How to calculate Quality factor of loop antenna?

[Jeetkumar]

Hi all,

I have 1 inch copper tube with 30 cm diameter of circular structure made from copper tube. the resonance frequency for my simulation is 17.83 MHz. i just want to measure the quality factor. can you plz help me with this, i came across formula which states Q = fc/(f2-f1)

Thanks in advance.

 

[D.A.(Tony)Stewart]

f2-f1 is the 3dB down bandwidth delta f.
fc is center.

In lumped element filters, ratio of center to -3dB bandwidth is also Q, is also related to ratio of reactive to real impedances on 2nd order filters for parallel mode.

Crystals however have Q factors of 10,000 or so make very sharp filters. Ceramic resonators are also good, cheaper but less Q.

 

[WimRFP]

If you have a network analyser or VSWR bridge, use a second loop to couple with the tuned loop.

Play with the distance of the coupling loop to the tuned loop and the frequency until you have a good match. Make sure the feedpoint is opposite to the ends of the loop to avoid loss due to common mode issues. Also make sure your loop is far away from any opbject as this will extract energy, hence gives wrong measurements. Check for common mode issues (if you touch the cable that goes to your instruments, and the VSWR changes, you have a common mode problem).

Measure the points where |S11| = 0.33 (that is VSWR=2) and subtract them. Now you have 71% of the -3 dB BW

so Q = 0.71*Fc/(BWvswr=2). fc is resonant (center) frequency.

There are more methods, but this one requires scalar measurement only.

 

[D.A.(Tony)Stewart]

Not used the VSWR method for measure Q but have used it for tuning center f of resonant antenna. I wonder if it correlates well for non-linear antenna.
It should work ok here. but -3dB emission level is the de facto method. using a relatively flat antenna over this band or visa versa using gen. and power meter. (which is also one scalar measurement.)

as a comment, I did this in mid-70's for a spun dipole in a Black Brandt VI rocket design. and using a return loss bridge I discovered how well a simple antenna measuring return loss is great sensor for human motion anywhere in the room.:roll:

 

[WimRFP]

Hello,

I don't see whether it doesn't correlate for a non-straight antenna. It is just an LC circuit with "some" radiation loss. As long as he excites it with RF level well below corona issues, it behaves as a linear circuit.

It depends on the background of Jeetkumar whether he has better feeling with |s11| = 0.33, VSWR=2, RL=9.6 dB, or impedance, voltage, current. It all depends on the available equipment and experience. Some signal source with an oscilloscope will work also.

The reason for mentioning inductive coupling is that the impedance of his circuit at resonance will be very high, too high to measure -3 dB impedance directly based on voltage division. When using a series approach, the impedance will be very likely too low, and it will be difficult to avoid loss due to common mode issues.

I use the inductive coupling method frequently. With high Q circuits, the distance between coupling loop is large, reducing problems with common mode currents.

Maybe he will come back with his available equipment.

 

[Jeetkumar]

Hi all, thanks for your valuable guidance, i have a question, i am working on WPT system which comprises of 2 transmitter coils and 2 receiving coils, the transmitter coils are made up of 1 inch diameter copper tube as i mentioned above, the diameter of tx coupling coil is 30 cm and that of tx resonating coil is 40 cm, while receiver side consist of resonating coil of 2 turns 1mm diameter copper wire with diameter of loop 49mm followed by rectangular spiral of approximate 42 x 42 mm size, i did simulation in HFSS and got good results, i have placed lumped capacitors in both tx and rx resonating coil in simulator, but in HFSS for matching tx coupling and resonating coil it provides an inbuilt operation of directly normalizing the tx and rx coupling coils/rectangular to 50 ohms, but in practical we need to have matching circuit, while looking for matching circuit design i came across Q factor which as mentioned in above comments in ratio of center frequency to -3db bandwidth, but if this is the case than in my design i am working on resonance frequency, so for both tx large copper tube and rx small rectangular spiral, i have same fc and f2-f1 as shown in final S21 graph, so is it possible both structure having same Q? and also in one of the online calculators for loop coil, when i place dimensions, it was giving me Q of 20,000 which calculating as per fc/(f2-f1), it gives me around 51.

I dont have network analyzer in my lab, and the only equipment we are left with is Oscilloscope, which is not showing any output except for noise. i am attaching the diagram of my design.

 

[Jeetkumar]

in following line in above comment there is a mistake in above explanation "but in HFSS for matching tx and rx coupling coil it provides an inbuilt operation of directly normalizing the tx and rx coupling coils/rectangular to 50 ohms". its just have inbuilt operation to normalize tx and rx coupling coil, we have not normalized directly tx and rx resonating coil. sorry for misprinting.

 

[FvM]

It's not quite clear, if your intention is calculation or measurement of resonator Q. Regarding calculation, I didn't see, how the Q number of 20000 is achieved. From the expectable coil resistance I calculated in your previous thread, I get sligtly below 10000, assuming no energy absorbers in the vicinity and lossless capacitors. The latter assumption is probably unrealistic in this Q range. In any, it won't be easy to verify the high Q value in a mesurement, needing at least sensitive equipment, e.g. a good VNA.

