Any analyzer can draw a spectrum. The one you trust is the one that can prove the distortion on its screen came from your device and not from its own front end.
Noise floor and sweep speed sell instruments. Distortion measurements are where instruments earn trust. When you report that a power amplifier's second harmonic sits at −54 dBc, someone downstream acts on that number: a systems engineer signs off an emissions budget, a production line ships a unit, a regulator closes a file. The measurement had better be right.
It is also the measurement most likely to be subtly wrong, because the analyzer contains the same physics as the device it is testing. The first mixer in any spectrum analyzer is a deliberately nonlinear component being driven by your signal. Feed it a strong fundamental and it will manufacture harmonics of its own, indistinguishable on screen from the ones your device actually produced. A distortion measurement is therefore two problems in one: measuring the device, and proving the instrument is not contaminating the answer.
This chapter works through both, then adds a third capability that shares the same hardware: the tracking generator, which turns a spectrum analyzer from a passive listener into a stimulus-response instrument that can sweep filters, cables, and amplifiers. By the end you will know where harmonics come from, how to measure them in dBc without fooling yourself, why frequency range matters more for harmonic work than for anything else in this book, and what scalar network analysis can and cannot do compared with a vector network analyzer.
Every real component is slightly nonlinear. Model its transfer function as a power series:
The $a_1$ term is the linear gain you designed for. The higher-order terms are the ones that generate distortion. Drive the device with a clean sine wave, $v_{in} = V\cos(\omega_0 t)$, and the squared term expands to
A DC offset plus a brand-new tone at exactly twice the input frequency: the second harmonic. The cubed term expands the same way and produces a component at $3\omega_0$ (the third harmonic) plus a term at $\omega_0$ that subtracts from the fundamental, which is where gain compression comes from. The pattern generalizes. The nth-order term of the series generates the nth harmonic, a tone at exactly $n \cdot f_0$.
Where does the nonlinearity live in practice? Amplifiers running near compression are the classic source. Mixers are nonlinear by design; that is how they mix. Oscillators and frequency multipliers produce harmonic ladders as a side effect of how they work. Saturating output stages, overdriven ADC front ends, and magnetic components all contribute. Even a corroded or loose connector can act as a crude diode and generate measurable harmonics from a clean signal passing through it, which is why harmonic and intermodulation checks are a standard diagnostic for aging cable plants and antenna systems.
Look at the amplitude dependence in those expansions. The second harmonic is proportional to $V^2$, so when the fundamental rises 1 dB, the second harmonic rises 2 dB. The third harmonic is proportional to $V^3$ and rises 3 dB for every 1 dB of fundamental. These slopes, 2 dB/dB for second order and 3 dB/dB for third order, are the fingerprint of nonlinear distortion and the foundation of the intercept-point concept.
Extrapolate the fundamental (slope 1) and a harmonic (slope 2 or 3) on a dB-versus-dB plot and the lines eventually cross. The crossing is a fiction, since real devices compress long before reaching it, but the extrapolated intercept is a compact, drive-level-independent way to specify linearity. The second harmonic intercept (SHI) characterizes second-order behavior; the third-order intercept (TOI or IP3) characterizes third-order behavior. One number per mechanism, valid across the device's linear operating range. Hold that thought: in Section 8.4 the same math describes the analyzer itself.
The standard way to express a harmonic is dBc, decibels relative to the carrier:
A fundamental at +10 dBm with a second harmonic at −44 dBm gives a second harmonic of −54 dBc. The measurement procedure is marker arithmetic. Put a marker on the fundamental at $f_0$, put a delta marker on $2f_0$, and read the difference directly. Repeat at $3f_0$, $4f_0$, and as far up as your specification requires. Modern analyzers automate the walk, but it is worth doing manually at least once so you know what the automation is doing.
Two practical settings matter. First, resolution bandwidth. Harmonics of a CW signal are themselves CW tones, so narrowing the RBW lowers the displayed noise floor without changing the tone amplitudes at all, exactly the RBW behavior Chapter 5 derived from the FFT bin width. Narrow RBW is how you dig a −70 dBc harmonic out of the noise; the cost is sweep or acquisition time. Second, reference level. Keep the fundamental near the top of the screen but comfortably below the analyzer's compression point, for reasons the next section makes painful.
