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I was thinking about the recent discussions on what K band sensitivity to run in Advanced mode and the post by BRD/Vortex about the impact of each setting on detector sensitivity, and thought I would crunch the numbers myself. Not sure if anyone has bothered working this out before, a quick search didn't turn up anything.
Stop now if you don't care about the math, the moral of the story is the % sensitivity settings correlate with the expected difference in detection range.
Looking at an equation for radar detector range, we see that the maximum range of a radar detector is inversely proportional to the square root of the detector sensitivity.
For example, see: copradar.com: Radar Range Equation
Where the relative sensitivities must first be converted from the logarithmic decibel scale (yielding the relative sensitivities below), and taking the square root of this gives the relative detection range:
Thus the Advanced setting percentages actually correlate well with the calculated difference in ideal detection range assuming all other factors are equal. One interesting thing to note is that City mode (-15 dB) is the equivalent of an Advanced Mode setting of about 18% (e.g. 18% of the ideal range in Highway mode).
Stop now if you don't care about the math, the moral of the story is the % sensitivity settings correlate with the expected difference in detection range.
At first glance the sensitivity adjustments in Advanced seem somewhat arbitrary, differing by 1 dB as you start to decrease from 100%, and increasing to a 2.5 dB difference at the end. I knew the dB scale was logarithmic, but these numbers seemed rounded off enough that I wanted to calculate what the exact difference in expected detection range would be at each setting.
Looking at an equation for radar detector range, we see that the maximum range of a radar detector is inversely proportional to the square root of the detector sensitivity.
For example, see: copradar.com: Radar Range Equation
Thus if everything else is constant (radar power, frequency, antenna gain), the difference in expected range between two sensitivity settings can be calculated by:Radar Detector Range
Radar has a range loss inversely proportional to range to the 4th power (1/R[SUP]4[/SUP]). Radio communications range losses are inversely proportional to range squared (one-way path is 1/R[SUP]2[/SUP]). Signal power received (by a radar detector), where G[SIZE=-1]det[/SIZE] is detector antenna gain, can be expressed as shown below. By substituting radar detector minimum signal for power received, detector maximum range can be estimated if radar power and antenna gain are known (ERP -- effective radiated power).
P[SUB]det[/SUB] = Power Received by Detector
G[SUB]det[/SUB] = Detector Antenna GainRadar propagation loss is proportional to 1/R[SUP]4[/SUP] (2-way signal path), while a radar detector would be picking up the signal on the direct (1-way) path with loss proportional to 1/R[SUP]2[/SUP] (a hugh advantage for the detector). Another hugh advantage is the radar is receiving a reflection (RCS), most of the reflective energy is directed away from the radar. The radar has the advantage of a much larger antenna (more gain) and more sensitive (to radar signal) receiver. However, good radar detector should be able to detect a radar before the radar detects the vehicle, but not always.
R/R[SUB]0[/SUB] = sqrt(S[SUB]0[/SUB]/S)
Where the relative sensitivities must first be converted from the logarithmic decibel scale (yielding the relative sensitivities below), and taking the square root of this gives the relative detection range:
| K band sensitivity | dB change (logarithmic) | Relative Sensitivity (S/S[SUB]0[/SUB]) | Relative Detection Range (R/R[SUB]0[/SUB]) |
| 100% | 0 | 100.00% | 100.00% |
| 90% | -1 | 79.43% | 89.13% |
| 80% | -2 | 63.10% | 79.43% |
| 70% | -3 | 50.12% | 70.79% |
| 60% | -4.5 | 35.48% | 59.57% |
| 50% | -6 | 25.12% | 50.12% |
| 40% | -8 | 15.85% | 39.81% |
| 30% | -10.5 | 8.91% | 29.85% |
| City | -15 | 3.16% | 17.78% |
Thus the Advanced setting percentages actually correlate well with the calculated difference in ideal detection range assuming all other factors are equal. One interesting thing to note is that City mode (-15 dB) is the equivalent of an Advanced Mode setting of about 18% (e.g. 18% of the ideal range in Highway mode).
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