Input impedance of a round straight copper antenna

Question

I got some help from a discussion of yesterday about network impedance matching for transferring data between antennas (Basic RF signal amplifier). The discussion was about that the current and the voltage gain of amplifiers are trivial. Important issue is the impedance between amplifier and antenna. I researched again and I have seen there are smart calculations to get the values for resistors of transistor-based amplifiers. Starting off from here was a little complicated, so messed up with the prepared calculators on internet. There are good ones. But my problem is with the antenna. It is 12.3 cm long and has 2 mm diameter, is copper and runs at 8 MHz. On a webpage of https://chemandy.com/calculators/round-wire-impedance-calculator.htm I gave in the information I predicted before and it resulted the following value:

Z = 0.01442 Ω + j 5.585232 Ω

The antenna is a shortened one. What can I do with this value? I need an amplifier that works with maybe common-emitter amplifier. From where can I start to calculate the needed resistors for impedance matching. Are there any good starter kits on internet I could council? There is also another webpage https://www.analog.com/en/design-center/interactive-design-tools/rf-impedance-matching-calculator.html about RF impedance matching as calculator. Is there a general way to make up a hacky experiment to make this more clearly?

Answer 1

You are trying to transmit over 10m at 8MHz, this is less than a quarter of a wavelength. All the antenna design stuff you are quoting is about radiation fields in the far field whereas you are in the near field. Forget radiation, your system will be dominated by simple capacitive or inductive coupling. Inductive coupling is likely the easiest. Make a couple of coils, maximize the current in the transmit coil (probably by resonance), and worry about the size and orientation of the receive coil and the sensitivity of the receiver.

Think 13MHz store security systems.

Answer 2

An 8 MHz radio wave has a wavelength of about 38 meters in free space. A half-wave dipole antenna would be about 19 meters in length. A quarter-wave monopole antenna would be about 9.5 meters in length. A 1/10th wave small loop antenna would have a circumference of about 3.8 meters and a diameter of about 1.21 meters.

When antennas are significantly small relative to the wavelength of the signal they are attempting to radiate, then their efficiency generally drops. The radiation resistance of the antenna becomes very small, often a few m\$\Omega\$. As a result, the ratio of power that is radiated to the power that is converted to heat becomes small.

Since you only

need to transmit for about 10 meters not more.

you will probably be able to get by with an poorly matched and hence inefficient antenna/amplifier combination. You can make up for the inefficiencies by using an amplifier with sufficient power.

The rest of this answer will discuss how you could drive a 1/10th wavelength loop antenna.

[It is important to note that small loop antennas radiate parallel to the plane of the loop, not perpendicular, as large loop antennas do. Check that the antenna is oriented properly before deciding the amplifier or antenna doesn't work].

According to this loop antenna calculator, a loop with a 3.85 meter circumference, and a 2 mm diameter wire, driven at 8 MHz, will have

• a radiation resistance of 20 m\$\Omega\$
• a loss resistance of 452 m\$\Omega\$
• a radiation efficiency of 4%
• an inductance of 1.08 uH
• a required tuning capacitance of 365 pF

(to be continued)

Answer 3

There was a discussion two or three years ago. Very short range indoor RF transmitter - receiver circuits It is less technical but satisfied me in that way. Shortened antennas have several technical disadvantages. I can now navigate through antennas better.

Answer 4

But my problem is with the antenna. It is 12.3 cm long and has 2 mm diameter, is copper and runs at 8 MHz. On a webpage of https://chemandy.com/calculators/round-wire-impedance-calculator.htm I gave in the information I predicted before and it resulted the following value: Z = 0.01442 Ω + j 5.585232 Ω

The website you have visited has not listed the wrong formula. But what they do not tell you is the efficiency of the antenna. The calculation is just in physics. The antenna will not give the necessary power to reach longer distance. It would radiate useless with this given value. If you have an 8MHz crystal then, the antenna would be originally at about 37.5 meters long for full wave, but it is only 12.3 centimeters. This will not work if definite efficiency is expected.