Q Meters and RLC Bridges
When you wind an inductor for a filter, an antenna loading coil, or an impedance-matching network, you are making an engineering decision: you have chosen a core material, a number of turns, a wire gauge, and a winding style. But unless you measure the result, you do not know whether the inductor has the inductance your design requires or whether its quality factor (Q) is high enough to achieve the filter's specified insertion loss. A Q meter tells you both, at the operating frequency, with the actual component in hand.
Q is the ratio of the reactive impedance to the series resistance of an inductor: Q = XL/Rs = ωL/Rs. An inductor with Q = 200 has a reactance 200 times its series resistance — almost all of the component's impedance is reactive and very little energy is lost. An inductor with Q = 20 loses 10× more energy per cycle. Filter performance, oscillator phase noise, and antenna loading coil efficiency all depend directly on the Q of the inductors in the circuit.
What Is Q?
The quality factor Q is a dimensionless ratio that describes how lossy a reactive component is. For an inductor:
Q = XL / Rs = 2πfL / Rs
Where XL is the inductive reactance (2πfL) and Rs is the equivalent series resistance — the sum of the wire's DC resistance, the skin-effect resistance at the operating frequency, and the core loss (if a ferromagnetic core is used). High Q means low loss. Air-core coils achieve Q of 200–500 at HF frequencies. Ferrite-core coils may achieve Q of 100–200 at their designed operating frequency, dropping sharply above the core's useful frequency range.
Q also describes resonant circuit bandwidth. For a series or parallel resonant circuit, the 3 dB bandwidth BW₋₃dB is related to Q by:
Q = fr / BW₋₃dB
Where fr is the resonant frequency and BW₋₃dB is the −3 dB bandwidth. This means a high-Q resonator (narrow bandwidth) is a more frequency-selective circuit. Conversely, measuring the resonant frequency and bandwidth of a circuit containing a coil lets you calculate the coil's Q — which is exactly how a Q meter works.
How a Q Meter Works
A Q meter (also called a Boonton meter, from the classic Boonton 160A and 260A models) works by resonating the inductor under test with a calibrated capacitor at a known frequency. The instrument applies a small constant-voltage signal to the circuit; at resonance, the voltage across the capacitor rises to Q times the applied voltage. Measuring this voltage directly gives Q.
The internal structure of a Q meter:
- Oscillator: Generates a calibrated RF signal at the test frequency (usually variable from about 50 kHz to 50 MHz in a classic Q meter)
- Low-impedance injection resistor: A very small resistor (typically 0.02–0.04 Ω) in series with the circuit under test, to maintain a constant current into the circuit regardless of its impedance
- Calibrated variable capacitor: Tuned to resonate with the test inductor. The capacitance value is read directly from the calibrated dial and used to calculate inductance: L = 1/(4π²f²C)
- High-impedance voltmeter: Measures the voltage across the capacitor at resonance. This voltage, divided by the injection voltage, equals Q
The Q meter measurement principle. At resonance, the voltage across the tuning capacitor (Vc) rises to Q × Vinj, where Vinj is the small constant injection voltage. The Q reading is direct: Q = Vc / Vinj. The calibrated capacitor dial gives C at resonance, from which inductance is calculated as L = 1/(4π²f²C). A worked example shows that C = 32.2 pF at resonance with f = 7.15 MHz gives L = 15.4 µH and, with Q = 180, an effective series resistance of only 3.8 Ω.
View LargerAn inductor wound on a T-68-2 powdered-iron toroid for a 40m bandpass filter is measured on a Q meter at 7.150 MHz. The Q meter capacitor tunes the circuit to resonance at C = 32.2 pF. The Q meter reads Q = 180.
Inductance: L = 1/(4π² × (7.15×10⁶)² × 32.2×10⁻¹²)
= 1/(4 × 9.870 × 51.12×10¹² × 32.2×10⁻¹²)
= 1/(4 × 9.870 × 1646) = 1/(65,062) = 15.37 µH
Reactance at 7.15 MHz: XL = 2π × 7.15×10⁶ × 15.37×10⁻⁶ = 690 Ω
Series resistance: Rs = XL/Q = 690/180 = 3.83 Ω
The inductor has 3.83 Ω of effective series resistance at 7.15 MHz — low enough for good filter performance.
Self-Resonant Frequency
Every inductor has a self-resonant frequency (SRF) where its distributed capacitance resonates with its inductance. Above the SRF, the component behaves as a capacitor rather than an inductor — it has negative reactance. Operating an inductor above its SRF defeats its purpose. The Q meter is the classic tool for measuring the SRF: as the test frequency approaches the SRF, the apparent Q drops sharply (because the distributed capacitance is effectively shorting out the reactive voltage), and above the SRF the meter no longer resonates normally.
