# Calculators: LC Resonance

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Enter new numbers and see the remaining output value change. Floating point format ("1.1E-6") works; engineering units ("1.1u", etc.) do not.

Note that the units are simply ratios, so their actual units do not matter (as long as the same units are used for all steps). They're labeled in μF, μH, Ω and MHz for convenience. (Equally valid are F, H, Ω and Hz, without having to change any numbers.)

## LC Resonance

An LC tank has a characteristic resonant frequency, at least if it is loaded lightly enough to resonate (more on that later). The resonant frequency occurs when the capacitive and inductive reactances cancel. L = μH, C = μF, = F =   MHz F = MHz, L = μH, = C =   μF F = MHz, C = μF, = L =   μH

## Resonant Impedance

An LC tank also has a characteristic impedance (this is different from the terminal impedance). The ratio of voltage to current circulating in the loop corresponds to the ratio of values. L = μH, C = μF, = Z =   Ω Z = Ω, L = μH, = C =   μF Z = Ω, C = μF, = L =   μH

## Frequency and Q Factor

Set up the circuit shown below, using a frequency generator (with reasonably constant voltage output over the testing range). L and C are the resonant tank under test, R1 represents the source resistance (including the generator's own output resistance, and any added if needed) and R2 represents the equivalent loss of the tank (don't connect a physical resistor here). Sweep the frequency until you find resonance. While probing the source and tank voltages with the oscilloscope (use 10× probes if possible), varying frequency above and below resonance slightly should look like this: Measure the frequency under the middle condition, where the tank voltage amplitude is highest (the phase shift will also tend to line up, which may be easier to eyeball when Q is low). Measure the source and tank voltage. (If the source's resistance is a large part of R1, measure the open-circuit voltage with the tank disconnected.)

If the voltage drop is small (V2 / V1 > 0.5), you may get better measurements with a larger R1. Likewise if V2 / V1 ≈ 0, try a smaller R1. Source Resistance R1 = Ω Resonant Frequency Fo = MHz Known Component: Inductor Capacitor Known Value C = μF Source Voltage V1 = V Tank Voltage V2 = V Unknown Value L = μH Resonant Impedance Zo = Ω Loss Resistance R2 = Ω Q Factor Q =

## Parasitic Capacitance by Difference

This method is useful for finding the unknown capacitance across a coil, or the residual, parasitic or equivalent capacitance of any kind of resonator. First, measure the resonant frequency using the voltage divider circuit and peak-tracking method shown above. Then, connect a known capacitor in parallel, and repeat the measurement.

This method is exact for lumped constant components only. For equivalent parallel resonators, if the resonant mode is widely spaced from other modes, it should also work well (in which case, the resulting RLC values should correspond to the lumped equivalent circuit for that mode). If the modes are closely spaced (e.g., the higher modes of a stub transmission line or helical resonator), or repeated or overlapping (e.g., the nearly coincident poles of a filter), don't expect a useful result.

The voltage divider items are optional. They just repeat the above calculation, and are provided for convenience. V1 and V2 should be measured under the first condition (without Cx), though for small values of Cx, the voltage ratio should be similar at either frequency, so that it doesn't matter much. Natural Resonant Frequency Fo = MHz Loaded Resonant Frequency FL = MHz Added Capacitance Cx = μF Capacitance C = μF Inductance L = μH Resonant Impedance Zo = Ω Source Resistance R1 = Ω Source Voltage V1 = V Tank Voltage V2 = V Loss Resistance R2 = Ω Q Factor Q =

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