Understanding Above-the-MUF Predictions
Is it possible to operate above the predicted MUF?
George Lane: The old rule was that if you went above the MUF, no signal propagated back to earth. Measurements have shown that if the signal power is strong enough, you can get a return signal on the earth at frequencies above the MUF. The loss becomes very great as the difference between the operating frequency and the MUF [Foperating - MUF] becomes large. The measured data showed that the availability of blobs of higher electron density fell off at the normal distribution rate with respect to the afore mentioned difference between operating frequency and MUF.
The MUF is the middle value of the daily variations of MOF at that hour so it might only occur once in the month! We really need to think about the MOF (hourly median maximum observed frequency on a single day). For frequencies below the MOF we have spectral reflection of the wave from the ionospheric layer. At the MOF itself, the low ray and the high ray add for 3 dB enhancement (this is called the junction frequency). As we go above the MOF, the ray penetrates deeper into the ionosphere. Here in the upper regions of the ionosphere there exists blobs of ionized gases. As the ray passes through a blob, it is slightly bent. After passing through enough blobs it is reflected back toward the earth. This is called the Above-the-MUF mode. Just above the MOF the loss is not too much more than spectral reflection. But as the operating frequency is higher than the MOF, the losses go up exponentially as there are fewer and fewer blobs with sufficient electron density to bend the ray.
Eventually as the frequency goes higher and higher all of the energy penetrates the ionosphere and is lost. In VOACAP the Above-the-MUF loss is limited to 25 dB. Personally, I think it is too low and probably should be allowed to go to 40 to 50 dB.
So what is VOACAP doing? It is computing the distribution of the MOFs over the days of the month. MUFDAY tells you the fraction of the days for which the operating frequency is below the MUF. For those days which are Above-the-MUF, Above-the-MUF losses are included. You will see the SNR LW getting larger and larger as the operating frequency approaches the MUF. As you go above the MUF, SNR LW approaches 27 dB which is a function of that 25 dB limit, I mentioned before.
If you only need a few days per month to meet your REQ SNR, then you may well be able to work frequencies at or above the MUF. But if you require REL = 90%, then SNR LW comes into play and the SNRxx is much lower.
Good SNR and REL predictions above the MUF
Let us consider the example below. VOACAP predicts good values of SNR and REL at 13.7 MHz and 15.4 MHz. However, the MUFday is 0.38 and 0.12 respectively. So, is it feasible to operate on those frequencies?Dec 2001 SSN = 110. Minimum Angle= 3.000 degrees YLE PORI JOHANNESBURG AZIMUTHS N. MI. KM 61.47 N 21.58 E - 26.25 S 28.00 E 174.24 356.94 5275.6 9769.6 XMTR 2-30 REC705 #01[hfcc\HFBC_218.P15 ] Az=160.0 OFFaz= 14.2 350.000kW RCVR 2-30 2-D Table [default\SWWHIP.VOA ] Az= 0.0 OFFaz=356.9 3 MHz NOISE = -145.0 dBW REQ. REL = 90% REQ. SNR = 67.0 dB MULTIPATH POWER TOLERANCE = 10.0 dB MULTIPATH DELAY TOLERANCE = 0.050 ms 1.0 13.1 6.1 7.2 9.7 11.9 13.7 15.4 17.7 21.6 25.9 0.0 0.0 FREQ F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 - - MODE 4.0 7.6 7.8 3.3 4.0 4.0 7.8 7.8 7.8 7.8 - - TANGLE 12.0 7.6 7.8 3.3 12.0 12.0 22.0 4.0 8.0 7.8 - - RANGLE 34.4 34.2 34.2 33.9 34.3 34.6 35.2 34.6 35.5 34.9 - - DELAY 360 290 297 314 332 387 466 402 574 458 - - V HITE 0.50 1.00 0.99 0.95 0.73 0.38 0.12 0.01 0.00 0.00 - - MUFday 142 146 143 142 138 145 157 198 268 289 - - LOSS 44 35 39 48 47 41 29 -5 -77 -96 - - DBU -87 -90 -87 -84 -83 -90 -102 -143 -212 -233 - - S DBW -167 -153 -156 -162 -165 -168 -169 -171 -173 -176 - - N DBW 80 63 69 78 83 78 68 28 -39 -58 - - SNR 13 16 12 10 11 16 26 66 133 138 - - RPWRG 0.74 0.24 0.57 0.74 0.78 0.70 0.51 0.03 0.00 0.00 - - REL 0.00 0.00 0.00 0.64 0.00 0.00 0.00 0.00 0.00 0.00 - - MPROB 0.35 0.19 0.28 0.34 0.38 0.33 0.23 0.03 0.00 0.00 - - S PRB 25.0 9.7 11.2 19.2 25.0 25.0 25.0 25.0 25.0 9.1 - - SIG LW 17.7 4.9 4.9 6.2 11.6 21.5 25.0 25.0 25.0 4.9 - - SIG UP 26.7 12.4 13.8 21.2 26.7 26.8 26.8 26.8 26.8 13.3 - - SNR LW 18.5 7.6 7.1 7.8 12.7 22.2 25.7 25.7 25.7 7.6 - - SNR UP 19.7 21.9 21.9 18.3 19.7 19.7 21.8 21.8 21.8 21.7 - - TGAIN -0.9 -2.1 -1.9 -7.0 -0.9 -0.9 0.0 -5.4 -1.8 -1.9 - - RGAIN 54 51 55 57 56 51 41 1 -66 -71 - - SNRxx
George Lane: The MUF = 13.1 MHz at that hour. So a broadcast frequency of 13.7 is only a little bit above the MUF. At least 38% of the days will be below the MUF (MUFday = 0.38) and reception will be great. On 62% of the days reception will be not-so-good to terrible... So on almost half of the days of the month propagation will be just great. That is why the median SNR should be high.
