Simultaneous Specific Absorption Rate Ratio Summation and Peak Location Separation

Probe

An automated robot lowers an isotropic E-field sensor into a head or body phantom filled with tissue-equivalent liquid while two radios transmit at maximum rated output. Spatial SAR distributions measured across the grid reveal local energy absorption peaks generated by each individual radiating element. When a portable device contains co-located transmitters operating simultaneously, evaluating RF exposure demands isolating the spatial location of maximum SAR for each radio band.

Test software maps these absolute three-dimensional coordinates inside the phantom shell, identifying peak Cartesian positions (x1, y1, z1) and (x2, y2, z2) down to sub-millimeter precision.

Dual-transmitter configurations introduce overlapping field distributions that alter local absorption maxima. Measuring these fields relies on scan resolutions tight enough to prevent artificial smoothing of adjacent peaks. Area scans locate broader energy regions, while fine-grid zoom scans extract exact spatial peak coordinates and local SAR values normalized to peak tune-up tolerance thresholds.

Peak separation calculation requires three-dimensional coordinate accuracy derived directly from uncompressed area scan zoom grids.

When multi-radio systems operate concurrently, radio frequency exposure evaluation follows strict spatial resolution steps in the laboratory chamber:

• Coordinate Shift occurs when host enclosure flexing or improper phantom mounting skews the absolute zero point between consecutive transmitter scans.
• Grid Coarseness masks secondary energy peaks when spatial step sizes exceed five millimeters during high-frequency zoom scans above three gigahertz.
• Liquid Volumetric Evaporative Drift alters the dielectric properties of tissue-simulating fluid over extended multi-band measurement sequences, creating false SAR amplitude reductions.
• Sensor Boundary Distortion occurs when probe tips approach within two millimeters of the curved phantom surface, introducing capacitive coupling errors in spatial peak identification.

Ignoring sensor displacement or peak misidentification during initial scanning forces invalid spatial calculation parameters into downstream compliance files. A miscalculated baseline spatial peak invalidates the entire multi-transmitter evaluation package, triggering mandatory complete re-scans of every simultaneous transmission mode at full commercial lab rates.

Arithmetic

Regulatory frameworks published under FCC KDB 447498 D01 and ISED RSS-102 SPR-001 establish specific conditions where individual transmitter SAR values may be summed directly to prove compliance. When the simple sum of 1g SAR values across concurrent transmitters remains at or below 1.6 W/kg (or 4.0 W/kg for 10g extremity exposure), further spatial analysis is unnecessary. When this arithmetic summation exceeds the regulatory exposure threshold, the simultaneous transmission peak location separation ratio provides a mathematical pathway to evaluate compliance without immediate physical volume scan testing.

The simultaneous transmission peak location separation ratio formula evaluates the spatial decay of electromagnetic field superposition between two transmitter peaks:

SPLSR = frac(SAR1 + SAR2)1.5d

Here, SAR1 and SAR2 represent the standalone 1g SAR values in W/kg, adjusted for maximum production tune-up tolerance. The variable d represents the three-dimensional separation distance between the peak SAR locations in centimeters, calculated directly from the spatial coordinates:

d = sqrt(x1 – x2)2 + (y1 – y2)2 + (z1 – z2)2

Compliance is established if the calculated ratio is less than or equal to 0.04 for 1g SAR evaluation, or less than or equal to 0.10 for 10g extremity SAR evaluation. Crossing these numerical boundaries changes testing obligations fundamentally.

Spatial decay ratios prevent redundant volumetric testing when antenna separation distances compensate for high cumulative energy absorption.

Sequential Steps for Simultaneous SAR Ratio Summation and Peak Location Evaluation

1. Determine all active simultaneous transmission configurations applicable to the operational modes of the host device.
2. Extract peak 1g or 10g SAR values for each standalone radio transmitter from primary laboratory test reports, applying maximum tune-up power scaling factors.
3. Sum the scaled standalone SAR values for each concurrent transmitter pair; if the cumulative sum is less than or equal to 1.6 W/kg for 1g SAR, record compliance and stop analysis.
4. Extract the absolute Cartesian coordinates (x, y, z) corresponding to the highest spatial SAR peak for each radio in the pair when the cumulative sum exceeds 1.6 W/kg.
5. Calculate the straight-line three-dimensional separation distance d in centimeters between peak coordinate sets.
6. Compute the spatial decay fraction using the peak location formula.
7. Verify whether the resulting ratio satisfies the compliance threshold of 0.04 or less for body exposure.

Consider a compact handheld diagnostic terminal containing a cellular 5G mid-band radio, a 6 GHz Wi-Fi transceiver, and a short-range Bluetooth module. Testing yields maximum standalone 1g SAR figures scaled to tune-up limits under specific test positions on the flat phantom.

Evaluating the simultaneous combination of Cellular Band n78 and 6 GHz Wi-Fi demonstrates the operational procedure. Summing individual standalone ratios yields 0.98 W/kg plus 0.74 W/kg, totaling 1.72 W/kg. The value exceeds the 1.6 W/kg standard threshold, making peak location separation analysis mandatory.

