# Factor and bandwidth relationship

On the Functional Relation between Quality Factor and Fractional Bandwidth. Miloslav Capek, Member, IEEE, Lukas Jelinek, and Pavel Hazdra. Frequency response: Resonance, Bandwidth, Q factor. Resonance . By combining Equations (), (), () and () we obtain the relationship between. Then the relationship between resonance, bandwidth, selectivity and quality and capacitor at resonance, the quality factor and the bandwidth of the circuit.

A high-quality bell rings with a single pure tone for a very long time after being struck. A purely oscillatory system, such as a bell that rings forever, has an infinite quality factor.

## Q Factor and Bandwidth of a Resonant Circuit

More generally, the output of a second-order low-pass filter with a very high quality factor responds to a step input by quickly rising above, oscillating around, and eventually converging to a steady-state value. Like an overdamped system, the output does not oscillate, and does not overshoot its steady-state output i.

**Q FACTOR AND BANDWIDTH**

Like an underdamped response, the output of such a system responds quickly to a unit step input. Critical damping results in the fastest response approach to the final value possible without overshoot. Real system specifications usually allow some overshoot for a faster initial response or require a slower initial response to provide a safety margin against overshoot.

In negative feedback systems, the dominant closed-loop response is often well-modeled by a second-order system. The phase margin of the open-loop system sets the quality factor Q of the closed-loop system; as the phase margin decreases, the approximate second-order closed-loop system is made more oscillatory i. Quality factors of common systems[ edit ] A unity gain Sallen—Key filter topology with equivalent capacitors and equivalent resistors is critically damped i.

Figure below Below the resonant frequency, the series resonant circuit looks capacitive since the impedance of the capacitor increases to a value greater than the decreasing inductive reactance, leaving a net capacitive value.

Above resonance, the inductive reactance increases, capacitive reactance decreases, leaving a net inductive component.

At resonance the series resonant circuit appears purely resistive. Below resonance it looks capacitive.

Above resonance it appears inductive. Current is maximum at resonance, impedance at a minumum.

Current is set by the value of the resistance. Above or below resonance, impedance increases. Impedance is at a minumum at resonance in a series resonant circuit. The resonant current peak may be changed by varying the series resistor, which changes the Q.

### Q Factor and Bandwidth of a Resonant Circuit | Resonance | Electronics Textbook

Figure below This also affects the broadness of the curve. A low resistance, high Q circuit has a narrow bandwidth, as compared to a high resistance, low Q circuit. Bandwidth in terms of Q and resonant frequency: The upper and lower band edges read from the curve are Hz for fl and Hz for fh.

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. A parallel resonant circuit is resistive at resonance, inductive below resonance, capacitive above resonance.

Impedance is maximum at resonance in a parallel resonant circuit, but decreases above or below resonance.