An antenna measurement is two measurements, and this lesson is the theory behind both. The radiated half asks what the antenna does in every direction, and it runs on a range. The terminal half asks how much of the power you deliver actually gets in, and it runs on a vector network analyzer. The question underneath them is the same: how much of what the instrument reports is the antenna, and how much is the setup around it.

Take the pattern first. Point a plane wave at the antenna from direction \((\theta,\phi)\), record what comes out of the terminals, and repeat for every direction. Reciprocity says the receive pattern equals the transmit pattern, so we may run the measurement in whichever direction is convenient — and everyone runs it in receive, because it is easier to move a receiver than a transmitter. That is also why the antenna under test is the end that rotates in Lesson 11: you would rather not run transmit power through a rotary joint.

The catch is the wave itself. What you can buy is a source antenna at a finite distance, and a finite distance means curvature.

A plane wave is flat in amplitude and flat in phase across the aperture, and a real range violates both. Keeping the two apart matters because the fixes are unrelated: amplitude taper is cured by choosing a different source antenna, and phase curvature only by moving the source farther away or abandoning the far-field range altogether.

The usual amplitude specification is under 0.25 dB of taper edge to edge. Seen from the source, the AUT subtends roughly \(D/r\). If the source pattern rolls off across that angle, the AUT is illuminated more strongly in the middle than at the edges, and an unintended amplitude taper is an amplitude taper all the same. Lesson 22 shows exactly what one does to a pattern: it broadens the main beam and lowers the sidelobes. Measure through a tapered illumination and you report an antenna better behaved than the one on the positioner.

Take a source a distance \(r\) away on boresight. The path to a point \(x\) off the aperture center is \(\sqrt{r^2 + x^2} \approx r + x^2/2r\), so the extra path at the edge, where \(x = D/2\), is \(\Delta\ell\) above. Multiply by \(k = 2\pi/\lambda\) to turn path into phase, then allow the edge to lag the center by at most an eighth of a wavelength. The criterion you have quoted since Lesson 5 is 22.5° of edge phase error, written as a distance, and every other far-field number in this course descends from that one tolerance.

Nobody builds a 1.8 km anechoic chamber, and that is the reason compact ranges and near-field scanners exist. The first number is not exotic either: seventeen meters is an ordinary requirement for an ordinary antenna, and it is already a large and expensive room.

Read the top two rows carefully, because they state what the rule delivers. At \(r = 2D^2/\lambda\) you have not measured the true pattern. You have measured one whose first sidelobe reads −12.9 dB instead of the textbook −13.3 dB and whose nulls are twenty decibels shallow. What you have measured correctly is the main beam, the beamwidth, and the gain. If you need a −40 dB sidelobe or a null depth you can defend, go to \(5D^2/\lambda\) or further, or stop using a far-field range altogether.

This failure mode is dangerous because it is quiet. A pattern measured at a quarter of the far-field distance still looks like a pattern: about the right main-beam width, sidelobes present, smooth. It is wrong only in the places you care about most.

The first three are far-field ranges: they physically deliver an approximate plane wave to the AUT, so all three still owe the full \(2D^2/\lambda\) or the optics that stand in for it. The fourth changes the question entirely.

One thing holds each of them back, and the four have nothing to do with one another. Weather and the ground bounce limit an outdoor range. Absorber reflectivity limits a chamber, which is what the next two frames are about. Diffraction off the reflector’s rim and feed spillover limit a compact range. Phase stability, the probe, and the hours the scan takes limit a near-field measurement.

Compute \(2D^2/\lambda\) first, because it decides the rest. A meter-class antenna at a few gigahertz needs tens of meters, which is an ordinary chamber and where most work belongs: the room is shielded, the schedule does not depend on the weather, and the quiet zone is a specified, measured number. An antenna too large for any room you can afford goes outdoors, where the distance is free and everything else is not.

When the far-field distance is out of reach, there are two ways out and they suit different antennas. A compact range keeps the measurement in the time domain you are used to — turn the antenna, record the pattern — and suits a directive antenna whose quiet-zone requirement is a meter or two, because the reflector has to be roughly twice that. A near-field scan handles anything, including a low-gain antenna that needs full spherical coverage, and it is the only option when the sidelobes and nulls have to be right, since it never approximates the plane wave in the first place. What it costs is time and complexity: hours to days of scanning, a probe that has to be characterized, and phase stability throughout.

