Radio Range vs. Frequency

Question

Let's say you have two mobile simplex transceivers running on (for example) SSB. Mobile means that the antenna height and TX power have limitations. Say if we limit the Antenna height to 2m and the TX power to 100w. In an urban environment the optimum frequency is not clear. VHF/UHF does not like obstructions, but there is less noise than say HF. Lower HF would do well getting around obstructions, but noise could be bad and poor antenna efficiency could easily waste most of the transmitter power. What frequency would be best?

Answer 1

This is an interesting question and while we may not be able to get to an exact answer, we can certainly explore the issues to consider.

First we start by calculating a primitive link budget. The transmitter has an output power of 100 watts or 30 dBm. If we assume a 50 ohm input impedance receiver will have adequate reception (20 dB of quieting) with a 0.5 μV signal across its input, this is a -113 dBm signal. Both of these values may be calculated using:

$$dBm=10\log{\frac{P}{.001}} \tag 1$$

where P is the power in watts.

The difference between these two values, 163 dB, is the maximum, total attenuation that will be acceptable in the communications link to support reliable communications .

The first loss we must consider is the FSPL (free space path loss) for the various bands in question. This will account for the power density due to the gradual spreading of the signal and for the effective aperture of the reference isotropic antenna. A decibel version of FSPL is:

$$FSPL_{dB}=20\log(d)+20\log(f)+32.45 \tag 2$$

where d is the distance in kilometers and f is the frequency in megahertz.

If we calculate the FSPL for the 80 meter band at 25 kilometers (about 15 miles) between stations, we find it is ~72 dB. The same distance on 70 cm has an FSPL of ~113 dB.

The FSPL must be subtracted from our primitive link budget of 163 dB. So for 80 meters, we have 91 dB of remaining link budget and for 70 cm we have 50 dB of remaining link budget. This remaining budget must account for all antenna gains/losses and any additional attenuation in the path such as building, trees, terrain, etc.

Since the question places a two meter limit on the height of the antenna, we can make some rough estimates with respect to antenna gain. A 2 meter vertical antenna on 80 meters will have a gain of approximately -20 dBi near the horizon. A 2 meter tall collinear vertical on 70 cm could have a gain of approximately 8 dBi near the horizon.

With the same antenna on both vehicles, the total antenna gain on 80 meters is -40 dBi. We add this to the remaining link budget of 91 dB for 80 meters which leaves us with 51 dB. This is the total additional attenuation that we could tolerate and still carry out successful communications on 80 meters. Note that remaining link budget has gone down because the antennas introduce addition loss in the link. Similarly, we have 66 dB remaining on the 70 cm budget. In this case, the budget has gone up because the antennas have introduced gain in the link. In both cases, this a significant amount of additional attenuation that we could tolerate on the links.

From this point, models can be used to estimate the additional attenuation in an urban environment. This will typically include estimates for the various materials and the terrain between the stations. For the upper frequency bands in particular, re-radiation and multipath must also be considered. Man-made noise is even creeping into the UHF range. For the lower frequency bands, propagation effects, such as NVIS (near vertical incidence skywave), and atmosperic plus man-made noise could also come into play.

Answer 2

Good things to recognize in understanding the performance of this system are that:

1. The software often used to evaluate these situations usually is set by the operator to consider only the "far field" radiation, and ignore the surface wave
2. The far-field calculations of MoM software such as NEC assume a flat reflecting plane for systems not evaluated for their performance in free space, and show the field or gain existing for an infinite distance from the radiator
3. The propagation environment of item 2 above does not apply to relatively short, terrestrial, point-point paths over real, curved Earth
4. If the surface wave is not included, NEC and similar software is not appropriate to evaluate the performance of short, point-point terrestrial paths — such as used by a VHF/UHF HT to reach a repeater.

Below is a NEC4.2 study of a 6m transmit system linking to a distant repeater, including its radiation at the lower elevation angles producing the surface wave.

It can be seen that the radiation from an elevation angle of only 0.8° is responsible for the field intensity arriving at the repeater antenna (Earth curvature has a ~negligible effect on this analysis, for this path length).

A NEC far-field (only) analysis for this setup would show almost no radiation from this transmit antenna at an elevation angle of 0.8°.

Added later: It would be useful to me and perhaps others if the person downvoting this answer would add a comment to it offering the reason for doing so. Nothing given in the answer is factually inapplicable as a response leading to an accurate analysis of the question asked in the OP.

Answer 3

What's the optimum place to live?

What's the optimum car to buy?

Like your question, these are complicated questions without an easy answer. There are many trade-offs involved, and simultaneously optimizing all of them is usually not possible. And often, practical requirements override the myriad technical issues. For example, the best place to live is one where you have a job, family, or friends. The best frequency is one where there's a repeater in range that you're licensed to use. If you're installing the repeater, the best frequency is one that's available.