L10 - Measurement Lab: Impedance and S-parameters#
Measurement Lab: Impedance and S-parameters
Today the prediction meets a real piece of wire and a real instrument.
Lesson 10 Lab · Antennas, Phased Arrays, and Radar Systems · Dr. Neil Rogers
Printing
To print the slides, switch to present mode and print: one slide a sheet, with room for notes. Print from read mode for the whole lesson.
Learning Objectives
- I can measure the impedance and S-parameters of an antenna using a vector network analyzer and interpret the results.
Lesson 9 did the explaining. It set out what the analyzer measures, why calibration is a statement about where zero is rather than about accuracy, what the reference plane does to your numbers, and what a one-port measurement can never tell you. None of that is repeated here, and you should have it open beside you. Today is a lab period: you will be standing at an instrument for most of it, and everything below is procedure, judgment at the bench, and what to write down.
What You Can Wreck
A bad measurement costs you an afternoon. Everything below costs the rig.
What |
Cost |
Ruined by |
|---|---|---|
Absorber |
$750/sq ft |
leaning, stacking |
VNA port |
$85k |
cross-thread, over-torque, cable stress |
Horn |
$5k |
dropping |
Cable |
$1k |
kinking |
The RF is milliwatts, so nothing here will hurt you. That is exactly why this frame exists: the cost of carelessness lands on the hardware rather than on you, and it lands in four figures before anyone notices.
The port is the expensive one, and the damage spreads. Start the threads by hand and square, tighten with the wrench rather than by feel, and turn the nut and not the cable body. A cross-threaded or over-torqued port is a bench repair on an eighty-five thousand dollar instrument, and the same damage transfers to the next connector it mates with — which on this rig is a calibration module. Never leave a cable hanging off a port either: side load at the connector is cable stress, and it is the slow version of the same failure. Cap what you are not using, and touch a grounded surface before you touch a center pin.
The horn is dropped, not worn out. Two hands, support its weight while you mate it, and never hang it from its own connector.
The cable is kinked, not worn out. Respect the bend radius, do not coil it tight, do not lay it where somebody will step on it, and do not pull it straight out of a tight bend.
The absorber is priced by the square foot. The pyramids shed if you brush them and a crushed tip is a permanently worse quiet zone, so nobody leans on the walls and nothing gets rested on the floor pyramids. There is no repairing a tip; there is only buying more absorber.
One more that costs nothing to avoid: nothing that transmits goes into an analyzer port. The port is an input, and it is not built to be driven.
Good Practice
Calibrate, verify, then measure. In that order.
Log the sweep settings before you calibrate.
Change one thing at a time.
Name and export every capture as you take it.
And write down what you expect before you look. A prediction you committed to in writing is the only way a surprise can teach you anything; a prediction you made after seeing the answer is not a prediction.
What You Are Doing Today
Calibrate one port, then prove the calibration is good.
Capture one sweep of your antenna’s reflection.
Read resonance, impedance, VSWR and bandwidth off the marker.
Break it three ways and export a file for each.
Lesson 7 told you a half-wave dipole should sit near \(73 + j42.5\ \Omega\) and resonate slightly short of \(\lambda/2\). By the end of the period you will know what your particular piece of wire actually does, how far that is from the prediction, and which of the two you believe.
The single most useful habit this lab can leave you with is the order of operations: calibrate, verify, then measure. An unverified calibration is an unmeasured antenna, and the difference costs about ninety seconds to check and an afternoon to discover afterwards.
Rehearse the Chart First
Ten minutes on this before you touch the instrument. It shows one physical resonance in both languages at once; drag across either plot and the marker tracks the same frequency on both. Watch three things. First, the dip in dB, the real-axis crossing on the chart, and the VSWR minimum are the same event seen three ways — which is Lesson 9’s “four names for one number” made visible. Second, slide \(R\) at resonance away from \(50\ \Omega\) and the dip gets shallower while the resonant frequency does not move: mismatch and resonance are independent. Third, raise \(Q\) and the bandwidth pinches shut, which is why fat conductors are wideband and thin ones are not.