Absorber is carbon-loaded foam, cut into pyramids, and it is specified by reflectivity in dB. Performance scales with pyramid height in wavelengths, so low-frequency absorber gets enormous: a chamber rated to 200 MHz has meter-long spikes on the walls.

Which reflectivity level you need is set by the lowest signal you intend to believe, not by the main beam. A reflection 40 dB below the main beam is nothing next to the main beam and a great deal next to a sidelobe thirty decibels down, because both levels are referenced to the same peak.

The quiet zone is a specified volume, usually a sphere or cylinder centered on the positioner, inside which the stray field is guaranteed below the reflectivity spec. It is measured rather than assumed, typically by dragging a probe through the volume and recording the ripple.

An antenna that overhangs the quiet zone is being measured in a room rather than in a chamber, and no amount of care with the rest of the setup recovers that. It is the first thing to check when a chamber measurement disagrees with a simulation for no reason you can name.

The quiet zone is also the specification most often assumed rather than looked up. It is quoted as three things at once — a volume, a level, and a band — and an antenna can sit inside the volume while the measurement runs outside the band. Read all three off the chamber’s documentation, measure the AUT’s largest dimension against the first, and know which one you were working inside before you write down a sidelobe level.

This is Lesson 14’s reflector geometry doing a different job. There the collimated wave was aimed at a satellite; here it only has to reach the far side of the chamber. Two costs come with it. A meter of quiet zone needs close to a two-meter reflector, built to a fraction of a wavelength — so the reflector is a precision instrument in its own right. And a hard edge acts as a line source sitting right inside your test volume, which is why the rims are shaped to scatter the edge contribution away from it.

Put a small probe a few wavelengths in front of the antenna and record amplitude and phase at a grid of points on a surface. Because the field sampled on a surface enclosing the antenna determines the field everywhere outside it, that grid is enough.

Near-field to far-field transformation is not a new physical principle. It is Lesson 6’s relationship run in the other direction, and three practical consequences follow immediately from that fact alone.

All three are rules for the scan itself, and each one comes straight out of the transform. Phase is why a near-field range is built around a vector network analyzer and phase-stable cables, and why the probe position has to be known to a small fraction of a wavelength. Sampling at \(\lambda/2\) is the same Nyquist argument as Lesson 6’s spatial spectrum: undersample, and the transform produces lobes in the far-field pattern that the antenna does not have.

The third rule is the one with a number attached, and it answers “how far out is far enough” in two parts. The standoff \(d\) is how far the probe sits in front of the aperture, and three to five wavelengths is the usual choice: far enough that the evanescent part of the reactive near field has died away and the probe is not loading the antenna, close enough that the scan plane does not have to be enormous.

The extent \(L\) is the other part, and it is what decides how much of the pattern you get. Energy leaving the aperture edge at angle \(\theta\) lands on the scan plane a distance \(d\tan\theta\) further out, so a plane of length \(L\) captures everything inside the \(\theta_\text{max}\) above and nothing outside it. Past that angle the transform is working from data it does not have, and the pattern it returns is truncated rather than measured. Doubling the angle you want means roughly doubling the plane, which is why a planar scan is quoted with a valid angle beside it and why it says nothing whatever about back lobes.

Write Friis for each measurement and the algebra is immediate: every term but the two gains appears identically in both, so the difference of the two received powers is the difference of the two gains. This is the method you will use in Lesson 11 and again for the midterm.

The horn is the largest term in the result and the only absolute number in the setup. Its calibration certificate gives gain against frequency, usually good to two or three tenths of a decibel, and that uncertainty passes straight through to \(G_\text{AUT}\) — there is no averaging it away, so measure at the frequency the certificate lists and interpolate carefully between listed points.

What the subtraction removes is narrower than “everything we do not know”. It removes the terms that are identical in the two measurements: transmit power, source gain, range, cable loss, and the room. Anything that changes between them stays in the answer. A cable bumped during the swap, a mount that does not put the two antennas in the same place, a polarization alignment redone by eye — each of those is a real gain error, and each is why Lesson 11 has you record the horn and the AUT back to back without touching anything else.