Audio and power engineers often summarize distortion as total harmonic distortion:
expressed as a percentage or in dB. THD is a fine pass/fail number, but it throws away the most diagnostic information a spectrum analyzer gives you: which harmonic dominates. A distortion signature dominated by the second harmonic points at an asymmetric transfer function, a bias-point error, or a single-ended stage. A signature dominated by the third harmonic points at symmetric compression, the kind a well-balanced push-pull stage or a saturating amplifier produces. Two devices with identical THD can have entirely different problems. Measure each harmonic individually in dBc; compute THD afterward if a specification demands it.
Here is the constraint that catches more people than any other. To measure the nth harmonic of $f_0$, the analyzer must tune to $n \cdot f_0$. There is no workaround. A device operating at 10 GHz puts its second harmonic at 20 GHz and its third at 30 GHz. A Ku-band transmitter at 13.5 GHz puts its third harmonic at 40.5 GHz. The rule of thumb is that harmonic work needs an analyzer with 2 to 3 times the reach of the device under test, which means a 20 GHz analyzer, generous as it sounds, cannot finish third-harmonic verification on anything above about 6.7 GHz.
| Device operating frequency | 2nd harmonic | 3rd harmonic | Analyzer reach needed (through 3rd) |
|---|---|---|---|
| 2.4 GHz (ISM) | 4.8 GHz | 7.2 GHz | 7.2 GHz |
| 5.8 GHz (ISM) | 11.6 GHz | 17.4 GHz | 17.4 GHz |
| 10 GHz (X-band) | 20 GHz | 30 GHz | 30 GHz |
| 13.5 GHz (Ku-band) | 27 GHz | 40.5 GHz | 40.5 GHz |
| 15 GHz (Ku-band) | 30 GHz | 45 GHz | 45 GHz |
This is where a 40 GHz instrument earns its keep. X-band and Ku-band harmonic verification is routine work in satellite communications, radar, and point-to-point links, and it is simply out of reach for the mid-range analyzers that stop at 7.5, 13.6, or 20 GHz. The measurement itself is not exotic. The frequency range is the whole game.
Compact RTSAs such as the BNC ICX family reach 40 GHz with 100 MHz of gap-free bandwidth, which covers second-harmonic work on anything up to 20 GHz and third-harmonic work through Ku-band. The manufacturer's analysis software includes a dedicated harmonic-analysis mode that parks measurement markers on $n \cdot f_0$ automatically and tabulates each harmonic in dBc, per the published datasheet. The frequency-range rule still applies; the point of a 40 GHz compact instrument is that the rule stops being the bottleneck.
Now the uncomfortable part. The analyzer's first mixer, driven hard by your fundamental, generates its own second harmonic through exactly the $a_2 v^2$ mechanism of Section 8.2. That internally generated tone lands at $2f_0$, precisely on top of the harmonic you are trying to measure. The screen shows the sum, and nothing on the screen tells you which part is real.
Manufacturers specify this self-distortion through the second harmonic intercept. The internally generated second harmonic, relative to the fundamental, is
where mixer level is the power actually reaching the first mixer: input power minus input attenuation. Work an example with numbers published for entry-class bench analyzers: an SHI of +45 dBm at a mixer level of −20 dBm gives an internal second harmonic of −(45 − (−20)) = −65 dBc. Published figures for portable analyzers in this class run from −50 to −80 dBc depending on band. The consequence is blunt. On an analyzer generating −65 dBc internally, a device harmonic specified at −70 dBc is unmeasurable at that mixer level; the analyzer's own distortion floor sits above the thing you are trying to see.
There is a beautifully simple test for contamination, and it should be a reflex. Add 10 dB of input attenuation. The analyzer corrects its reference level automatically, so the displayed fundamental does not move. A true device harmonic does not move either; it is just a signal, attenuated and re-corrected like the fundamental. But the analyzer's internal contribution depends on mixer level, which just dropped 10 dB, so the internal second harmonic drops 10 dB relative to the fundamental. If the displayed harmonic falls when you add attenuation, the analyzer was generating part of it. Keep adding attenuation until the reading stops changing. When two consecutive attenuator steps give the same dBc value, you are reading the device.
