Hi guys, I tried posting this in the other forums but a screen comes up saying I don't have the privleges or the admins blocked me or something.
So:
I am working on a UHF small loop antenna. I want to model it as its equivalent square loop antenna. Note: I am working on a small inductively coupled loop, not those huge 3 m loops for radio operators and DXing.
The book I am using is Antenna Theory: Analysis and Design 3rd Edition by Constantin Balanis, great book. Also Antennas by John D. Krause
1: How do I know it qualifies as a small loop?
Balanis gives the stipulation that the radius of the circular loop must be less than lambda/(6*pi) which in my case it is.
2: what is the geometry of my antenna?
It consists of a small circular loop on a dielectric board (I think its FR-4) the antenna is not solid wire, it consists of conductive pcb trace, probably etched copper or conductive ink. The circular trace is then connected to two additional traces ending in a female sma connector. There is no ground, the traces connect to the hot wire and negative terminal of the sma to complete the circuit.
______
/ \
| | Pathetic, but it will have to do.
\ _ _ /
| |
| |
| |
OOOO
3. Now to model both designs. I need to compute the external inductance of the loops. I can find these on an impedance analyzer and compute it, which I did for the circular loop. I want to solve for the inductance analytically, and subsequently I can modify my loop geometries/change dimensions for the square.
Note: internal inductance is neglected.
Balanis gives two equations that approximate the inductance values.
La=unot*a *[(ln (8*a/b))-2] eqn 5-37a // circular loop
a=radius of loop
b=radius of wire, in my case width/2 of trace.
I found this circular indutance, equated it to the square loop inductance formula and I extracted the parameters so I can build a square loop of the same inductance.
La=2*unot*a/pi *[ln (a/b)-0.774] // square loop
4. Now this handles the values for the antenna. The races that connectto the sma and the loop have their own inductances and contribute to the overall inductance. I need to find that.
Originally, I thought I could model it as another circular loop, given the length of the traces. I found the perimeter/circumference and then found the radius. I computed the inductance of the traces as a circular loop. As a first order approximation it wasnt too bad becoz the sum of the circular loop plus the traces =X nH. My exerimental value for the loop was Y nH on the analyzer. A percent error of 10.5% not bad for a rough guess.
However, I decided to be more scientific in my approach, so i tried to model the traces as two parallel wires. In Microwave Engineering 3rd edition, Pozar stated:
L= mu/pi * cosh^-1 (D/2A)
D is the separation distance between the wires center
A is the radius of the wire.
I have traces so I used the halfwidths as the radii, respectively. However, the results were way too large. So I have to model the traces as something else.
I read that some EMC books used flux calculations to derive the inductance values, but that is a bit tedious in computation time. There is also some 3-D model answers, but I just need a fairly accurate approximation.
5. My question is: Has anyone done work similar in this area, and if so could one provide some reference texts or articles or something to assist me? I like my first order guess. I'll go with that just to run a rough em simulation.
Am I leaving out some details? Yes. I would not like to divulge them if neecessary. I'd like to just discuss the physics.
If anyone can help me, I'd be most apprecitive.
Thanks.
So:
I am working on a UHF small loop antenna. I want to model it as its equivalent square loop antenna. Note: I am working on a small inductively coupled loop, not those huge 3 m loops for radio operators and DXing.
The book I am using is Antenna Theory: Analysis and Design 3rd Edition by Constantin Balanis, great book. Also Antennas by John D. Krause
1: How do I know it qualifies as a small loop?
Balanis gives the stipulation that the radius of the circular loop must be less than lambda/(6*pi) which in my case it is.
2: what is the geometry of my antenna?
It consists of a small circular loop on a dielectric board (I think its FR-4) the antenna is not solid wire, it consists of conductive pcb trace, probably etched copper or conductive ink. The circular trace is then connected to two additional traces ending in a female sma connector. There is no ground, the traces connect to the hot wire and negative terminal of the sma to complete the circuit.
______
/ \
| | Pathetic, but it will have to do.
\ _ _ /
| |
| |
| |
OOOO
3. Now to model both designs. I need to compute the external inductance of the loops. I can find these on an impedance analyzer and compute it, which I did for the circular loop. I want to solve for the inductance analytically, and subsequently I can modify my loop geometries/change dimensions for the square.
Note: internal inductance is neglected.
Balanis gives two equations that approximate the inductance values.
La=unot*a *[(ln (8*a/b))-2] eqn 5-37a // circular loop
a=radius of loop
b=radius of wire, in my case width/2 of trace.
I found this circular indutance, equated it to the square loop inductance formula and I extracted the parameters so I can build a square loop of the same inductance.
La=2*unot*a/pi *[ln (a/b)-0.774] // square loop
4. Now this handles the values for the antenna. The races that connectto the sma and the loop have their own inductances and contribute to the overall inductance. I need to find that.
Originally, I thought I could model it as another circular loop, given the length of the traces. I found the perimeter/circumference and then found the radius. I computed the inductance of the traces as a circular loop. As a first order approximation it wasnt too bad becoz the sum of the circular loop plus the traces =X nH. My exerimental value for the loop was Y nH on the analyzer. A percent error of 10.5% not bad for a rough guess.
However, I decided to be more scientific in my approach, so i tried to model the traces as two parallel wires. In Microwave Engineering 3rd edition, Pozar stated:
L= mu/pi * cosh^-1 (D/2A)
D is the separation distance between the wires center
A is the radius of the wire.
I have traces so I used the halfwidths as the radii, respectively. However, the results were way too large. So I have to model the traces as something else.
I read that some EMC books used flux calculations to derive the inductance values, but that is a bit tedious in computation time. There is also some 3-D model answers, but I just need a fairly accurate approximation.
5. My question is: Has anyone done work similar in this area, and if so could one provide some reference texts or articles or something to assist me? I like my first order guess. I'll go with that just to run a rough em simulation.
Am I leaving out some details? Yes. I would not like to divulge them if neecessary. I'd like to just discuss the physics.
If anyone can help me, I'd be most apprecitive.
Thanks.