None of this is an argument for leaving the setup uncharacterized. The three-antenna method on the next page measures absolute gain with no calibrated antenna at all, and that is how the horn’s own certificate was produced. The absolute number matters because a link budget needs it: a 3 dB gain error is a factor of two in received power and a factor of \(\sqrt{2}\) in range.

A complete pattern is a function on a sphere, and measuring the whole sphere finely is expensive, so we take slices. A conical cut does the opposite of a great-circle one — holds \(\theta\) fixed and sweeps \(\phi\), tracing a ring at a constant angle off boresight — and is used for tracking antennas and for checking rotational symmetry. Two principal cuts fully describe a well-behaved pencil beam and say nothing at all about the diagonal planes, where the sidelobes of a rectangular aperture frequently sit.

The two principal planes are named for the antenna’s polarization, not for anything about the range. The E-plane is the plane that contains boresight and the direction the antenna’s electric field points: for a vertical dipole it is any vertical plane through the wire, and for a rectangular horn it is the plane through the narrow dimension. The H-plane contains boresight and is perpendicular to the E-plane, which is the same as saying it contains the magnetic field. Fix the polarization and the two planes are fixed with it.

That definition needs the antenna to have one polarization direction, so it applies to a linearly polarized antenna and to nothing else. A circularly polarized antenna has a field that rotates once per RF cycle, so there is no plane holding E, and “E-plane” is meaningless for it. Measure two orthogonal great-circle cuts instead — commonly called the \(\phi = 0^\circ\) and \(\phi = 90^\circ\) cuts, since there is nothing else to name them after — and quote axial ratio against angle in place of a cross-pol pattern.

Cross-pol is the power a linearly polarized antenna radiates into the polarization it is supposed to reject. Measure it by rotating the source antenna 90° about the line of sight and repeating the cut. It is worse off-axis than on, which is why it is quoted as a pattern rather than as a single number, and a well-built linear antenna sits 20 to 30 dB below its co-pol level on boresight.

A pattern measurement has a floor, and it comes from two places. The chamber contributes one: the absorber’s reflectivity is a stated level, and below it what you record is the room. The receiver contributes the other, its own noise, added in power to everything it records. Whichever is higher is the one you have, and on a good range it is usually the chamber.

Either way the number is the same kind of number, and you measure it rather than assume it. Take the peak, switch the source off, take the floor, and their difference is your dynamic range — 42 dB in the figure above.

Everything above that floor by a comfortable margin is the antenna. The main beam is at the top of the range, the half-power points are 3 dB down, and the first sidelobe of a uniform aperture is 13 dB down, so all three sit 29 dB or more clear of a 42 dB floor and none of them is in question. The nulls are the opposite case. A true null goes to \(-\infty\), the floor does not, and the measured trace simply flattens onto the floor wherever the antenna’s own level drops beneath it. The depth you read at a null is the depth of your receiver, not of your antenna.

That is what “limited by our 42 dB dynamic range” means: the measurement cannot resolve anything more than 42 dB below the peak, so every number extracted from that region is a bound rather than a value. Write the bound. “At least 25 dB deep, limited by our 42 dB dynamic range” is a defensible sentence; “25 dB deep” claims something the instrument never showed you.

This is the payoff of the chamber specifications earlier in the lesson. Absorber reflectivity and the quiet-zone level are a floor quoted to you on paper; the receiver’s noise is a floor you measure on the day. Lesson 11 asks you to measure yours with the source switched off, and then to say, row by row, which of your extracted numbers clears it and by how much.

Everything so far measured the antenna from a distance; the rest of this lesson stands at its terminals. There is one connector, one cable, and one complex number per frequency, and that number carries everything we have been predicting on paper since Lesson 4. Lesson 7 told us a half-wave dipole should sit near \(73 + j42.5\ \Omega\) and resonate slightly short of \(\lambda/2\); Lesson 10 is where that prediction meets a real piece of wire.

