What you need

Step 1: calibrate

A VNA measures what it sees at its reference plane, the point at which it was calibrated. Calibrate at the far end of the cable that will connect to the test object, so that the cable’s own length and loss are removed from the measurement.

1. Set the sweep: for the monopole, 100–170 MHz; for rings, 1–900 MHz. Use at least 201 points.
2. Connect the open, then the short, then the 50 Ω load to the end of the port-1 cable, saving each step. For S21, connect the two cables together for the “through” step.
3. Check the calibration: with the load connected, the SWR should read close to 1.00 across the sweep. If it does not, repeat.
4. Save the calibration and note the date, sweep range and room temperature in the log.

Step 2: the reference monopole

Mount a 523.5 mm straight wire vertically in the SMA socket at the centre of the ground plane, away from walls and metal furniture. Connect it to port 1, sweep 100–170 MHz, and record the frequency and value of the SWR minimum. Export the sweep as a Touchstone file (.s1p). Remove and remount the wire, and repeat twice more.

import hashlib
import io
import numpy as np

# 1) Make a synthetic sweep: a series RLC model of a quarter-wave monopole,
#    36.5 ohm at resonance near 136 MHz (stand-in for a real NanoVNA export).
f = np.linspace(100e6, 170e6, 141)
R, f0, Q = 36.5, 136e6, 8.0
X = R * Q * (f / f0 - f0 / f)
z = R + 1j * X
s11 = (z - 50) / (z + 50)
buf = io.StringIO()
buf.write("# Hz S RI R 50\n")
for fi, s in zip(f, s11):
    buf.write(f"{fi:.0f} {s.real:.6f} {s.imag:.6f}\n")
text = buf.getvalue()             # for a real file: text = open("monopole.s1p").read()

# 2) Read a Touchstone .s1p file (Hz, S-parameters, real/imaginary format)
def read_s1p(text):
    rows = [l.split() for l in text.splitlines() if l.strip() and l[0] not in "!#"]
    data = np.array(rows, float)
    return data[:, 0], data[:, 1] + 1j * data[:, 2]

freq, s = read_s1p(text)
swr = (1 + abs(s)) / (1 - abs(s))
i = np.argmin(swr)
band = freq[swr < 2]
print(f"minimum SWR {swr[i]:.2f} at {freq[i]/1e6:.1f} MHz; "
      f"SWR < 2 from {band[0]/1e6:.1f} to {band[-1]/1e6:.1f} MHz")
print("sha256", hashlib.sha256(text.encode()).hexdigest()[:16], "...")
# minimum SWR 1.37 at 136.0 MHz; SWR < 2 from 130.0 to 142.0 MHz
# sha256 88dee9347b65844b ...

Step 3: rings and probes

Fix the two probe loops in the fixture 20 mm from where the ring will sit, on opposite sides, with their planes parallel to the ring’s plane. Connect one to port 1 and one to port 2, and calibrate S21 with the probes in place but no ring (“through” is then simply the empty fixture). Sweep 1–900 MHz and save the result as the baseline. Then place each ring in the fixture in turn, sweep, and save. The quantity of interest is the change in S21, in decibels, between the baseline and each ring.

Step 4: check the frequency scale with the RTL-SDR

A VNA’s frequency scale comes from its internal crystal oscillator, which may be off by tens of parts per million. An RTL-SDR receiver gives an independent check. Tune it to a signal whose frequency is fixed by regulation, such as aircraft transponder replies at 1090 MHz or a local broadcast station’s published carrier, note the frequency at which the receiver shows the signal, and compute the receiver’s error in parts per million. Then set the NanoVNA to output a single frequency (CW mode) near the monopole’s resonance, receive it with the corrected RTL-SDR, and compare.

f_true = 1090.000e6               # Hz, aircraft transponder reply frequency
f_seen = 1090.025e6               # Hz, where the receiver shows it
ppm = (f_seen - f_true) / f_true * 1e6
print(f"receiver error {ppm:+.1f} ppm")
f_vna_set = 136.000e6             # NanoVNA CW output setting
f_vna_seen = 136.0061e6           # as shown by the receiver
f_vna_true = f_vna_seen / (1 + ppm / 1e6)
print(f"VNA output {f_vna_true/1e6:.4f} MHz, error {(f_vna_true - f_vna_set)/f_vna_set*1e6:+.1f} ppm")
# receiver error +22.9 ppm
# VNA output 136.0030 MHz, error +21.9 ppm

Step 5: keep a log and publish

Every sweep is worth keeping. A measurement log with one row per sweep makes the data usable by others:

Safety and the law

Summary

• A NanoVNA (to about 1.5 GHz) and an RTL-SDR receiver (to about 1.77 GHz), with cables, a ground plate, probe loops and a non-conducting fixture, are enough for every measurement in this book.
• Calibrate at the end of the cables, verify with the 50 Ω load, and repeat every measurement three times.
• Export sweeps as Touchstone files; a few lines of Python find the SWR minimum and fingerprint the file.
• Use the RTL-SDR to check the frequency scale against signals of known frequency.
• Keep a log, publish raw files with their hashes and DOIs, and report results whichever way they come out.