Measure impedance of PCB antenna with very small ground plane

I have recently been designing different PCB antennas with very small ground planes due to design restrictions. I use a VNA to measure the impedances, but am having trouble measuring them correctly.

I know that the error in the impedance measurement is because the cable to the VNA is relatively large compared to the ground plane area. Therefore the cable is electrically a part of the antenna.

The design in the picture has a radius of 15mm. The cable has a diameter of 1.37mm.

How do I measure the impedance of such a small design?

Note, the question is not meant specifically for the design below, but more in general on how to do this.

• Why are you assuming the ratio of cable-diameter to antenna diameter will set the accuracy? A smaller center-conductor would allow a smaller outer diameter. Commented Sep 21, 2018 at 4:19

With the cable in place, do a SOL calibration with the short, open and 50 ohm SMT resistor load at the antenna location, you will also need to dial in the electrical length of the cable, (easily done in either short or open states).

This effectively calibrates out the effect of the cable and means you are measuring at the cable end, but you will want to make sure your setup is mechanically stable (or use the very expensive 'phase stable' cables from the likes of Gore, if you have to ask you cannot afford them).

My usual method for this sort of thing is to make my test board up with a SMA connector that way I can either have my reference plane at the connector or at the aerial depending, and the 'at the connector' case is easy to calibrate because I have the appropriate (very expensive) cal kit.

• Ok, I think this is probably the best method, calibrating on the board, with the cable in place. I have before used a temporary SMA connector mounted on the board, but for this small design, there is no room. Commented Sep 24, 2018 at 7:47

Whatever you use, calibrate the antenna cable with a dummy 50 Ohm load. ( suitable RF part ) before attaching the antenna.

How do I measure the impedance of such a small design?

parameters

The easiest acceptance test is a Return Loss (RL measurement over a given bandwidth, BW.
Size does not matter in how to compute or measure impedance.

Cable and connector quality matters a lot.

If not part of the design, always use semi-rigid coax to SMA or your preference depending of GHz. If not sure about cable quality, compare anyways to semi-rigid coax (similar diam.)

I assume you are familiar with http://www.antenna-theory.com/basics/main.php

The conductor inductance L(nH) is primarily controlled by geometry or length/diam. ratio.

The capacitance is strongly affected by the dielectric gap and relative Dk constant or the spacing between conductors.

From reactive power, we get the formula for Characteristic Impedance, $$\Z_o^2=\dfrac{L}{C}\$$. From propagation delay, we get the 1/4 $$\\lambda\$$ conjugation effect (or impedance inversion).

simple measurement methods. RL or SWR

-Variable RF Generator, a splitter or return loss bridge with a (hot carrier or pin diode) peak detector, RF cap and mV DMM. -Measure output terminated with 50 Ohms and above high impedance Vdc in mV.
-All 3 ports on splitter are 50 Ohm terminated.
-Compute -15db equiv. mV for return signal limit

better measurements using direction coupler 1 GHz scope and SWR meter
- Or use an RF Gen. & Spectrum Analyzer with return loss bridge.
- or use a VNA, vector Impedance Analyzer with Smith Chart.

Add a ferrite clamp or a bead around the coaxial cable. It will remove the common mode currents from the cable. Use a clamp which provides high enough impedance in your frequency of interest.

EDIT: I noticed you have not soldered the outer conductor of the cable in to the ground plane of the antenna! You most definetely should! And to make it work properly (without any parasitic inductance, and other non-wanted issues) you must solder the shield of the coax to the ground plane as close from the end of the cable as possible.

• Yes, I have successfully used ferrite clamps before, but for this very small design, the mass of the clamp seems to disturb the antenna more than help. Yes, I did indeed solder the outer conductor of the cable to the gnd plane, right at the point of the feed. Commented Sep 24, 2018 at 7:41
• Try using a semirigid coax, with a small bead, maybe that wont interfere as much.
– user94729
Commented Sep 24, 2018 at 9:48