Instrument documentation
Multi-channel electromagnetic field synthesis, visualization and analysis environment
The EM Field Instrument is a browser-based technical workstation for inspecting coherent sine-wave systems.
It combines a multi-channel signal generator, time-domain oscilloscope, normalized 3D electromagnetic field
engine, polarization selector, Poynting-vector flow visualization, spectrum analyzer, vector phasor analyzer, Lissajous state-space laboratory and audio monitor into one
interactive laboratory-style interface.
The tool is intended for technicians, engineers, lab users, educators and researchers who want to study how
frequency, phase, amplitude and harmonic relationships modify a resulting composite field.
1. Purpose of the instrument
The instrument is designed to make wave superposition visible and measurable. Each active channel represents
a coherent sinusoidal source. The active sources are summed into the resulting signal Σ and evaluated in
several synchronized views.
- Signal synthesis: define controlled sine components by frequency, phase and amplitude.
- Time-domain inspection: observe the resulting waveform and channel contributions.
- Spatial field interpretation: inspect a normalized plane-wave field model in 3D.
- Spectral inspection: identify dominant components, beat spacing and frequency ratios.
- Vector inspection: inspect active channel phasors, resultant magnitude and cancellation behavior.
- State-space inspection: visualize Lissajous / orbital trajectories derived from the active waveform.
- Auditory monitoring: listen to the same synthesized waveform without added effects.
2. Channel setup
The channel selector defines how many sources are active. The instrument supports one to six active channels.
Inactive channels are forced to zero contribution and are removed from the scope, audio model, 3D field model
and the shared analysis panel, including spectrum, phasor and Lissajous views.
- 1 CH: single-tone reference mode.
- 2 CH: interference, phase and beat experiments.
- 3 CH: useful for three-phase and 120° phase studies.
- 4–6 CH: harmonic stacks, complex modulation and multi-source comparison.
3. Frequency control
Frequency can be adjusted with the slider or entered directly as a numeric value. The valid range is 1 Hz to
20 kHz per channel. The upper range was selected so the synthesized waveform can still be used for audio
monitoring on normal computer audio hardware.
- Slider: fast exploratory adjustment.
- Numeric field: exact entry for known frequencies.
- Shared URL state: frequency values are stored in the browser URL for reproducible setups.
4. Phase control
Phase defines the angular offset of each channel relative to its own sine reference. Phase is expressed in
degrees from 0° to 360° and is internally converted to radians for calculation.
- 0°: reference alignment.
- 90°: quadrature relationship.
- 120° / 240°: typical three-phase separation.
- 180°: inverted component relative to a same-frequency reference.
5. Amplitude control
Amplitude is controlled with a precision stepper instead of a small slider. This gives stable handling when
small changes matter. The control supports 0.001 resolution and a range from 0.000 to 5.000.
- − / + buttons: coarse interactive adjustment.
- Numeric entry: direct precision value entry.
- 0.000: effectively removes the channel contribution while keeping the channel visible.
6. Digital scope · time-domain analyzer
The digital scope displays all active channels and the summed result Σ. It is the primary view for waveform
shape, phase interaction, constructive interference, destructive interference and beat patterns.
| Readout | Meaning | Interpretation |
|---|
| Vpp | Peak-to-peak value | Maximum minus minimum of the visible composite waveform. |
| RMS | Root-mean-square value | Effective magnitude of the visible waveform window. |
| Freq | Zero-crossing frequency estimate | Estimated from average zero-crossing intervals of Σ. |
| Period | Estimated period | Calculated from the detected frequency when valid. |
| Zero-X | Zero-crossing count | Number of sign transitions in the displayed time span. |
| Samples | Evaluated data points | Adaptive sample density used for the visible scope waveform. |
7. Time span and animation
The span control sets the visible time window of the digital scope. It also influences the 3D propagation
window so the spatial field view stays coupled to the same base timing concept.
- Short span: detailed inspection of fast oscillation and phase relation.
- Long span: beat patterns, modulation envelopes and low-frequency structure.
- RUN: starts 3D field evolution.
- Speed: controls the animation phase increment, not the physical frequency itself.
8. 3D field engine
The 3D view presents a normalized plane-wave model. The propagation axis is displayed in base-wavelength
units so the geometry remains readable even when the physical wavelength is extremely large at low frequency.
- E-field: synthesized electric-field trace.
- B-field · c: magnetic component scaled by c for comparable visual magnitude.
- Propagation axis: normalized spatial axis, displayed in λ₀ units.
- Camera: orbit, zoom and inspect the field without changing the signal model.
9. Polarization modes
The polarization control modifies the transverse field geometry used by the 3D engine. It is intended for
visual and conceptual comparison of linear, circular and elliptical field motion.
- Linear: one dominant transverse electric-field axis.
- Circular: equal quadrature component, producing rotating field geometry.
- Elliptic: reduced quadrature component, producing elliptical field motion.
- Orbital: replaces the conventional transverse field presentation with a signal-derived state-space trajectory based on E(t), quadrature state and normalized dE/dt.
