For a VLF receiving loop, the exact wire length is usually far less critical than people expect.
At VLF (about 3–30 kHz):
- Wavelengths are 10–100 km
- 150 m of wire is electrically tiny (a very small fraction of a wavelength)
So you are not building a resonant half-wave antenna. You are building a magnetic loop whose performance depends mainly on:
- Total enclosed area
- Number of turns
- Loop inductance
- Loss resistance
- How you terminate or tune it
WHAT MATTERS MORE THAN EXACT LENGTH
- Total Loop Area
Sensitivity is proportional to:
V proportional to N * A * (dB/dt)
Where: N = number of turns
A = area of the loop
Increasing turns increases signal roughly linearly.
Adding or removing 5–10 m of wire will not radically change performance unless it significantly changes the number of turns.
- Inductance (and Resonance if Tuned)
If you tune it with a capacitor:
f = 1 / (2 * pi * sqrt(L * C))
Wire length affects:
- Total turns -> inductance
- Inductance -> resonant frequency
But you can always retune by adjusting C. So the wire length does not need to be exact.
- Resistance (Losses)
22 SWG copper (about 0.7 mm diameter) over 150 m is roughly:
5–6 ohms DC resistance
At VLF, skin effect is mild, so AC resistance will not be dramatically higher.
A few extra metres will not significantly degrade Q unless you are pushing for very high Q.
WHEN LENGTH REALLY MATTERS
Length matters more if:
- You are targeting a specific inductance
- You want resonance with a fixed capacitor
- You are building a calibrated field strength system
- You are maximising Q
Otherwise, it is forgiving.
PRACTICAL ADVICE
Instead of worrying about exact length:
- Maximise area
- Use as many turns as mechanically sensible
- Keep joints minimal
- Twist the feed downlead
- Use a high-impedance preamp at the loop
If feeding a sound card or SDR, the preamp usually matters more than exact wire length.
ROUGH GUIDELINE
Within +/-10% of 150 m: negligible difference for reception.
Even +/-20% is usually fine — just retune.
The VLF signals i am detecting vary from 15 kHz to 25 kHz. Does that affect lengths needed?
Short answer: no — that frequency range does not make the exact wire length critical.
At 15–25 kHz:
- Wavelength at 15 kHz ≈ 20 km
- Wavelength at 25 kHz ≈ 12 km
Your 150 m of wire is still electrically tiny (less than 0.002 lambda).
So it is operating purely as a magnetic loop, not a resonant antenna.
WHAT CHANGES BETWEEN 15 AND 25 kHz?
- Inductive reactance increases with frequency
X_L = 2 * pi * f * L
So:
- At 25 kHz the loop’s reactance is about 67% higher than at 15 kHz.
- The loop voltage output also rises with frequency because induced voltage is proportional to dB/dt.
This means the loop naturally gives slightly stronger output at the higher end of your range.
- Resonance (if tuned)
If you are tuning with a capacitor:
f = 1 / (2 * pi * sqrt(L * C))
To cover 15–25 kHz, you need about a 2.8:1 capacitance range.
Example: If 25 kHz resonance needs 10 nF, then 15 kHz needs roughly 28 nF.
But the wire length itself does not need to change — you just adjust C.
- Broadband (untuned) operation
If you are feeding a high-impedance preamp and running broadband:
- No change in wire length needed.
- The loop will cover 15–25 kHz easily.
- Sensitivity variation across that range is modest.
In fact, making the loop resonant and narrowband would reduce your ability to monitor the whole range at once.
WHEN WOULD LENGTH MATTER?
Only if:
- You wanted the loop self-resonant in that band.
- You were trying to maximise Q at a single frequency.
- You were building a calibrated system.
For general VLF monitoring across 15–25 kHz, the 150 m length is perfectly suitable.
Practical suggestion for that band:
- Use a high-impedance FET preamp at the loop.
- Keep the downlead twisted or screened.
- Avoid trying to force resonance unless you only care about one transmitter.
If you like, tell me the physical size of the wooden cross and whether you are tuning it or running straight into an SDR — I can estimate the likely inductance and optimal input impedance.
