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?

• More specifics would help us answer your question. What is the range between the stations? – rclocher3 Aug 15 '18 at 13:55
• Is this a hypothetical question? If so, why are you asking it? The whole concept of 'range' is so nebulous as to be practically a useless concept as such. If it is not a hypothetical question, why not ask the question you want to ask instead? i.e. Give details, and get the real-world problem solved properly – Scott Earle Aug 16 '18 at 1:05
• Yep, typically, your practical question is general enough. Generalizing can always be done later – start by asking a question as precise as possible. You can write something like "I'd like to understand the calculations that lead to the result" to make sure the answer you're getting to your precise question can be applied to other similar problems, but generally, we're pretty good in answering in a way that helps people understand what our considerations were. – Marcus Müller Aug 16 '18 at 7:32
• Of course as a practical question, the answer is probably our #2 FAQ: ham.stackexchange.com/questions/352/… – Phil Frost - W8II Aug 16 '18 at 11:46
• Clearly you understand there are many factors that go into determining the "best" frequency. There's no way we're going to cover them all in anything less than a small book. This would be a better question if you focused on something specific, like how to estimate antenna gain given size constraints, or how path loss in urban environments depends on frequency. – Phil Frost - W8II Aug 21 '18 at 15:13

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.

• Don't forget the noise floor, which is something like 50 dB higher on 80m. – Phil Frost - W8II Aug 16 '18 at 19:26
• @PhilFrost-W8II Good point, Phil. I added this to my answer. Thanks. – Glenn W9IQ Aug 16 '18 at 20:35
• @GlenW91Q good answer +1 .So low frequency is not looking too good .So if there were few obstructions then 70cm would win .80 meter noise will be worse than 70cm .If there were lots of buildings would 80m win? – Autistic Aug 17 '18 at 10:32
• @Autistic Thank you. Consider that the -113 dBm example is between S2 and S3 (per the ITU guideline). If urban noise is at an S8 level, -79 dBm, then you would need at least a -76 dBm signal at the receiver - and more than that for comfortable copy. An urban noise survey is needed to make an informed decision. You would likely have more success at the mid to high HF frequencies as antenna gain improves and noise generally drops. – Glenn W9IQ Aug 17 '18 at 10:49
• This accounts for linik budget, but you must separately consider propagation. 80m will easily propagate 100mi with groundwave propagation, independently of power. 70cm struggles to go 5mi because it does not refract nearly as much as HF and is nearly entirely line of sight. This assumes SSB and no tower. On the other hand, if we allow FM on 70cm, then you could be talking to a repeater, which could easily get you 100-150mi on 5w. – user10489 Aug 21 '18 at 11:20

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.

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.

• This should be converted to a comment, because it does not attempt to answer the question. It merely states that the question is not an answerable question. – Mike Waters Aug 16 '18 at 18:33
• @MikeWaters "Not an answer" would be "I have same ploblem halp please!" Perhaps rather than censoring answers you should focus on closing bad questions. – Phil Frost - W8II Aug 16 '18 at 18:57
• While I don't agree that this is a clear-cut case for a comment rather than an answer — if you think the question is bad, why not vote to close it? As a duplicate, even? – Kevin Reid AG6YO Aug 16 '18 at 19:50
• (As moderators, our close votes are unilateral, so I at least tend to wait for at least one other person to vote unless it's an obvious decision.) – Kevin Reid AG6YO Aug 16 '18 at 19:55
• @KevinReidAG6YO OK, I voted. I think the answers here show plainly good answers are impossible. The question admits there are already many factors (noise, propagation, antenna gain) and there are still more not considered by the OP. The best answer is Glenn's, which necessarily glosses over most of the details, like how to figure antenna gain, or how to predict path loss, etc, and doesn't really say anything which hasn't already been said in ham.stackexchange.com/questions/352/… – Phil Frost - W8II Aug 21 '18 at 15:09