RESONANT CIRCUITS

1-9 Figure 1-5.—Relationship between X_L and X_C as frequency increases. First, note that f_r, (the resonant frequency) is that frequency (or point) where the two curves cross. At this point, and ONLY this point, X_L equals X_C. Therefore, the frequency indicated by f_r is the one and only frequency of resonance. Note the resistance symbol which indicates that at resonance all reactance is cancelled and the circuit impedance is effectively purely resistive. Remember, a.c. circuits that are resistive have no phase shift between voltage and current. Therefore, at resonance, phase shift is cancelled. The phase angle is effectively zero. Second, look at the area of the curves to the left of f_r. This area shows the relative reactances of the circuit at frequencies BELOW resonance. To these LOWER frequencies, X_C will always be greater than X_L. There will always be some capacitive reactance left in the circuit after all inductive reactance has been cancelled. Because the impedance has a reactive component, there will be a phase shift. We can also state that below f_r the circuit will appear capacitive. Lastly, look at the area of the curves to the right of f. This area shows the relative reactances of the circuit at frequencies ABOVE resonance. To these HIGHER frequencies, X_L will always be greater than X_C. There will always be some inductive reactance left in the circuit after all capacitive reactance has been cancelled. The inductor symbol shows that to these higher frequencies, the circuit will always appear to have some inductance. Because of this, there will be a phase shift. RESONANT CIRCUITS Resonant circuits may be designed as series resonant or parallel resonant. Each has the ability to discriminate between its resonant frequency and all other frequencies. How this is accomplished by both series- and parallel-LC circuits is the subject of the next section. NOTE: Practical circuits are often more complex and difficult to understand than simplified versions. Simplified versions contain all of the basic features of a practical circuit, but leave out the nonessential features. For this reason, we will first look at the IDEAL SERIES-RESONANT CIRCUIT— a circuit that really doesn't exist except for our purposes here.