Calculating distance d between Cellular (x1 = -12.4, y1 = 45.2, z1 = -175.1) and Wi-Fi (x2 = 38.6, y2 = -62.1, z2 = -172.8):

d = sqrt(38.6 – (-12.4))2 + (-62.1 – 45.2)2 + (-172.8 – (-175.1))2 mm

d = sqrt(51.0)2 + (-107.3)2 + (2.3)2 = sqrt2601 + 11513.29 + 5.29 = sqrt14119.58 = 118.83 mm = 11.883 cm

Applying the ratio formula with distance expressed in centimeters:

SPLSR = frac(0.98 + 0.74)1.511.883 = frac(1.72)1.511.883 = frac2.25611.883 = 0.190

The result of 0.190 exceeds the 0.04 maximum threshold substantially. Calculating spatial decay shows that antenna separation alone fails to mitigate the overlapping exposure field, so the filing cannot move forward under basic analytical separation rules.

Antenna separation distance dictates ratio decay far more rapidly than incremental reductions in transmitter output power.

Chamber

When peak location separation ratios exceed regulatory limits, laboratory testing must transition to full volumetric SAR summation scans. Volumetric SAR summation combines two complete three-dimensional spatial SAR distributions measured independently across identical phantom geometries. Measurement software overlays the two volumetric data matrices point-by-point, performing spatial interpolation to construct a composite multi-transmitter SAR field.

Volumetric measurements demand precise mechanical repeatability. Re-positioning the device under test between test passes introduces spatial alignment errors. Automated SAR measurement systems utilize high-resolution optical aligners and rigid phantom fixtures to hold positional drift below 0.2 millimeters across multi-hour measurement matrix operations.

Volumetric scan overlays generate complex three-dimensional energy fields that reveal constructive spatial accumulation impossible to predict through simple point peak analysis alone. High-density arrays of localized hotspots merge into broad absorption regions, shifting peak location coordinates entirely.

Volumetric SAR reconstruction is mandated standard procedure whenever spatial separation ratios exceed regulatory boundaries.

Chamber duration escalates rapidly when full volumetric summation scans enter the test plan. A standalone SAR measurement cycle takes approximately fifteen to thirty minutes per channel and configuration. Volumetric scans demand extended fine-mesh grid distributions spanning the full physical footprint of both radiating antennas, extending scan times to over two hours per simultaneous mode.

Simultaneous transmission evaluation is sometimes treated as requiring only numerical software post-processing of existing data files, though failing threshold metrics necessitates additional chamber setup time and physical measurements.

Docket

Submitting simultaneous SAR test documentation to Telecommunication Certification Bodies demands precise structure in compliance reports. Regulatory bodies evaluate multi-radio exposure data through specialized review channels. Under FCC administration, specific simultaneous transmission configurations trigger Pre-Approval Guidance submission procedures before a certification body can grant market access.

ISED Canada enforces parallel documentation structures under RSS-102 SPR-001. Filings must incorporate explicit spatial separation map attachments, matrix table breakdowns for every concurrent mode, and full probe calibration trace files that cover the active operating frequency bands.

When Does an Antenna Shift Require PAG Submission?

Physical altering of internal component layouts shifts radio frequency exposure profiles. Modifying antenna placements during host integration triggers regulatory review thresholds depending on layout tolerances:

• Spatial Drift Exceeding Five Millimeters invalidates original baseline coordinate tables, demanding fresh standalone and simultaneous SAR assessments.
• Permissive Change Class II Filings incorporating new modular radio combinations must recalculate every ratio matrix using current tune-up tolerances.
• Enclosure Material Alterations near radiating structures alter near-field antenna loading, shifting localized peak SAR coordinates inside the tissue phantom.
• Co-located Transmitters Operating Above Six Gigahertz introduce power density evaluation overlaps under FCC KDB 987594, forcing mandatory pre-approval submission pathways.

Telecommunication Certification Bodies review multi-radio exposure packages using systematic checklist steps to ensure data integrity:

Missing coordinate data for any localized peak forces an immediate administrative hold on the certification dossier. Reviewing engineers verify that standalone SAR values used in summation matrices match the highest scaled values recorded across individual equipment test reports.

Under FCC KDB publication 447498 D01 clause 6.2, simultaneous transmission evaluation documentation must list every active combination and its corresponding ratio, rejecting filings that present incomplete operational mode matrices.

Budget

Failure to model simultaneous SAR separation metrics during early physical layout planning costs tens of thousands of dollars in commercial test chamber fees and weeks of lost market access. Standalone SAR testing for a modern multi-band device averages $12,000 to $20,000 across standard frequency bands. When mathematical peak separation ratios fail to satisfy regulatory thresholds, adding volumetric SAR summation scans increases lab fees by $8,000 to $15,000 per mode while adding three to five days of continuous chamber occupancy.

Schedule delays represent the primary commercial exposure. A product held in pre-approval guidance review due to invalid peak separation calculations sits in certification queues for four to eight weeks. Early antenna placement modeling costs a fraction of a single re-test cycle, establishing clear physical isolation boundaries before board layouts freeze and tooling molds open.

Engineering teams that integrate multi-radio modules must evaluate physical separation distances alongside standalone RF performance metrics before finalizing host product geometries.