According to the first order ionospheric delay term, the time delay experienced by the GNSS signal is directly proportional to the Total Electron Content (TEC) in the ionosphere, and inversely proportional to the square of the frequency of the carrier wave. Based on this, the GPS L2 (1227.60 MHz) carrier is slower than the GPS L1 (1575.42 MHz) carrier by a factor of ________ for a given TEC (Rounded off to the nearest integer).
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Ionospheric delay is inversely proportional to the square of the carrier frequency, so compare (f_L1 divided by f_L2) squared for a fixed TEC.
Step 1: State why the lower frequency signal delays more.
Because ionospheric delay $\Delta t = k\, TEC/f^2$ (k a constant), a smaller carrier frequency $f$ produces a larger $1/f^2$ term and hence a larger delay. Since $f_{L2} = 1227.60\ MHz$ is lower than $f_{L1} = 1575.42\ MHz$, the L2 signal must be delayed more than L1.
Step 3: Take the ratio of the two delay factors.
\[ \frac{\Delta t_{L2}}{\Delta t_{L1}} = \frac{1/f_{L2}^2}{1/f_{L1}^2} = \frac{6.6357\times10^{-7}}{4.0291\times10^{-7}} \]
Step 5: Round to the nearest integer and conclude.
\[ \frac{\Delta t_{L2}}{\Delta t_{L1}} \approx 2 \] The GPS L2 carrier is therefore delayed by roughly twice as much as the L1 carrier for the same ionospheric TEC, confirming the earlier symbolic derivation.
