Quality Factor and Bandwidth of Parallel Resonant Circuits

In this article, you’ll learn about Q factor and bandwidth of parallel resonant circuits. This article is linked with 7 other articles you might be interested in reading:

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A parallel resonant circuit is resistive at the resonant frequency. (Figure below) At resonance X_L=X_C, the reactive components cancel. The impedance is maximum at resonance. (Figure below) Below the resonant frequency, the parallel resonant circuit looks inductive since the impedance of the inductor is lower, drawing the larger proportion of current. Above resonance, the capacitive reactance decreases, drawing the larger current, thus, taking on a capacitive characteristic.

Impedance is maximum at resonance in a parallel resonant circuit, but decreases above or below resonance. Voltage is at a peak at resonance since voltage is proportional to impedance (E=IZ). (Figure below)

A low Q due to a high resistance in series with the inductor produces a low peak on a broad response curve for a parallel resonant circuit. (Figure below) conversely, a high Q is due to a low resistance in series with the inductor. This produces a higher peak in the narrower response curve. The high Q is achieved by winding the inductor with larger diameter (smaller gague), lower resistance wire.

The bandwidth of the parallel resonant response curve is measured between the half power points. This corresponds to the 70.7% voltage points since power is proportional to E². ((0.707)²=0.50) Since voltage is proportional to impedance, we may use the impedance curve. (Figure below)

In Figure above, the 100% impedance point is 500 Ω. The 70.7% level is 0.707(500)=354 Ω. The upper and lower band edges read from the curve are 281 Hz for f_l and 343 Hz for f_h. The bandwidth is 62 Hz, and the half power points are ± 31 Hz of the center resonant frequency:

 
           BW = Δf = fh-fl  = 343-281 = 62 
           fl = fc - Δf/2 = 312-31 = 281 
           fh = fc + Δf/2 = 312+31 = 343 

           Q = fc/BW = (312 Hz)/(62 Hz) = 5

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Article extracted from Lesson in Electric Circuits AC Volume Tony R Kuphaldt under Design Science License. Heading and title are modified/added. Additionally, the content is visually edited and rearranged for purpose of ease in skimming.