Q of a circuit
What is Q
The Q or Quality factor of a resonant circuit is the ratio of stored power to dissipated power in the Reactance and Resistance of the circuit.
Generally speaking, a higher Q corresponds to a narrower bandwidth.
How is Q calculated?
Note that at resonance, a series circuit "appears" to be purely resistive (it behaves like a resistor). Below resonance it appears to be capacitive (it behaves like a capacitor), and above resonance it appears to be inductive (behaves like an inductor)
<math>Q=\frac{P_{stored}}{P_{dissipated}}=\frac{I^2X}{I^2R}=\frac{X}{R}</math> where:
- X = capacitive or inductive reactance at resonance
- R = series resistance
- P = Power
- I = Current
This formula is for all series resonant circuits and also works for parallel resonant circuits in which a small resistor is in series with the inductor.
If there is a large resistor in parallel with both the inductor and the capacitor, the formula becomes:
<math>Q=\frac{P_{dissipated}}{P_{stored}}=\frac{I^2R}{I^2X}=\frac{R}{X}</math>
Admittance
For a given circuit element , the admittance is the reciprocal of the impedance.
Admittance is most useful in parallel AC circuit calculations where there are no series components. The equivalent admittance of a parallel circuit is the sum of the admittances of the components.
Electronic Theory | |
Physical quantities | Current * Gain * Impedance * Power * Q of a circuit * Radiated Power Measurement * Reactance* Resistivity * Resonance * Voltage |
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