This article discusses about Q Factor and its importance and how Q factor can be measured using Q Meter

1. Electrical & Electronic Measurement
Part – XI
Q Factor and Q Meter
ER. FARUK BIN POYEN
faruk.poyen@gmail.com
AEIE, UIT, BU

2. Contents:
 Q Factor
 Q Meter
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3. Q Factor: Definition
 Quality factor or Q factor is a dimensionless parameter that describes
how underdamped an oscillator or resonator is.
 It is defined as the ratio of the peak energy stored in the resonator in a
cycle of oscillation to the energy lost per radian of the cycle.
 It describes the damping in the circuit.
 It also provides an indication of the resonator’s bandwidth relative to its
centre frequency.
 Values for quality factor are often seen quoted and can be used in
defining the performance of an inductor, a capacitor or tuned circuit.
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4. Q Factor:
 Higher Q indicates a lower rate of energy loss and the oscillations die
out more slowly.
 A pendulum suspended from a high-quality bearing, oscillating in air,
has a high Q, while a pendulum immersed in oil has a low one.
 Resonators with high quality factors have low damping, so that they ring
or vibrate longer.
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5. Q Factor: Numerical Representation
 Mathematically, Q factor is the ration of the energy stored in the
oscillating resonator to the energy dissipated per cycle by damping
processes.
𝑄 = 2𝜋
𝑒𝑛𝑒𝑟𝑔𝑦 𝑠𝑡𝑜𝑟𝑒𝑑
𝑒𝑛𝑒𝑟𝑔𝑦 𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑 𝑝𝑒𝑟 𝑐𝑦𝑐𝑙𝑒
= 2𝜋𝑓𝑟
𝑒𝑛𝑒𝑟𝑔𝑦 𝑠𝑡𝑜𝑟𝑒𝑑
𝑝𝑜𝑤𝑒𝑟 𝑙𝑜𝑠𝑠
 𝑓𝑟= resonant frequency
𝑄 =
1
2ζ
⇒ ζ 𝑑𝑎𝑚𝑝𝑖𝑛𝑔 𝑟𝑎𝑡𝑖𝑜𝑛 =
1
2𝑄
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6. Q Factor: Interpretation
 A system with low quality factor (Q < 1⁄2) is said to be overdamped.
 A system with high quality factor (Q > 1⁄2) is said to be underdamped.
 A system with an intermediate quality factor (Q = 1⁄2) is said to be
critically damped.
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7. Q Factor: Effects
 Bandwidth (BW) – With Q factor increasing, bandwidth of the tuned
circuit filter is reduced. Losses are decreased and energy storage is
better.
 Oscillator Phase Noise – Q factor is increased and the phase noise is
decreased.
 General spurious signals – With higher Q factor value, the circuit will be
able to remove the spurious signals.
 Ringing – With Q factor increasing, the losses decrease which otherwise
means that the ringing will be more.
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8. Q Meter:
 Q-meter is an equipment used in the testing of radio frequencies.
 A Q-meter measures the quality factor (Q-factor) of a circuit expressing
how much energy is dissipated per cycle in a non-ideal reactive circuit.
 For inductors, in a resonating circuit,
𝑄 =
𝑋 𝐿
𝑅
=
𝜔𝐿
𝑅
 For LC band pass filters
𝑄 =
𝐹𝑟
𝐵𝑊
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9. Q Meter: Circuit Diagram
 A high value of Q is always desirable as it means high inductive
reactance and low resistance.
 A low value of Q indicates that the resistance component is relatively
high and so there is a comparatively large loss of power.
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10. Q Meter: Components
 Q – Meter consist of
 Variable calibrated capacitor
 Variable frequency AC voltage source
 Coil to be tested or measured.
 All the elements are connected in series.
 The capacitor voltage V and the source voltage E are monitored by
voltmeters.
 One terminal of the coil is connected to the signal generator (AC source)
while the other terminal is connected to the variable capacitor
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11. References:
 https://www.electronics-notes.com/articles/basic_concepts/q-quality-
factor/basics-tutorial-formula.php
 https://www.rp-photonics.com/q_factor.html
 https://en.wikipedia.org/wiki/Q_factor
 https://en.wikipedia.org/wiki/Q_meter
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