The instrument you are about to use draws the same two plots from real data, with the same marker linking them. Everything you do on this widget you will do again in twenty minutes on your own trace, where the curve is noisier and nobody labels the resonance for you.
The Rig
The chamber’s VNA, driven from the dashboard in a browser.
One test cable on port 1, and a torque wrench.
The calibration module, for the Calibrate… wizard.
A dipole with a known nominal resonance, on a foam block.
Everything today happens on the dashboard’s Sweep tab, which captures at the current position and never moves the tower. It is the one measurement this rig can make with nothing but an analyzer attached.
The foam is not optional equipment — it is what lets you take your hands off the antenna while you read the screen, and Lesson 9 explained why that matters. Standing the antenna in the chamber enforces the rule for you: with the door shut you cannot be holding the element and reading the trace at the same time, which is exactly the mistake this lab is trying to train out of you.
A torque wrench is worth using if the bench has one: an under-tightened SMA connector is a slow, intermittent way to lose a calibration.
The service will even run with no positioner attached at all, and says so — the scan button reads no positioner and everything that turns the tower is grayed out, while the Sweep tab keeps working. That is the shape of today’s measurement: one port, one sweep, nothing moving.
Step 1 — Set the Sweep
VNA section: start and stop bracketing the expected resonance by ±30%.
Points at least 401. Log the IF bandwidth and power too.
The Parameter dropdown is for scans. A capture chooses its own.
A capture takes its frequency settings from this same panel, so a sweep and a scan can never quietly disagree about what was measured. Changing any of them after you calibrate leaves the instrument interpolating a correction across a span it never measured; the panel flags it and the log warns again.
The default span is wide enough for a horn and wrong for your element: a 101-point sweep across a gigahertz is a 10 MHz grid, and a thin dipole’s whole VSWR \(\le 2\) band can be 40 MHz. Four points across a resonance will not find its minimum and cannot give you a crossing frequency worth quoting. Points also set how finely you can place the marker, because the marker steps from one measured frequency to the next and not between them. This is the one setting where the default will quietly cost you the measurement, so change it before you calibrate, not after.
Step 2 — Calibrate, Then Verify
Calibrate… → 1-port, port 1. Reference plane: the cable ends.
Acknowledge, run it, put the cable back.
Verify: terminate the cable in \(50\ \Omega\) and press Sweep. Return loss better than 30 dB across the band. Screenshot it.
A one-port calibration corrects reflection on that port alone, needs only that one cable end on the module, and is the right choice for a single antenna. The two-port option also corrects transmission, which is what Lesson 11 needs and what today does not.
The wizard asks which plane you calibrated because nothing in the data afterwards can tell. Lesson 9 made that argument on paper; the dropdown is the argument made unavoidable, and the answer is written into the record — and into the header of every file you export — so that a measurement read weeks later still says what it was referenced to. Pick the one-port option and the checklist rewrites itself to match: one cable end to unmate, one port of the module to mate, and nobody sent into the chamber to disconnect an antenna for no reason.
The cal pill in the strip along the bottom is the other half: it reads cal, uncal, or cal? when the instrument will not say. An uncalibrated sweep is valid data and is never blocked, but it should not be possible to take one without noticing.
Verifying against a load is the step that catches everything else — a cable swapped after the calibration, a loose connector, a sweep changed without meaning to. It works because the load is a standard the calibration did not use to define itself, so a good answer is evidence rather than arithmetic.
Step 3 — Capture the Antenna
Connect it, set it on the foam, and take your hands off.
Sweep tab, Capture: S11 only.
Press Sweep. The tower does not move.
One sweep per parameter, so asking for all four costs four times the wait and measures three things that are not there — your antenna has one port. The Smith chart and the magnitude plot fill in together as the trace arrives.
