is not limited to circuits. For example, if the frequency of music (similar to the frequency of the source in circuits) is equal to the natural frequency (similar to the resonant frequency of circuits) of a tuning fork, the tuning fork will enter a state of resonance with sustained significant vibration.