The block diagram is the whole instrument. A source sweeps frequency, one directional coupler samples the wave going out, a second samples the wave coming back, two receivers record both in magnitude and phase, and the instrument divides one by the other. Because both samples come from the same source, anything the source does wrong — drift, ripple, amplifier gain variation — divides out of that ratio. That is why a pocket NanoVNA and a bench instrument a thousand times more expensive agree on a well-calibrated one-port measurement to within a fraction of a dB.

An antenna has one connector, so it is a one-port device and the diagram has one port in it. The double subscript on \(S_{11}\) is the general scattering-parameter convention, in which \(S_{mn}\) is the wave leaving port \(m\) for a wave incident on port \(n\); with one port the only entry that exists is \(S_{11}\), and it is the reflection at that port. A two-port measurement — \(S_{21}\), insertion loss, a through standard — belongs to a filter or an amplifier, and to the pair of antennas in Lesson 11, not to the antenna on the bench in Lesson 10.

All four appear on instrument menus, and all four are computed from the single complex number the analyzer measured. Nothing else is being measured. Watch the units, because they are not the same down the column: the first two rows are decibels and differ only in sign, the third is a dimensionless ratio, and the fourth is a percentage of power.

The fourth row is the one to carry into a design conversation. \(\vert\Gamma\vert\) is an amplitude ratio, so the fraction of power reflected is \(\vert\Gamma\vert^2\), which at the course bar is 11%.

The course bar is VSWR \(\le 2\), from Lesson 4, and every bandwidth in this course is quoted against it. Lesson 3 is where that rule came from: an impedance bandwidth means nothing until you say what bar you measured it at. Say VSWR, every time.

The table above is what you need when somebody else does not. Datasheets and papers quote return loss, \(\vert S_{11}\vert\), and VSWR interchangeably, and all three are the same measurement; convert whatever you are handed back to VSWR before you compare it to anything of ours.

\(\Gamma\) and \(Z_L\) carry the same information, and the formula above converts one to the other. The analyzer measures \(\Gamma\) and displays \(Z_L\), which is convenient, because \(\Gamma\) tells you whether the antenna is acceptable and \(Z_L\) tells you what to do about it.

Take the marker reading above one line at a time. The magnitude, \(\vert\Gamma\vert = 0.28\), is a VSWR of 1.78, so this antenna clears the VSWR \(\le 2\) bar of the previous frame; on that number alone we would ship it. The real part of the impedance, \(31\ \Omega\), is well under the \(70\ \Omega\) or so a resonant dipole shows, which says some of the power reaching the antenna is going somewhere other than radiation — a lossy balun, a nearby conductor, or a poor ground. And the reactance is negative, \(-12\ \Omega\), which is the actionable part.

A negative reactance is capacitive, and a dipole is capacitive below its resonance and inductive above it. Reading \(X < 0\) therefore means resonance sits above the frequency we are looking at, and the element is electrically short. Lengthening it moves resonance down toward the marker. That inference — sign of \(X\), then which way to trim — is most of what Lesson 10 asks you to do at the bench.

Calibration is what this frame is about, and it is the first thing you do at the analyzer in Lesson 10. Three error terms dominate a one-port measurement. Directivity is the coupler leaking a little of the outgoing wave into the receiver that is supposed to see only the returning one, so the VNA reads a reflection even from a perfect load. Source match is the test port not being exactly \(50\ \Omega\), so energy the antenna sends back is partly re-reflected at the port and sent to the antenna again. Tracking is the reference path and the test path having different gain and different phase, both varying with frequency.

Three unknowns need three knowns, and that is all a short-open-load calibration is. You measure all three, the instrument solves three equations at every point in the sweep, and from then on it subtracts its own error before showing you anything. Two-port work adds a through standard — hence SOLT — but a one-port antenna measurement needs only the three.

Calibration does not make the instrument more accurate. The plane where you attached the standards becomes the plane where \(S_{11} = 0\) means “perfectly matched”, and everything on the far side of it is part of your device under test whether you meant it to be or not.

With \(\lambda_g = c\ v_f / f\), that pigtail is \(0.46\lambda_g\) long — nearly a full rotation of the Smith chart, and the impedance read off it is not the antenna’s in any useful sense. The wave traverses the extra length twice, out and back, which is where the factor of two comes from.