A capture is not a scan and is not written to runs/. It lives in the browser
until you export it, which is deliberate: the service ships complex
S-parameters and nothing else, and every derived number you are about to read
— dB, impedance, VSWR, return loss — is computed from them on the page. The
payload stays a measurement rather than a measurement plus somebody’s
arithmetic.
If you do ask for several parameters, STOP declines to start the next one rather than interrupting the sweep in flight. A single sweep is one exchange with the instrument and there is nowhere to interrupt it.
Step 4 — Four Names for One Number
The Marker picks a frequency. The readout gives it all at once:
\(Z = R + jX\), and \(\vert \Gamma \vert\),
VSWR, and return loss in dB.
The Smith chart is not a fifth quantity — it is the same number, plotted.
The magnitude plot is \(\vert S_{11} \vert\) in dB against frequency; the Smith chart is the locus of \(\Gamma\); the marker sits at one frequency on both. Move it and watch all four numbers change together, because they are four ways of writing one measurement down.
This is Lesson 9’s “four names for one number” with the instrument doing the conversion instead of you:
with \(Z_0 = 50\ \Omega\), which on this instrument is a fact and not a setting. Two readings are worth recognizing on sight. The readout says open where \(\Gamma\) reaches +1, because the impedance there is unbounded rather than merely large. And it says VSWR ∞ whenever \(\vert \Gamma \vert \ge 1\): a passive antenna cannot reflect more power than it receives, so that is noise, or a calibration that no longer matches the sweep, and quoting a number from it would dress the problem up as a measurement.
Read the resonance twice, once as the dip in dB and once as the reactance passing through zero — the real-axis crossing on the chart. The two readings disagree when something is wrong with the reference plane, and that disagreement is the cheapest diagnostic you have.
Step 5 — Bandwidth off the Marker
Step the marker out either side of resonance to the two VSWR \(= 2\) frequencies.
Record both, and the fractional bandwidth between them.
The bar is VSWR \(\le 2\), the same bar Lesson 4 set and Lesson 9 quoted. Quote the bandwidth in VSWR, never in decibels: Lesson 3’s rule is that the number means nothing without the bar attached to it.
On the log-magnitude trace that bar sits at −9.5 dB, so the magnitude plot finds the crossings quickly and the marker confirms them exactly. Interpolate between the two bracketing points rather than quoting whichever one happens to be closer; with 401 points across ±30% of a 900 MHz resonance the grid is about 1.3 MHz, and a 44 MHz bandwidth quoted to the nearest grid point is carrying 3% of avoidable error.
The File Is the Record
Export writes a Touchstone file:
.s1pfor one reflection parameter.
The header carries what a plot cannot:
hardware or simulated,
which parameters were actually measured,
the calibration, its ports, and its reference plane.
Export every configuration before you change anything, and name what you keep. A trace on a screen is a measurement that cannot say what it was taken under; this file can, and that is the difference between data you can defend in three weeks and a screenshot.
Two details in that header are there because of how easily a file lies. A
capture of a single reflection parameter is written as .s1p rather than an
.s2p with the other three columns zeroed — a zero-filled .s2p claims a
through path of exactly zero and an infinitely reflective second port, and a
reader will plot those numbers quite happily. And if you do capture a partial
set, the header names what was not measured and written as zero. The
Touchstone column order for a two-port file is \(S_{11}\), \(S_{21}\), \(S_{12}\),
\(S_{22}\), which is not the order most people expect and is the usual source of
transposed data.
Step 6 — Compare Against Prediction
Is the measured resonance above or below a \(\lambda/2\) calculation?
Which way would you trim the element?
Write the answer down before you move on.
The sign of the reactance answers the second question on its own, and Lesson 9 worked the inference: negative reactance is capacitive, the element is electrically short, and it wants to be longer. Committing to an answer in writing before you check it is the whole point of the step.