My cross has radius from centre of 67cm, or length each beam from end to end is 134cm.
Good — that gives us something concrete to work with.
Your cross:
- Radius (centre to end) = 0.67 m
- Beam length end-to-end = 1.34 m
If you are winding around the four tips, the loop is effectively a square roughly:
1.34 m × 1.34 m
So the enclosed area per turn is approximately:
A ≈ 1.8 m^2
How many turns are you likely getting from 150 m?
Perimeter per turn ≈ 4 × 1.34 m ≈ 5.36 m
Number of turns:
150 m / 5.36 m ≈ 28 turns
So you likely have around 28 turns.
Estimated inductance
For a multi-turn square loop of that size:
L will be roughly in the range:
5 mH to 10 mH
(Exact value depends on spacing between turns and winding geometry.)
What that means for 15–25 kHz
Inductive reactance:
X_L = 2 * pi * f * L
If we assume 7 mH as a mid estimate:
At 15 kHz: X_L ≈ 660 ohms
At 25 kHz: X_L ≈ 1100 ohms
That is perfectly reasonable for VLF reception.
If you want to tune it
Using:
f = 1 / (2 * pi * sqrt(L * C))
If L ≈ 7 mH:
To resonate at 25 kHz: C ≈ 5.8 nF
To resonate at 15 kHz: C ≈ 16 nF
So a variable capacitor covering roughly 5 nF to 20 nF would span your band.
Does this change your required wire length?
No.
Your geometry is already well suited to 15–25 kHz.
Adding or removing 10–20 m of wire would only slightly shift inductance and required tuning capacitance. It would not suddenly make the loop “right” or “wrong” for that band.
More important than length in your case:
- Use a very high impedance input (FET gate or op-amp buffer).
- Keep the downlead twisted tightly.
- Keep the loop away from house wiring.
- If indoors, expect mains harmonics to dominate.
Given your size and turn count, this is a very respectable VLF loop for that band.
If you’d like, I can estimate expected output voltage levels for typical VLF field strengths so you know what signal levels to expect into your SDR.
Excellent — let’s estimate realistic signal levels for your loop.
From what you’ve described:
- Square loop about 1.34 m × 1.34 m
- Area per turn ≈ 1.8 m^2
- About 28 turns
- Total effective area N*A ≈ 50 m^2
That is a healthy VLF loop.
- Typical VLF Field Strengths
Strong VLF transmitters (15–25 kHz band) typically produce magnetic field strengths at UK distances on the order of:
B ≈ 0.1 to 1 picotesla (pT)
In very good conditions you might see a few pT.
For calculation, let’s use:
B = 1 pT = 1 × 10^-12 tesla
- Induced Voltage Formula
For a magnetic loop:
V = N * A * omega * B
where
omega = 2 * pi * f
Let’s calculate at 20 kHz.
omega ≈ 125,600 rad/s
So:
V ≈ 50 * 125,600 * 1 × 10^-12
V ≈ 6.3 microvolts
- Expected Signal Levels
For B = 1 pT at 20 kHz:
You can expect roughly 5 to 10 microvolts RMS.
If B = 0.1 pT: About 0.5 microvolts.
If B = 5 pT (strong station, good alignment): 30 microvolts or more.
So realistic signal levels:
~0.5 to 30 microvolts depending on transmitter and conditions.
- What This Means for Your Front End
Your loop reactance is around 800–1000 ohms in-band.
If you connect directly to a 50 ohm SDR input:
You will severely attenuate the signal.
You need:
- Very high input impedance (at least 50k to 1M ohm).
- Low noise.
- Mounted right at the loop.
A simple JFET source follower works very well at these levels.
- Noise Reality Check
Indoors, you will almost always be limited by:
- Mains harmonics
- SMPS noise
- LED lighting
- Broadband hash
Outdoor placement often improves SNR by 10–20 dB.
Your loop size is large enough that atmospheric noise may dominate in a quiet rural location — which is exactly what you want.
- Quick Sanity Test
If you tune to a known strong VLF transmitter and see tens of microvolts equivalent at the preamp output, your loop is behaving properly.
If you only see nanovolts, something is loading it too heavily.