10. Poynting-vector flow
The S-control enables a sparse energy-flow layer. The particles are not charge carriers. They are visual
indicators for directional energy transport according to the field relationship S = E × B.
- S ON: shows directional energy-flow indicators.
- S OFF: removes the flow markers for a cleaner field-only view.
- Purpose: helps connect field geometry with propagation direction.
11. Spectrum analyzer
The spectrum panel shows analytic bins derived directly from the configured sine components. It is not a
noisy sampled FFT display. When multiple active channels share the same frequency, their amplitudes are
vector-summed using phase information before display.
| Output | Meaning | Use case |
|---|
| Dominant | Largest frequency bin by amplitude | Quickly identifies the strongest configured spectral component. |
| Beat | Smallest spacing between active frequency bins | Useful for two-tone experiments and slow envelope behavior. |
| Ratio | Approximate frequency relationship | Useful for harmonic stacks and integer-ratio tuning. |
12. Vector Phasor Analyzer
The Vector Phasor Analyzer displays each active channel as a rotating vector. The vector angle is calculated from
θ = 2πft + φ, using the configured frequency, phase and amplitude of the channel. Same-frequency channels produce
a conventional static phasor relationship when RUN is stopped; different-frequency channels rotate at their own
angular rates during RUN mode.
| Readout | Meaning | Interpretation |
|---|
| Resultant | Vector sum magnitude Σ | Large values indicate constructive vector addition; small values indicate cancellation. |
| Phase | Angle of the resultant vector | Expressed relative to the analyzer's real-axis reference. |
| Cancel | Cancellation index | 0% means little cancellation; values approaching 100% indicate strong vector cancellation. |
A balanced three-phase setup with equal amplitudes and 0° / 120° / 240° phase spacing should pull the resultant
vector close to the center. Non-harmonic systems show continuously evolving vector relationships during RUN mode.
13. Orbital / Lissajous Polarization Laboratory
The Lissajous laboratory is a dedicated analytical view for signal-state geometry. It plots X = E(t) against a
quadrature state derived from the same active channel configuration. The trace therefore originates from the real
signal model rather than from decorative particles or arbitrary animation.
| Readout | Meaning | Interpretation |
|---|
| Width | Horizontal span of the orbit | Shows the visible X = E(t) excursion. |
| Height | Vertical span and rotation sense | Shows quadrature-state excursion and whether the trajectory is clockwise or counter-clockwise. |
| Area | Polygonal enclosed-area estimate | Useful for comparing ellipse size, cancellation collapse and harmonic closure. |
Integer frequency ratios such as 1:1, 1:2, 2:3 or 3:4 form closed or slowly repeating figures. Non-harmonic
ratios evolve without exact closure. Near cancellation collapses the orbit toward the center.
14. 3D Orbital POL mode vs. Lissajous analysis
Orbital POL mode changes the 3D field panel into a spatial state-space representation using E(t), quadrature
B-state and normalized dE/dt. The Lissajous analysis view is a compact 2D laboratory plot focused on measurable
trajectory width, height, area, closure and rotation behavior.
- Orbital POL: 3D state-space field presentation in the main field window.
- Lissajous view: 2D oscilloscope-style persistence display for analytical comparison.
- Both: derived from the active channel frequencies, phases and amplitudes.
15. Audio monitor
The audio monitor renders only the active user-defined sine components. No effects, filtering, reverberation,
compression or artificial background layers are added. This makes the monitor useful for direct auditory
inspection of the same signal model shown in the scope.
- Level: speaker-safe output scaling.
- Source: summed active channels Σ.
- Best use: beats, harmonic intervals, phase cancellation and audible modulation.
Use low monitor levels first, especially with headphones or lab amplifiers.
16. Shareable setups
The instrument writes operating parameters into the URL. This allows exact setups to be shared, archived or
reloaded later without a separate project file.
- Stored: channels, frequency, phase, amplitude, time span, audio level, polarization, S-state and selected analysis view.
- Useful for: reports, documentation, teaching examples and lab notebooks.
- Note: changing controls updates the URL automatically.
17. Showpiece Experiment Library
The Showpiece Experiment Library now acts as a guided laboratory layer, not only as a preset loader.
Each entry loads a complete operating state: active channel count, frequency, phase, amplitude, time span, polarization mode and analysis view. The cards also describe purpose, observation targets, difficulty, demonstration value and expected analyzer response.
- Purpose: accelerate training, demonstrations and laboratory discussion without random presets.
- Reproducibility: loading an experiment updates the same URL state as manual operation, so the resulting setup can be shared or archived.
- Analytical coupling: experiments are selected to show clear relationships across the scope, spectrum analyzer, vector phasor analyzer, Lissajous laboratory and 3D field view.
- Favorites: the star control stores preferred experiments locally in the browser using localStorage.
- Filters: category buttons reduce the list to fundamentals, three-phase, Lissajous, harmonics, orbital, engineering, showpieces or favorites.
