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.
Therefore:
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 / I1 = 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. (http://www.ewerksinc.com) 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 http://www.Thingsthatgoblink.com
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.
Therefore:
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 / I1 = 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. (http://www.ewerksinc.com) 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 http://www.Thingsthatgoblink.com