The change in the phase path, AL, at VHF and above, is given by the integrated difference between the refractive index in the ionosphere and unity:
The negative sign indicates that the impact of the ionosphere is to reduce the phase path length relative to free space.
The group path length ASg — AS1 at VHF and above. To obtain the time delay ATK, we simply divide by the speed of radio propagation (i.e., c = 3 x 108 m/sec) to obtain:
Al\, (seconds) = A S/c = ~ 1.34 (10 7)f '2 (EC) (4.3)
The ionospheric time delay is an important parameter in connection with satellite navigation. Figure 4-10 illustrates how ATg varies with radio frequency, using the electron content as parameter. Note that the TEC may range between ~ 1016 and 1018 electrons/m2. The EC may be ~ 3 times larger for highly oblique paths. Taking the EC to be 3 x 10'8, and f = 1.6 GHz, we find ATg = 157 nanoseconds.
To obtain the phase change, we recognize that it is simply the phase path length AS times 2%/X where X is the wavelength. This leads to the result:
The range error associated with the ionospheric path is obtained by integrating (nK -1) along the refracted path, where ng is the group refractive index. This is just the change in group path length, and it is a positive number. At 100 MHz and above, ng ~ 1/n, where n is the real part of the index of refraction. Figure 4-11 gives the representative limiting values for range error (i.e., troposphere + ionosphere) at 100 and 200 MHz. In Figure 4-12 there is a display of the diurnal variation of elevation error and range error is given at 400 MHz for a typical midlatitude profile of electron density. To go from one frequency to another, recall that the scaling factor will be/ 2.
1018
SlO17
E1016
100 200 500 1000
Frequency (MHz)
2000 3000
Figure 4-tO: Ionospheric time delay as a function of radio frequency with electron content as parameter. From ITU-R [1996].
104 8 6
tT 2
cr 4
102 8 6
4 2 101
- 1 |
1 |
1 |
I |
I |
I |
I | |
- | |||||||
- | |||||||
- |
- | ||||||
_ 100 |
Mc/s - |
Dav |
- | ||||
- | |||||||
- | |||||||
- |
- | ||||||
^ 100 |
Mc/s - |
Niqht | |||||
200 |
Mc/s - |
Day | |||||
— | |||||||
- ~ - | |||||||
- | |||||||
1 |
100 Mcy |
's - Nigh |
it |
__ - | |||
\ \ |
- | ||||||
lonoi |
spheric error snhfirio error |
- | |||||
- \> |
trnnr | ||||||
- \ |
> |
RH = relative humidity | |||||
- |
N > |
000% | |||||
RH | |||||||
1 |
I |
"** -Mi |
-- |
I |
0 10 20 30 40 50 Elevation Angle (deg)
Figure 4-11: limiting values for ionospheric and tropospheric range errors From Millman 119671.
Was this article helpful?
Post a comment