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Measurements & Instruments
Measurement map
| Quantity | Typical instrument / method | Main caveat |
|---|---|---|
| $S_{11},S_{21}$ | Vector network analyzer (VNA) | calibration plane, cables, fixtures |
| Spectrum / harmonics / spurs | Spectrum analyzer | RBW/VBW, detector, overload |
| EVM / constellation / demodulation | Vector signal analyzer (VSA) | reference model, equalization, phase noise |
| Time waveform / pulse | Oscilloscope | analog BW, sample rate, probe loading |
| RF power | Power meter / calibrated sensor | sensor range, mismatch, crest factor |
| Noise figure | Noise source + analyzer / Y-factor | ENR calibration, gain stability |
| Antenna gain/pattern | Anechoic range / near-field scanner | far-field criterion, chamber reflections |
| Electric field | calibrated isotropic probe / antenna / atomic sensor | perturbation, polarization, calibration |
| Magnetic field | Hall, fluxgate, search coil, OPM | bandwidth, offset, orientation |
| Optical transmission | photodiode + TIA | responsivity, linearity, bandwidth |
| Optical frequency | wavemeter / comb / reference spectroscopy | absolute calibration, drift |
1. Vector network analyzer
A VNA measures complex traveling-wave ratios. For a two-port device,
\[\begin{bmatrix}b_1\\b_2\end{bmatrix}= \begin{bmatrix}S_{11}&S_{12}\\S_{21}&S_{22}\end{bmatrix} \begin{bmatrix}a_1\\a_2\end{bmatrix}.\]Practical workflow
- Choose frequency span, IF bandwidth, power, averaging and number of points.
- Warm up cables and fixtures if precision matters.
- Calibrate at the desired reference plane: SOLT, TRL, ECal or another suitable method.
- Verify calibration with a known standard or thru.
- Measure the DUT without changing cable geometry unnecessarily.
- Save complex data, not just screenshots.
2. Spectrum analyzer
Use a spectrum analyzer for carrier power, harmonics, spurious emissions, occupied bandwidth, phase-noise-related skirts and interference searches.
Key settings:
- RBW: frequency selectivity and noise bandwidth;
- VBW: post-detection smoothing;
- reference level / attenuation: overload protection versus sensitivity;
- detector: peak, RMS, sample, quasi-peak depending on task;
- sweep time: tied to span and filters.
A narrower RBW reduces displayed noise power approximately with $10\log_{10}B$, but also slows measurement and may hide fast events.
3. Vector signal analysis and EVM
A VSA demodulates a known modulation format. Error vector magnitude is conceptually
\[\mathrm{EVM}_{RMS}= \sqrt{\frac{\sum_k|S_k-S_{k,ref}|^2}{\sum_k|S_{k,ref}|^2}}.\]EVM is a compact metric that can include amplifier nonlinearity, IQ imbalance, phase noise, frequency error, noise, compression and channel effects. Interpretation depends strongly on the equalization and reference definitions used.
4. Oscilloscope
An oscilloscope connects electromagnetic systems to time-domain behavior: pulses, envelopes, beat notes, transients, switching, detector signals and TIA outputs.
Useful rules:
- analog bandwidth should exceed the highest spectral content you want to preserve;
- sample rate should comfortably exceed Nyquist and support desired timing resolution;
- averaging improves uncorrelated noise but can erase nonstationary behavior;
- a 10× probe or active probe changes circuit loading differently than a 50 Ω input.
For a nominally Gaussian system, a rough rise-time relation is
\[t_r\approx\frac{0.35}{BW}.\]5. RF power measurement
Power meters are often more accurate than spectrum analyzers for absolute average power. Directional couplers allow forward/reflected measurements in high-power paths.
Mismatch uncertainty matters because source and sensor reflection coefficients interact. For pulsed/high-PAPR signals, ensure the sensor supports the waveform’s crest factor and bandwidth.
6. Noise figure
For the Y-factor method,
\[Y=\frac{P_{hot}}{P_{cold}},\]combined with the calibrated excess-noise ratio of the source. Noise-figure work is sensitive to source ENR calibration, connector loss, gain variation, image responses and analyzer noise floor.
7. Antenna patterns, gain and efficiency
Far-field range
A common criterion is
\[R_{FF}\gtrsim\frac{2D^2}{\lambda}.\]Measure amplitude and phase versus angle with a calibrated source/receive geometry.
Near-field scanning
Planar, cylindrical or spherical near-field measurements can be transformed computationally to the far field. This is invaluable when the required far-field distance is impractically large.
OTA systems
Modern wireless devices are often evaluated over the air because the antenna, enclosure, transceiver and beamforming algorithms behave as one coupled system.
8. EMC and compliance measurement
EMC measurements usually separate into:
- conducted emissions;
- radiated emissions;
- conducted immunity;
- radiated immunity;
- ESD / EFT / surge depending on product class;
- coexistence / desense / self-interference investigations.
Instrumentation can include LISNs, current probes, CDN/BCI fixtures, antennas, preamplifiers, spectrum/EMI receivers, RF power amplifiers, field probes and chambers.
A compliance result is not just a spectrum: detector type, bandwidth, distance, antenna factor, cable loss, preamplifier gain and chamber/site validation all matter.
9. Electric-field measurement
Possible methods include:
- calibrated dipole/monopole probes;
- isotropic E-field probes;
- electro-optic sensors;
- antenna-factor conversion;
- Rydberg-atom electrometry.
For an antenna-factor method,
\[E=AF\,V\]under the calibration convention used. Probe perturbation, polarization, near-field structure and spatial averaging can dominate uncertainty.
10. Magnetic-field measurement
- Hall sensor: DC to moderate-frequency local field, compact but offset/temperature sensitive.
- Fluxgate: precise low-frequency vector field.
- Search coil: AC magnetic field; induced voltage scales with $d\Phi/dt$.
- Optically pumped magnetometer: atomic Larmor/Zeeman response, potentially extremely sensitive.
- NMR probe: accurate field magnitude in suitable ranges/materials.
11. Optical readout for atomic systems
A common chain is
\[\text{atom-field interaction}\rightarrow \text{optical susceptibility}\rightarrow \text{transmission / phase / polarization}\rightarrow \text{photodetector}\rightarrow \text{TIA}\rightarrow \text{digitizer}.\]Measure and record:
- detector responsivity and transimpedance gain;
- 3-dB bandwidth;
- optical power and saturation margin;
- laser linewidth and frequency reference;
- beam waist and overlap;
- scan linearity;
- RF source calibration and cable loss;
- lock-in/reference phase if demodulating.
12. Calibration hierarchy
A strong experiment separates instrument calibration from physical-model calibration.
Examples:
- VNA calibration moves the electrical reference plane.
- Power-sensor calibration establishes absolute RF power.
- Antenna calibration establishes gain/antenna factor.
- Atomic AT splitting can provide field calibration through a known transition dipole.
- A photodetector transfer function converts current to measured voltage.
13. Measurement uncertainty
For independent input quantities $x_i$, first-order uncertainty propagation is
\[u_y^2\approx\sum_i\left(\frac{\partial y}{\partial x_i}\right)^2u_{x_i}^2.\]In practice, distinguish:
- random repeatability;
- calibration uncertainty;
- systematic bias;
- drift;
- model uncertainty;
- spatial variation;
- bandwidth / filtering uncertainty.
14. A reusable measurement checklist
Related pages
EMI/EMC · RF & Microwave · Antennas · Ground-State Magnetometry · Rydberg Semiclassical Optics · Theory ↔ Experiment