The equation above is the whole correction, and it is worth seeing rather than taking on faith. A lossless line of length \(\ell\) multiplies a wave by \(e^{-j\beta\ell}\) on the way out and again on the way back, so the reflection seen at the near end is the reflection at the far end times \(e^{-j2\beta\ell}\):

The magnitude of that factor is 1, so \(\vert S_{11}\vert\) is untouched and the dB plot looks correct while the impedance is wrong. Multiply by the inverse, \(e^{+j2\beta\ell}\), and the antenna’s own \(\Gamma\) comes back. Port extension is the instrument doing exactly that multiplication: you tell it \(\ell\) (or let it find \(\ell\) from an open), and it rotates every point in the sweep by \(2\beta\ell\). Because the correction is a unit-magnitude phase term, it cannot undo loss and it cannot undo a real mismatch inside an adapter — those need the cal plane moved instead, which is Fix 1.

At 990 MHz that same pigtail is exactly a half guided wavelength, \(2\beta\ell\) is a full 720°, and the impedance repeats — the one frequency where the uncorrected reading happens to be right, and a good illustration of why “it looked fine at one marker” is not a check.

This is what the sweep looks like on the instrument, and it is one measurement drawn twice. \(\vert S_{11}\vert\) against frequency is on the left and the same points are on the Smith chart on the right; the resonance is the dip on one plot and the real-axis crossing on the other, at the same frequency. Lesson 10 has you produce both of these for your own antenna.

Read the bandwidth against VSWR \(\le 2\), which is the bar from Lesson 4 and the one every number in this course is quoted against. The trace above is plotted in decibels, where that bar lands at −9.5 dB; set the analyzer to VSWR format instead and the line is simply 2, which is the display to use in Lesson 10 when you measure your own.

Fractional bandwidth is what lets us compare a 900 MHz antenna to a 2.4 GHz one, and it is the number with a sanity range attached: a thin-wire dipole lands between 3 and 10%. The trace above bottoms out at VSWR 1.40 and crosses VSWR 2 at 877 and 924 MHz, so \(\text{BW} = 47\ \text{MHz}\) on \(f_0 = 900\ \text{MHz}\), or 5.2% — entirely believable. If you measure 1%, suspect the setup before the antenna; a resonant length of feed cable can manufacture a narrow dip that has nothing to do with the element.

You met the Smith chart in ECE 343 as a graphical impedance calculator. Today you only need to read one: it is the complex \(\Gamma\) plane with a normalized-impedance grid on top, center \(50\ \Omega\), left edge a short, right edge an open, upper half inductive and lower half capacitive. Those four skills cover almost everything you will see this semester, and you will rehearse them on a widget at the start of Lesson 10 before you read your own trace.

This cuts both ways on the bench. A deep, wide dip is necessary for a good antenna, not sufficient, and an antenna with a mediocre −8 dB match may still be the better radiator. It is also the reason the two labs come as a pair: Lesson 10 establishes that power went in, and only Lesson 11 establishes that it came back out, and in which direction.

Everyone builds the same antenna, a dipole, and that is deliberate. The project is not an antenna design exercise — Lesson 7 already gave you the design, Lesson 8 let you model it, and Lessons 10 and 11 put it on the two instruments. Handing the whole class one known antenna means the pattern, the gain, and the impedance are all predictable before anyone measures anything, so the work of the project is the comparison rather than the build. It also means ten independent measurements of the same object, which makes disagreement between them worth talking about.

The table is the point of the project. Lesson 1 defined gain and beamwidth and Lesson 3 defined polarization, so the report quotes all three. Lesson 5 set the far-field boundary and Lesson 6 gave the integral that produces the pattern, so you know what the pattern should look like before you measure it. Lesson 7 solved the dipole in closed form and Lesson 8 modeled it in NEC, so you have two independent predictions to compare against. Today gives the range and the analyzer, and Lessons 10 and 11 are the dress rehearsal on both. Nothing in the course so far is left out of it.

The full requirements are in the project description (PDF).

The next two periods are hands-on and deliberately thin on theory — you will be standing at an instrument, not at the board. Everything you need to justify what you do there has been said today, so bring this lesson with you: the range length you check with a tape in Lesson 11 is the \(2D^2/\lambda\) above, and the reference plane you calibrate at in Lesson 10 is the one drawn on the cal-plane figure.