So then, how about 11.9 MHz? 13.7 MHz is only 70% reliable (REL = 0.70) whereas 11.9 is 78% reliable (REL = 0.78). At the median, the Signal-to-noise ratio (SNR50) at 11.9 MHz is 5 dB higher than at 13.7 MHz. Clearly there is about 1 S-unit advantage to using 11.9 MHz band over that of the 13.7 MHz band on at least half of the days of the month. Also on the bad days of the month, 11.9 will work better than 13.7 MHz so that is another advantage.
I fear at 15.4 MHz, you are getting into the noise of the program. By that I mean, VOACAP will give predictions even when it has no idea what is going to happen. One would normally stay away from using this frequency for this reason:SNR10 = 94 dB-Hz SNR50 = 68 dB-Hz SNR90 = 41 dB-Hz
If we believe the prediction, then VOACAP is saying that 80% of the days of the month (bounded by SNR90 and SNR10) will have a SNR somewhere between 41 and 94 dB-Hz. That is a spread of 53 dB or a factor of 200,000! If the program could talk, it would tell you that it doesn't have any idea what is going to happen on 15.4 MHz. At best you can say there is a 12% (MUFday = 0.12) chance of good service and 88% chance it will be less than good.
There is one more variable that one should look at when dealing with frequencies way above the MUF. That is the Signal Power at the receiver, S PWR (aka S DBW). Often you will find that the power is actually at or below the receiver threshold. In that case the receiver thermal noise becomes controlling and the grade of service is much less than the SNR would indicate. In our example, 15.4 MHz has a predicted S PWR of -102 dBW. If we assume the receiver input impedance is 50 Ohms and that the transmission lineloss is minimal, then the median voltage at the input of the receiver is -102 + 137 or 35 dB relative to 1 microvolt, or 56 uV (see  below; see also: S DBW to S Meter Correlation Table). For a good receiver this is an adequate input voltage.
But if we impose a desired reliability of 90%, the signal power reaching the receiver is -102 dBW - 25 dB (SIG LW) = -127 dBW. Using the previous logic, then the voltage at the receiver under ideal conditions is only 3 uV. For most receive systems which have antenna efficiency, transmission line and impedance mismatch losses, this signal voltage does not overcome thermal noise even in a good commercial receiver.
If you look at S PWR at 17.7 MHz, you will find that the voltage at the input of the receiver has dropped to 0.5 uV which would require a very expensive receiver with good sensitivity and little impedance mismatch loss between the antenna and the receiver.
ConclusionsVOACAP makes the assumption that the external RF noise power is controlling. At high frequencies where the signal power and the noise power become very low, this assumption may fail. If we only look at the SNR, we may be fooled into thinking the grade of service will be good when in fact the receiver noise is greater than the signal plus external noise power.
The authors of IONCAP (the parent program for VOACAP) always warned us that we should only believe the predictions when the reliability was approximately 90% or higher. In your example, if I were the frequency planner for that broadcast, I would select 11.9 MHz as the best frequency. But I still would expect that on some days transmissions on 15.4 MHz will come booming in. The chances that transmissions on 17.7 MHz will be heard on any day of the month depends greatly on the receiver and its antenna.
So the conclusion is that reception on frequencies which are above the predicted MUF are certainly possible and in some cases reception will be possible on more than 15 days of the month at that frequency.
 Equations to Calculate The Median Voltage at the Input of the Receiver
Ohm's Law:E = I*R or I = E/R
Power formula:P = EIP is in Watts, E is in Volts and I is in Amps and R is in Ohms.
Then:P = E * [E/R] = (E^2)/R
Solve for Voltage:E^2 = [P*R]
Convert to dB:10 Log E^2 = 20 Log E = 10 Log [P*R]
Express E in terms of microVolts such that E(V) = E (uV) x 10^6, then:20 Log E + 20 Log [ 1V / 10^6] = 10 Log [P*R] E(dBuV) - 120 = 10 Log P + 10 Log R
Assume R = 50 Ohms:E(dBuV) - 120 = 10 Log P + 10 Log (50 Ohms) = P(dBW) + 17 E(dBuV) = P(dBW) + 17 + 120 = P(dBW) + 137
Finally, E in uV is 10^(dBuV/20) or antilog [(dBuV)/20]. Example: 35 dBuV = 10^(35/20) = 56 uV.
NoteVOACAP computes the signal power [S DBW] which is equivalent to the P(dBW) in the above equations. DO NOT confuse the predicted field strength in the VOACAP output, DBU (dB relative to 1 microVolt per meter), with the voltage at the receiver as given by dBuV (dB relative to 1 microVolt) in the above equations.