# Are my calculations wrong?

So I'm trying to make relatively a large square coil antenna that will operate at 125kHz frequency.

The width and height of antenna are 300mm (30cm) and wire diameter is AWG24 (0.51mm) and I'd like to keep number of turns pretty low (under 30).

To calculate inductance I entered antenna parameters to this calculator and came up with inductance value of 0.000731H (with number of turns being 22; width, height=300mm; wire diameter=0.51mm; permeability=1).

I then calculated resonant frequency with another calculator where I entered the inductance value I got before (0.000731H) and capacitance of 2.2nF. The resulting resonant frequency was 1.2550 Hertz which is only about 0.00125kHz, way below 125khz which I need.

Now to achieve 125kHz I could increase the inductance to 731H by making number of turns equal 22,000 but this idea doesn't seem to be very practical. Does anyone has any suggestions to solve this problem?

• Wouldn't increasing the inductance lower the resonant frequency? – Hearth Mar 24 at 17:41
• To increase the resonant frequency you need to decrease the product of the inductance and capacitance. Likely your capacitor is too big, but as your conclusions are backwards your calculation may be wrong. – Chris Stratton Mar 24 at 17:42
• Actually it looks like you've just mixed up decimals / prefixes in working with the calculator - how did you get 0.00125kHz ? What it actually proposes for your sample inductance and capacitance is 125.5 KHz – Chris Stratton Mar 24 at 17:45
• Sometimes it's useful to have a sense of scale and plausibility... a single digit Hz result is just not realistic so is either a user/transcription error a mistake in the web calculator code. – Chris Stratton Mar 24 at 18:25
• Just for a sanity check 1uH and 1uF resonate at 160KHz. So do 10uH and 0.1uF. So do 100uH and 0.01uF. – analogsystemsrf Mar 24 at 20:40

When I started life as a graduate EE in 1975 we had both slide rulers and HP Calculators and a Nova Minicomputer .

I was introduced to graph paper just like below which helps save time and quick check any RLC Z Qs,Qp vs f calculation.

How you learn to trust your results comes with experience. @analogsystemsrf and I think alike.

"1uH and 1uF resonate at 160KHz" which is also 1 Ohm.

How you choose Q depends on ESR and DCR for series resonance which for high values Qs is almost same as current gain and for Parallel resonance, Qp depends on load Rp and leakage Rc. So you can choose components with good impedance for desired Q ratios.

Also for inductors a straight wire is 1uH/m for 80:1 length, thickness ratio and 0.5 uH/m for ~6:1 ratio in air but large loops are around 25 x greater than a straight wire self inductance. 