Mysterious Circuit Q

So, you found an old piece of RF test equipment at a rummage sale. A friend who is a Ham radio enthusiast tells you it is a 'Q meter', and it appears to be in working order - great!

But, what is a Q meter?

A Q meter was used to measure the resonant rise of voltage across either of the reactive elements in a tuned circuit. This measurement resulted from injecting a small known radio frequency voltage across a very small series resistor which connected to the resonant circuit. The magnified or resonant voltage rise was then measured by a vacuum tube voltmeter (translation: high input impedance voltmeter). Since the amount of injected voltage was accurately known, the resonant voltage rise or circuit magnification factor could be directly calibrated in terms of the Q of the coil being measured. Although still popular with radio hobbyists, they have been largely replaced by network analyzers.

Why do I want to measure Q?

Q is a very common measure of performance for resonant circuits. It expresses a ratio of the total energy stored versus the energy dissipated in a circuit during one cycle of operation.

Using Q we can determine:

1. The damping effect when current is decaying in a resonant circuit.

2. Phase angle and power factor of tuned circuits.

3. Antenna characteristics.

4. Transmission-line parameters.

5. Selectivity of a tuned circuit.

6. The RF impedance of a coil.

7. The RF loss angle of a capacitor.

8. Dielectric constants.

Q and Series Resonant Circuits

In series resonant circuits, Q is calculated using the effective series resistance (Rs), a theoretical value representing all losses including those of the resonant coil and capacitor. Using Rs, Q is expressed as:

Q = ωL/Rs =1/(C x Rs); where ω = 2π x f.

Rearranging we find: Rs = ωL/Q = 1/Q x ωC - usually a very small quantity.

Q and Parallel Resonant Circuits

In a parallel resonant circuit, Q is calculated using the effective parallel resistance (Rp) a reflected value often represented by a parallel resistor connected across the tuned circuit. Using Rp, Q is expressed as:

Q = Rp/ωL = ωC x Rp

Again, by rearranging, we see Rp = Q x ωL = Q/ωC - usually a very large quantity.

Here we see that the impedance of a parallel resonant circuit is Q times the impedance of the reactive elements. In the series case, the current flowing at resonance is Q times the normal current flow.

Q and Damped Oscillation

In a damped oscillating circuit, Q expresses the logarithmic decrement ς of the circuit.


ς = π/Q = Rs/2f = 2 x (π^2) x f x C x Rs

As we know, R/2L is the damping coefficient -. since the equation for current decay is:

I2 / I0 = e ^(-RT/2L).

ς, which multiplies the damping coefficient by f, accounts for frequency.

Q and Phase Angle.

The vector relationship between the current and driving voltage in a resonant circuit is the familiar equation:

tanθ = ωL/Rs = Q; where θ is the phase angle

Q and Power Factor.

The relationship between Q and the power factor (cosθ) of an inductor or the ratio of the total effective resistance to the total circuit impedance can be shown to be:

Q = 1/cosθ; where θ is the phase angle.

Glen Taylor is the owner of eWerks Inc. ( for over 25 years he has been involved in the design and manufacture of industrial electronics. Glen holds a Master of Science degree (with distinction) in Electronic Product Development from the University of Bolton in the UK, a CID certification in circuit board design from IPC Designers Council, and is an authorized Microchip Design Partner. He is also a senior member of IEEE - Institute of Electrical and Electronic Engineers and ISA - International Society for Automation. For more tutorials visit his blog at


  1. Your blog is very informative. WLCI School of graphic designing also offers programmes in graphic design program and graphic design courses.
    For More Details :

  2. I certainly enjoyed the way you explore your experience and knowledge of the subject..pcb suppliers