Inductance of Square Coil Antenna on PCB

[amanno]

Hey guys, I am trying to design an Inductive Square Antenna Coil that will be milled onto my PCB. I am slightly confused when it comes to the matching circuit. To my understanding the matching circuit is there to have the same impedance value of the antenna, correct?

So my matching circuit consist of capacitors such that X_{L_ant} = X_{C_tun}, correct?
When I calculate the inductance value of my designed antenna I get a value around 980 μH, which makes X_L = ~83kΩ (f = 13.56 MHz). That just seems very high to me, I thought antennas were suppose to have an impedance of ~50 - 75 Ω.

My coil antenna has the following properties:
K₁ = 2.34, K₂ = 2.75
d_out = 33 mm
d_in = 17mm
N = 4
and I am using the equation below to calculate the inductance
L_ANT = K₁ × μ0 × N² × (d / (1 + K₂) × p)

I have tried playing with the properties of my designed antenna to reduce the impedance but I can't seem to bring it down low enough, which makes me think I am missing something.

Any help/guidance would be greatly appreciated! Thanks.

 

[tech99]

The inductance value you are quoting seems much too high. I would expect a few microhenries.
Notice that your antenna is too small to be efficient at this frequency. Regarding matching, if you place a capacitor in series with the inductance, so that there is resonance, you are left with just the resistance. This resistance is what we must match to. It is mainly losses in the coil, but with a very small radiation resistance in series. As a rough figure, take a total resistance value of something like 1% of the reactance. This assumes a "Q" value of 100.

 

[Tom.G]

http://coil32.net/online-calculators/pcb-inductor-calculator.html

Shows 950 nH. Did you slip a decimal somewhere?

They are low efficency, low radiation impedance, high Q devices which means the tuning capacitor must be highly accurate and highly stable to keep them tuned to the desired frequency, once the correct value is found. Due to their low impedance, you may need a matching network to the electronics rather than just a resonating capacitor.

 

[tech99]

http://coil32.net/online-calculators/pcb-inductor-calculator.html

Shows 950 nH. Did you slip a decimal somewhere?

They are low efficency, low radiation impedance, high Q devices which means the tuning capacitor must be highly accurate and highly stable to keep them tuned to the desired frequency, once the correct value is found. Due to their low impedance, you may need a matching network to the electronics rather than just a resonating capacitor.

Thank you Tom G all agreed. Matching can be obtained by the use of one additional capacitor shunting the external circuit but it is obvious Amanno will need help with this.

 

[amanno]

Thanks for the help guys,

I currently have a matching network between the chip and the antenna using a shunt capacitor. The shunt capacitor is wired from, the node between the matching capacitor and the antenna, and ground. How do you determine the best value for the shunt? I was going to use a value very similar to what I find for the matching capacitor. Does that sound about right?

 

[Tom.G]

Have at it tech99. Its been too many decades since I've done this!

 

[tech99]

Two circuits shown at the following URL, with approximate circuit values. I hope the image works!
The capacitor I have shown as variable needs to be finely adjusted. The other one can probably be left fixed.
https://www.flickr.com/photos/58337586@N08/24678783420/in/dateposted-public/

 

[amanno]

That is perfect, just the help I needed! Thank you!