Step 7 — Perturb, One Variable at a Time
One capture and one exported file each, same sweep, same calibration:
held clear, in free space,
with a hand 2 to 3 cm from the element,
lying flat on the bench.
One variable at a time, and record all three fully — you are producing the data for the table in your report, and a configuration you measured incompletely is one you will have to set up again. Lesson 9 predicted the direction of each shift; your job is the magnitude.
Rename each file as you save it — l10_freespace.s1p, l10_hand.s1p,
l10_bench.s1p. The export stamps the clock into the filename, which keeps
three captures apart and tells you nothing about which is which a week later.
Three files with the sweep unchanged between them are directly comparable,
which is the whole reason for not touching the VNA panel once you have
calibrated.
Three Failure Modes
Calibrating with one cable and measuring with another. Changing the sweep after you calibrated. Gripping the coax at the feed point while you read the screen.
The first two the dashboard can warn you about, and it does. The third one is the cruel one, because nothing warns you: you have perturbed the very measurement you are recording, and the trace looks entirely plausible. Set the antenna down on the foam stand and take your hands off it.
Deliverables
One page, at the start of Lesson 15:
An annotated \(\vert S_{11}\vert\) plot, both crossings marked.
A results table for all three configurations.
A Smith chart with the resonance marked.
A paragraph on the perturbations.
In detail:
An annotated \(\vert S_{11}\vert\) plot. Resonance marked, both VSWR \(= 2\) crossings marked, axes labeled with units.
A results table: \(f_0\), \(Z\) at resonance, VSWR \(\le 2\) bandwidth in MHz and in percent, for all three perturbation configurations.
A Smith chart with the marker on the resonance, and one sentence identifying that point as the real-axis crossing.
A paragraph on the perturbation results. What moved, in which direction, by how much, and why. Connect at least one observation to the near-field argument from Lesson 9.
Hand in the three exported files with it, and state the reference plane you calibrated at. A plot with no markers and no units is a screenshot rather than a measurement, and the paragraph carries the largest share of the grade.
The Bench Card
At the bench |
What to do |
What good looks like |
|---|---|---|
Sweep |
±30% around resonance, \(\ge 401\) points |
settings written down |
Calibrate |
1-port, port 1, at the cable ends |
reference plane recorded |
Verify |
\(50\ \Omega\) load, one capture |
return loss \(> 30\) dB, screenshotted |
Capture |
Sweep tab, \(S_{11}\) only |
Smith chart and magnitude together |
Resonance |
dip in dB and reactance through zero |
the two agree |
Bandwidth |
marker to both VSWR \(= 2\) points |
3 to 10% for a thin dipole |
Export |
one Touchstone file per configuration |
header states the calibration |
Perturb |
free space, hand, bench |
three complete captures |
The sanity range in the bandwidth row is the one number worth memorizing: if you measure 1%, suspect the setup before you suspect the antenna, because a resonant length of feed cable can manufacture a narrow dip that has nothing to do with the element.
Practice
Where This Is Going
Today established that power went in.
Lesson 11 establishes that it came back out, and in which direction.
Together they are the complete characterization of one element.
A VNA cannot see radiation, only mismatch, so the efficiency question this lab leaves open is answered on the range next period — same instrument, same dashboard, two ports instead of one, and a tower that moves. Further out the skills compound: Module 3 builds arrays from these elements, and every element in an array sees its neighbors as a mutual impedance — precisely the \(S_{11}\) shift you produced with your hand today.
The midterm project, due 2 Oct, asks you to build a dipole, tune it, measure it, and defend the numbers you report about it. The antenna itself is not in question — everyone builds the same one — so what you defend is the measurement. Tuning is this lab: capture, read the sign of the reactance, trim, capture again. Calibration and Smith-chart fluency are the rate-limiting skills on that project, so practice both here, where the cost of a mistake is an afternoon rather than a week.