 

[Jeetkumar]

Thanks Fvm, the thing is that i have to design matching circuit for tx and rx coupling coil, i designed it using capacitance matching technique, but it is not at all effective and the thing is that i dont know how to measure the impedance of copper tube, as i need to match it to 50 ohm coax cable to feed the signal. So that is the reason i was going through some literature where i came around a method in which he calculated impedance using formula XL= 2*pi*f*L and Xc = XL/Q.

The ultimate goal is to design matching circuit, which is really becoming headache.

 

[FvM]

The purpose of your setup is apparently wireless power transmission, thus the quantity of interest would be loaded Q rather than Q of the stand-alone loop. In a simplified view, you want to match your RF source to the distant load.

If my assumption is correct, an iterative tuning of both source and load impedance matching circuit would be necessary.

 

[Jeetkumar]

Yes you are right the aim is to match RF source to distant load, but i have no clue how to proceed further with matching circuit stuff, if you have any idea how this can be approached than it would be really helpful and also can you help me how to measure loaded Q for our design.

 

[FvM]

As basic information, you need a specification of transmitter and receiver coil inductance and coupling coefficient. And coil resistance of both.

If I remember right, similar problems have been discussed in wireless power articles.

 

[WimRFP]

Yes you are right the aim is to match RF source to distant load, but i have no clue how to proceed further with matching circuit stuff, if you have any idea how this can be approached than it would be really helpful and also can you help me how to measure loaded Q for our design.

What equipment do you have (inclusive signal sources)?

Inductive coupled loop antennas are frequently used by radio amateurs (HAM). So there is lots of info on the web (inclusive pictures).

try: https://www.dxzone.com/catalog/Antennas/20M/

 

[mtwieg]

For just measuring the Q of a loop antenna, using mutually decoupled pickup loops with a VNA is a good method. Load the loop antenna with a very high Q capacitor (should be higher than the coil itself), such that it resonates near the frequency of interest. Then bring the mutually decoupled pickups to the antenna so they couple weakly to is (like -40dB), and use the VNA to measure the S21 between the mutually decoupled loops. The Q of the S21 plot will be the Q of the loop antenna.

 

[Jeetkumar]

I have a functional generator, oscilloscope and spectrum analyzer.

 

[WimRFP]

If your function generator is stable enough (synthesizer), and you can vary the frequency with fine steps (or it can sweep), it can be done with mtwieg's method. Instead of the VNA, you use the spectrum analyser as RF detector to find the -3dB points.

To make sure you measure the unloaded Q, you need to do a second measurement where you increase the distance between the TX and RX coil and your thick copper coil. If you measure higher Q factor, you need to further increase the distance. with Q factors > 1000, every structure in the vicinity will absorb energy and lower the Q factor (from experience at 14 MHz).

I understand you are going to use two resonators (RX side and TX side) for power transfer (critically coupled BPF?). I don't know the distance between the coils, but once you have the coupling coefficient (you can get that from EM simulation or using approximated formulas), you can put the whole thing in a circuit simulator, saving you lots of time.

If your system has to work over a range of distances, it is still feasible, but becomes more complicated.

Other thing, what type of amplifier do you have? Why this question?. It is very likely that during the experimentation, the amplifier will se very bad loads.

For practical measurements in a 50 Ohms system, I would definitely invest in a return loss bridge, VSWR bridge, etc, to get fast idea on the mismatch. For this frequency you can make these things yourself and test with know resistances. It is standard instrumentation for many hams (radio amateurs).

 

[D.A.(Tony)Stewart]

What is desired result of antenna?
Specs?

If you want to wireless power transmission line as WimRFP suggests, please specify load and range.

I know a client who uses this to remote power LEDs for tunnel lights for pavement mounting of wireless lights.

Their patented design uses RF with sender and receiver ferrite coils to send about 1 Watt thru the pavement from a connection to a buried coaxial cable.

 

[D.A.(Tony)Stewart]

Design LC coil.. Air coil could be from Woofer or try with magnet for sender and drive from signal generator 1 ~ 20 MHz and try different resonant circuits to drive coil and parallel capacitor with high power. Prefer Polypropylene for low loss high voltage caps. say 100nF. Computer impedance of Cap. relative to free space. try step up coil in autotransformer mode if you want to impedance match to free space.

Receiver could have large flat bar ferrite with wound coil and stable low leakage polystyrene cap to resonate. If say driving non linear loads like back to back 1W LEDs then you have high Q resonant circuit until real power drives LEDs which gives 3V dc or so. This presents ESR of < 1ohm so mismatched impedance needs autotransformer with turns ratio like 100 ~ 50:1 to match impedance better using awg24 or 22

For coil design calc https://www.wa4dsy.net/filter/filterdesign.html

for low level transfer function.. use sweep generator to tune resonance of source, then load, then both.. manually sweeping with 50ohm generator for now then buffered with amp to simulate discrete design.

Then after maximum coupling achieved. measure input power and output vs distance. gap... Ferrite rods or steel rods with resonant windings can be used to couple larger distances like a pipe.

So in short you want to drive sender coil and transform up to higher voltage and high impedance, then couple to receive coil... high resonant LC coil voltage and transform (autotransformer or tapped coil) down impedance to drive higher current say 30 ~ 300mA max @ 3V (1W) across LEDs back to back.