Attenuation is not free. Every dB of input attenuation raises the displayed noise floor by 1 dB, while lowering the internal second-order distortion, in relative terms, by 1 dB. Distortion falls as the mixer level drops; noise rises. Somewhere between them is an optimum mixer level where internal distortion products equal the noise floor, and that crossing point is the analyzer's maximum distortion measurement range. Run the mixer hotter and distortion limits you; run it colder and noise does. Good harmonic technique is mostly the art of sitting at that optimum, and the 10 dB check is how you confirm you are on the safe side of it.
One more trap deserves a sentence: overload you cannot see. The mixer responds to the total power at its port, including signals far outside the displayed span. A strong out-of-span carrier, an FM broadcast tower next to your test bench, or the device's own fundamental while you zoom in on the harmonic can push the mixer into distortion while the screen looks innocent. When a harmonic measurement misbehaves, check the total input power, not just the tones you happen to be displaying.
Two hardware assists are worth knowing. A high-pass filter between the device and the analyzer, cutting off above $f_0$ but below $2f_0$, strips the strong fundamental before it reaches the mixer, so the mixer never sees enough power to distort. Preselected analyzers build a tunable version of this into the front end, and high-end lab instruments offer dedicated filter options for exactly this measurement. Either way the principle is identical: the best way to keep the mixer honest is to never show it the fundamental at full strength.
All of these instrument contributions, self-distortion, noise floor, attenuator accuracy, and reference-level correction, belong in the measurement's uncertainty budget. Chapter 12 builds that budget formally; this section is the reason distortion terms appear in it.
Everything so far treats the analyzer as a listener. A tracking generator (TG) makes it talk. A TG is a signal source phase-locked to the analyzer's sweep: at every instant it outputs a sine wave at exactly the frequency the analyzer is currently tuned to. Connect the TG output through a device under test and back into the analyzer input, and the trace on screen is the device's magnitude response versus frequency. That is scalar network analysis, and it turns one instrument into a filter tuner, a cable tester, and an amplifier flatness rig.
The classic measurements:
Raw TG measurements include everything in the path: the TG's own output flatness ripple, the test cables, the adapters. Normalization removes them. Connect the TG directly to the analyzer input through the same cables you will use for the measurement, store that trace as a reference, then have the analyzer subtract it from every subsequent sweep. The stored through-line becomes the 0 dB line. Insert the device, and what you see is the device alone. Normalization is the scalar world's substitute for VNA calibration: it corrects frequency-response error well, but it does not correct mismatch error, a distinction Section 8.6 returns to.
A worked filter flow makes it concrete. Normalize the through path. Insert a bandpass filter. Set the TG output to 0 dBm and pick an RBW that puts the displayed noise floor at, say, −90 dBm; the measurable dynamic range is then about 90 dB, which is what bounds how much stopband rejection you can actually verify. Read the corners, the ripple, and the rejection. For an amplifier, reverse one instinct: pad the TG output down (published TG output ranges run −20 to 0 dBm) so the amplifier stays well out of compression, or the "gain" you measure will be the compressed value, complete with freshly minted harmonics from Section 8.2.
A real-time analyzer adds one twist to this classic workflow. Because the RTSA front end digitizes a wide block at once, a swept TG measurement can run alongside the analyzer's other duties, and the gap-free capture means a drifting or intermittent device shows up as trace instability rather than as a mystery. Tuning a filter against a live, continuously updating trace is also simply pleasant: turn the tuning screw, watch the corner move, no waiting for a slow sweep to catch up.
The manufacturer of the latest generation of compact RTSAs publishes tracking generator options with −20 to 0 dBm output adjustable in 0.25 dB steps, ±2 dB level accuracy, and 10 Hz frequency resolution, and notes that the TG doubles as an independent CW source when the analyzer is doing something else. Those figures are the vendor's published specifications, not independent measurements, but they are representative of the class.
