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Publication Number: FHWA-HRT-10-037
Date: October 2010

Step Frequency Ground Penetrating Radar Characterization and Federal Evaluation Tests

Appendix F: Step Frequency GPR (SF GPR) Transmission Loss Calculations Through a Typical Concrete Bridge Deck

The following report contains supporting documentation and results of the calculations performed for the research initiative in this report. Since it is an unpublished internal working paper, it would not be otherwise accessible as a reference to use for the current report. The report in this appendix has not been edited or changed in any way from its original form as a working paper that was submitted to the SPS of the Interdepartment Radio Advisory Committee (IRAC).

Note that the term Lossspreading, is the same as the later abbreviated version Lossspr found in this appendix. The terms are mathematically equivalent. The definition was inadvertently left out of the original paper. They are both defined as the spreading loss in decibels. Since the paper is being reproduced unchanged, clarification is being provided in this foreword.

Step Frequency GPR (SF GPR) Transmission Loss Calculations Through a Typical Concrete Bridge Deck

February 15, 2007

The NTIA Spectrum Planning Subcommittee (SPS) Coast Guard representative requested additional documentation regarding Step Frequency GPR Transmission losses through a concrete bridge deck. This request was made to address potential interference concerns that could arise when a vessel crosses under a bridge deck while an SF GPR is being used to evaluate the bridge deck.

The total losses are computed based on the assumption that radar energy is transmitted through a concrete bridge deck superstructure with an average thickness equal to 1 foot and at a position 1 meter or more below the bridge deck, which is provided for reasonable clearance of the vessel underneath the bridge deck. These assumptions are consistent with United States Coast Guard 2005 CFR Title 33, Volume 1, Subchapter J – Bridges.


The following equation for losses was used to account for both transmission/attenuation losses and spreading losses [Daniels]:

Losstotal = Losstransmission+attenuation + Lossspreading

where:Loss subscript trans equals 2 plus minus parenthesis 20 plus minus log subscript 10 parenthesis 4 Z subscript m Z subscript a over absolute value Z subscript m plus Z subscript a close absolute value close parenthesis close parenthesis plus Loss subscript attenuation

Za = Characteristic impedance of air = 377 W

Zm = Characteristic impedance of concrete = 160 W

Lossatt = Attenuation loss in concrete = 3 dB/ft at Freq<1000 MHz

Lossatt = Attenuation loss in concrete = 6 dB/ft at Freq³1000 MHz

Loss subscript spr equals 20 plus minus log subscript 10 parenthesis lambda over 4 square root R close parenthesis.

Lower case lamdba equals Wavelength

R = Radial distance from source

This equation for Losstotalwas used to compute losses corresponding to each range of frequencies used by the Step Frequency GPR system. Table 1 presents the results:

Freq (Hz) l Spreading Loss (dB) Total Loss (dB)
140000000 2.142857 -15.36433275 -21.36433275
178000000 1.685393 -17.45017208 -23.45017208
588000000 0.510204 -27.82931856 -33.82931856
1285000000 0.233463 -34.61983459 -43.61983459
1800000000 0.166667 -37.54722214 -46.54722214
1995000000 0.150376 -38.44063004 -47.44063004
2000000000 0.15 -38.46237195 -47.46237195
1202000000 0.249584 -34.03986139 -43.03986139
1585000000 0.189274 -36.44235737 -45.44235737

Table 1. Calculations for Losstotal at representative Step Frequency GPR operating frequencies. Representative frequencies are selected as center frequencies within operating ranges defined in Tables 2 and 3.

Tables 2 and 3 describe emissions of the Step Frequency GPR within its operating range and include calculations for losses due to the concrete bridge deck compared with back lobe emission levels (subtracted from bore sight emission levels).

Frequency (MHz) Peak EIRP (dBm) Average EIRP (dBm) Concrete bridge deck loss (dB) D (bore sight -back lobe) (dB)
<140 -60.7 -93.7 21 5.0
140 – 216 -25.7 -58.7 23 10.1
216 – 960 -23.2 -56.2 34 14.1
960 – 1610 -32.3 -65.3 44 16.6
1610 – 1990 -20.3 -53.3 47 12.4
1990 – 2000 -18.3 -51.3 47 14.7
>2000 -53.3 -86.3 48 14.7

Table 2. Maximum back lobe EIRP levels for both peak and average power (1MHz resolution BW).

Frequency (MHz) Average EIRP (dBm) in 1 kHz BW Concrete bridge deck loss (dB) D (bore sight -back lobe) (dB)
1164 – 1240 -75.3 43 11.7
1559 – 1610 -75.3 45 12.7

Table 3. Emissions suppressed in specified bandwidths.

Note that the fourth column of Table 1 corresponds to the third column of Tables 2 and 3. Also note that emissions are reduced more by concrete bridge deck losses than bore sight minus back lobe levels.


Daniels, D.J., Surface Penetrating Radar, IEEE, December 1, 1996, pp. 300.

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