- Expected response: every card indicates which panel should show the most important behavior before the experiment is loaded.
| Recommended entry | Primary relationship | Useful observation |
|---|
| Single Tone Reference | One active source | Baseline waveform, single spectrum bin and one clean phasor. |
| Balanced 3-Phase | 0° / 120° / 240° phase system | Symmetric vectors, rotating space-vector behavior and near-zero resultant. |
| Circular Polarization | Equal quadrature components | Rotating transverse field and circular state-space behavior. |
| Beat Frequency | Closely spaced tones | Envelope modulation, phasor drift and spectral spacing. |
| Harmonic Flower | Integer frequency ratios | Closed orbital structures generated only from active signal data. |
| Vector Cancellation | Anti-phase equal-frequency sources | Small resultant vector despite large individual channel vectors. |
The library does not inject decorative geometry. All observed structures are generated from the active sine components and their configured phase, amplitude and frequency relationships. For first-time demonstrations, start with Balanced 3-Phase, Circular Polarization, Beat Frequency and Harmonic Flower because these setups activate meaningful behavior across all major analysis views. Use the filter buttons when teaching a specific topic or preparing a short presentation sequence.
18. Technical assumptions and model boundary
The instrument uses a normalized analytical plane-wave representation. It is not a full electromagnetic field
solver and does not model antenna geometry, boundary conditions, conductive losses, material permeability,
dielectric dispersion, near-field coupling or calibrated RF power density.
- Good for: coherent wave relationships, phase studies, harmonic structure, polarization concepts and teaching demonstrations.
- Not intended for: certified RF exposure analysis, antenna design sign-off, EMC compliance, finite-element simulation or calibrated power measurement.
- Laboratory rule: validate absolute voltage, current, phase, field strength and power with calibrated measurement equipment.
Treat this instrument as an analytical companion to real measurements. It is excellent for understanding
relationships, but real hardware behavior still depends on probes, grounding, bandwidth, parasitics,
coupling paths, sensor response and instrument calibration.
19. Example experiments
| Experiment | Suggested setup | What to observe |
|---|
| Single tone reference | 1 CH, 60 Hz, 0°, A = 1.000 | Clean sine wave, single spectral bin and stable 3D field geometry. |
| Phase cancellation | 2 CH, same frequency, phases 0° and 180° | Amplitude reduction or cancellation depending on equal amplitudes. |
| Beat frequency | 2 CH, 440 Hz and 444 Hz | Slow envelope in time domain and 4 Hz spacing in the spectrum readout. |
| Three-phase system | 3 CH, 50 Hz, phases 0° / 120° / 240° | Symmetric phase structure, near-zero phasor resultant and cancellation behavior. |
| Harmonic stack | 3–6 CH, integer multiples of F0 | Composite waveform shape, base-frequency readout and ratio display. |
| Circular polarization | Use polarization selector: Circular | Rotating transverse field geometry in the 3D panel. |
20. Advanced measurement panel
The advanced measurement panel adds compact electrical readouts for the summed waveform Σ. The values are
calculated from the same sampled scope signal and analytic spectrum bins used by the instrument, so the panel
remains synchronized with the visible time-domain and frequency-domain views.
| Readout | Meaning | Use case |
|---|
| Crest | Peak absolute value divided by RMS | Detects peaky or impulse-like composite waveform behavior. |
| Form | RMS divided by average rectified value | Shows how close the waveform is to an ideal sine reference. |
| Avg Rect | Mean of absolute Σ value | Useful for rectifier and envelope interpretation. |
| Mean | Arithmetic average of Σ over the visible scope window | Indicates DC offset or incomplete-cycle bias in the selected span. |
| THD | Harmonic-bin estimate relative to the lowest active bin | Useful for harmonic stacks; non-harmonic components are not counted as harmonic distortion. |
| Class | Signal classification | Identifies single tone, harmonic mix, non-harmonic mix or near cancellation. |
The phase table reports each active channel relative to CH1. For channels with a different frequency, the
displayed angle is an initial phase offset φ0 rather than a fixed phase relationship over time.
21. Revision notes
- V10: audio monitor added for direct waveform sonification.
- V11: keyboard frequency entry and 20 kHz frequency range added.
- V12: precision amplitude steppers replaced small amplitude sliders.
- V13: channel-count selector extended the instrument up to six channels.
- Phase 2: spectrum / harmonic analyzer added.
- Phase 3: polarization selector and Poynting-vector flow visualization added.
- V14: dedicated technical manual page added via the header help control.
- Phase 4: advanced measurement panel added for crest factor, form factor, average rectified value, DC offset, THD estimate, phase table and signal classification.
- Phase 4.1: adaptive 3D sampling added. Static and animated field views now raise point density only when visible cycles require it, with hard caps to protect browser performance.
- Phase 5: technical help system and laboratory documentation expanded for professional operation.
- Phase 6: Vector Phasor Analyzer and Orbital / Lissajous Laboratory added for synchronized vector and state-space analysis.
- Phase 7: Showpiece Experiment Library added with reproducible reference configurations, signature demonstrations, favorites and URL-shareable experiment states.
- Phase 7.5: EXP upgraded into a guided experiment laboratory with filters, difficulty labels, demonstration score, purpose text and expected analyzer response.
- Maintenance: analysis-panel resize handling and documentation wording refined for the combined Spectrum / Phasor / Lissajous view.