For toroid inductors used at HF, the SRF should be at least 3× the highest operating frequency to maintain satisfactory Q and linear reactance behavior. A 40m loading coil with SRF at 30 MHz still behaves well at 7 MHz; one with SRF at 9 MHz may show degraded Q and unexpected behavior near the upper end of the 40m band.
RLC Bridges
An RLC bridge (impedance analyzer or LCR meter) measures resistance, inductance, and capacitance across a wide frequency range. Modern RLC bridges for amateur use (such as the Peak Electronics Atlas LCR45, or the AIMTTI TA315 series) typically measure at one or more fixed frequencies (100 Hz, 1 kHz, 10 kHz, 100 kHz) and display R, L, C, Q, and dissipation factor D.
The limitation of most affordable RLC bridges is measurement frequency. A bridge that measures at 100 kHz cannot directly characterize an inductor's Q at 7 MHz, because Q is strongly frequency-dependent. For HF component characterization, either use a Q meter (designed specifically for RF frequencies) or use the VNA method: connect the component to a VNA port, measure S11 at the operating frequency, and extract Q from the Smith chart display by reading R + jX and computing Q = X/R.
Measuring Toroid Cores
To characterize an unknown ferrite or powdered-iron toroid core for use in HF work:
- Wind 10 turns of enameled wire on the core
- Measure the inductance at 100 kHz using an RLC bridge
- Calculate the core's AL (inductance per turn squared): AL = L / N² = L / 100 (for 10 turns)
- Compare to databook values for known cores to identify the core type and permeability
- Measure Q at the intended operating frequency using either a Q meter or the VNA method
AL for common toroid cores: T-50-2 (red, µ = 10) ≈ 49 nH/turn²; T-50-6 (yellow, µ = 8.4) ≈ 40 nH/turn²; T-68-2 (red) ≈ 57 nH/turn²; FT-37-43 (ferrite, µ = 850) ≈ 420 nH/turn².
Q and Filter Insertion Loss
Filter insertion loss is directly related to the Q of the inductors. For a simple LC bandpass filter with identical inductors of quality factor Qu (unloaded Q), the minimum achievable insertion loss is approximately:
IL (dB) ≈ 4.34 × n × fr / (Qu × BW₋₃dB)
Where n is the number of resonator sections. This formula shows that wider bandwidth, higher Q, and fewer sections all reduce insertion loss. Equivalently, for a given bandwidth and number of sections, higher Q inductors directly translate to lower insertion loss.
A 3-element bandpass filter for 7 MHz with 300 kHz bandwidth (Qloaded = f/BW = 7000/300 = 23.3). Using inductors with Qu = 100:
IL ≈ 4.34 × 3 × 7000 / (100 × 300) = 4.34 × 3 × 23.3 = 4.34 × 70 = 3.0 dB
With Qu = 200 inductors:
IL ≈ 4.34 × 3 × 23.3 / 200 × 100 = 1.5 dB
Doubling the Q halves the insertion loss. This is why high-Q inductors are critical in bandpass filter design.
Q from Resonant Frequency and Bandwidth Calculator
This calculator determines Q from a resonant frequency and −3 dB bandwidth measurement. This is the standard bench method for measuring Q using a VNA or Q meter: find the resonant frequency, then find the −3 dB frequencies on each side, and calculate Q = fr / BW. You can also enter Q and bandwidth to find the resonant frequency, or enter Q and resonant frequency to find the expected bandwidth.
Q / Bandwidth / Resonant Frequency Calculator
Enter any two values to calculate the third. Frequencies in MHz (or consistent units), bandwidth in kHz, Q dimensionless.
Frequently Asked Questions
Can I use a cheap LCR meter for RF coil work?
A cheap LCR meter measuring at 1 kHz or 10 kHz is useful for counting turns (does this coil have approximately the right number of turns for the target inductance?), sorting components, and measuring capacitors at audio frequencies. For RF work above 1 MHz, the LCR meter's measurement frequency is too low to capture the actual inductance, resistance, and Q at the operating frequency. Use a VNA (measure S11, extract R + jX from the Smith chart), a dedicated RF Q meter, or a quality LCR meter that measures at 1 MHz or higher (such as the DE-5000 or Atlas ESR70).
What Q should I aim for when winding inductors for HF bandpass filters?
For LC bandpass filters in the HF range, aim for Q ≥ 100 at the operating frequency. Powdered-iron toroids (T-68-2 for HF, T-68-6 for 10–30 MHz) typically achieve Q = 150–250 when properly wound with the right number of turns. Ferrite cores have higher permeability (and therefore require fewer turns for a given inductance) but their Q typically falls below 100 at HF due to core losses above 1–2 MHz. Air-core coils achieve Q = 200–400 but are impractical for compact designs and are not self-shielding. Silver-mica capacitors, not ceramic, should be used with high-Q inductors to avoid degrading the overall filter Q.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.