A tracking generator does not make a spectrum analyzer into a vector network analyzer, and it is worth being precise about the gap.
| Scalar (analyzer + TG) | Vector network analyzer | |
|---|---|---|
| Measures | Magnitude only | Magnitude and phase |
| Group delay | No | Yes |
| Complex impedance / Smith chart | No | Yes |
| Error correction | Normalization (frequency response only) | Full vector calibration (frequency response, directivity, source match, load match) |
| Mismatch ripple | Remains in the data | Corrected out |
| Typical accuracy | ±1 to 2 dB class | ±0.1 dB class after calibration |
| Setup effort | Connect and normalize, under a minute | Calibration kit or ecal, per-setup procedure |
| Cost | Included or a modest option on the analyzer | A second instrument, often costing more than the analyzer |
The honest summary: if the question involves phase, group delay, impedance matching, or fractions of a dB, you need a VNA. If the question is "where are this filter's corners, is this cable within loss spec, is this amplifier's gain flat across the band," scalar analysis answers it faster, cheaper, and with less operator ceremony. Filter production tuning, cable acceptance testing, and pass/fail line checks have run on scalar setups for fifty years for a reason. Choose by the question, not by the prestige of the instrument.
Tracking generators have historically been a low-frequency courtesy feature. The mainstream instruments make the pattern clear:
| Instrument class | Published TG ceiling |
|---|---|
| Rigol DSA832E-TG | 3.2 GHz |
| R&S FPC1500 (integrated TG) | 1 to 3 GHz |
| Siglent SSA3000X / X Plus family | 1.5 to 7.5 GHz depending on model |
| Keysight N9322C (stimulus/response) | 7 GHz |
| Latest-generation compact RTSAs (published options) | 4.5, 6, and 9 GHz |
| Keysight FieldFox with tracking options | 26.5 to 54 GHz, in a different price class |
| Big-iron lab analyzers (PXA, FSW class) | Typically none; external generator or VNA instead |
Above roughly 10 GHz, tracking capability almost disappears from the market. The FieldFox family is the notable exception, and it lives at a price point closer to a VNA than to a portable spectrum analyzer. Big lab analyzers skip the feature entirely on the theory that anyone who owns one also owns a signal generator or a VNA.
Against that backdrop, one claim deserves mention with its flag attached. The manufacturer behind the newest 40 GHz compact RTSA platforms has stated that a 40 GHz tracking generator option is coming to its newest platform, and describes it as unmatched in the market. As of this writing, that claim does not appear in any published specification (the same manufacturer's published TG options stop at 9 GHz), and it has not been verified on a bench unit. Treat it as a manufacturer's claim, not an established fact. If it holds, it is genuinely unusual: a tracking generator above 10 GHz is rare, and one anywhere near 40 GHz would put scalar filter tuning and gain sweeps across K-band and Ka-band into an instrument class that has never had them. That is the appropriate framing. Not "the only one on the market," a phrase that ages badly, but "unusual enough to verify, and significant if true."
A field team is commissioning a 12 GHz power amplifier feeding a Ku-band uplink. The compliance file requires the second harmonic at 24 GHz and the third at 36 GHz, both against a −50 dBc limit. Both harmonics land inside a 40 GHz analyzer's range, so the team measures them directly at the PA output through a calibrated coupler: second harmonic −54 dBc, third −61 dBc. Before writing either number down, the engineer runs the Section 8.4 reflex, stepping in 10 dB more input attenuation. Both readings hold within 0.5 dB, so the distortion is the amplifier's, not the analyzer's, and the numbers go in the file.
Same visit, second job: the 1.2 GHz IF bandpass filter ahead of the upconverter has drifted. The team switches to the tracking generator, normalizes through the test cables, inserts the filter, and retunes it against the live trace until the passband is centered with 0.8 dB of ripple and the corners sit where the link budget expects them. Ten years ago this visit needed a microwave spectrum analyzer and a separate network analysis setup. Here it needed one box and a directional coupler.
The Chapter 8 questions are an interactive quiz. Pick an answer for each, get instant scoring, and see why each answer is right. Your progress is saved on this device.
Take the interactive quiz →Chapter 9 leaves the vendor's software entirely and opens the instrument to the open-source SDR ecosystem: SDR++ as a universal receiver front end, GNU Radio flowgraphs for custom signal processing, SoapySDR as the hardware abstraction layer, and what a programmable RTSA looks like when the analysis chain is yours to build. If you have ever wanted to write your own demodulator and point it at 100 MHz of live spectrum, that chapter is for you.