Maintaining the Required Grade of Service

Calculating the Circuit Reliability for a Given Hour

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Let us assume you wish to know on how many days in a month a certain grade of service can be maintained on a given hour between two locations. The grade of service is expressed in VOACAP by the parameter REQ.SNR (the required signal-to-noise ratio in dB-Hz). This is a critical setting that must be considered carefully. The correct value to select is dependent on the transmission mode, and the reception quality we like to maintain. As a rule of thumb, a reasonable listening quality in the AM mode can be maintained by using the REQ.SNR value of 67, for CW the REQ.SNR can be, say, 27 and for SSB, 45. Remember always to set REQ.REL. to 90%.

The Basic Formulas

For this exercise, you will need two formulas for calculations. The formula 1 is for cases where your REQ.SNR is lower than the predicted SNR, and the formula 2 for cases where your REQ.SNR is greater than the predicted SNR.

The formulas 1 and 2 will calculate the parameter z. As such, the parameter z has no meaning; you will need to use the Z Tables to translate it to a probability (%) value and to the corresponding number of days in a month. Also you need to run VOACAP to get the values of SNR, SNR LW and SNR UP for your circuit.

When your required SNR (REQ.SNR) is equal to or less than the predicted SNR, use the following:

(1) z = (SNR - REQ.SNR) / (ABS(SNR LW) / 1.28)

When your required SNR (REQ.SNR) is greater than the predicted SNR, use the following:

(2) z = ABS(SNR - REQ.SNR) / (ABS(SNR UP) / 1.28)

1. Case Scandinavian Weekend Radio

Calculate the number of days in December 2001 that Scandinavian Weekend Radio (Virrat, Finland) can be heard in Copenhagen (Denmark) at 1800 UTC at the REQ.SNR level of 67. The frequency is 6170 kHz, and the monthly smoothed sunspot number (SSN) is expected to be 110.

SWR uses a 100-watt transmitter with a horizontal half-wave dipole (beamed at 150 degrees) at 8 meters above the ground. The receive antenna in Copenhagen is the default shortwave whip antenna, SWWHIP.

This is what we get as a result from VOACAP by running the circuit (Method 20):

 Dec    2001          SSN = 110.                Minimum Angle= 3.000 degrees
  VIRRAT              COPENHAGEN (KOBENHAV  AZIMUTHS          N. MI.      KM
  62.38 N   23.62 E - 55.72 N   12.57 E    225.33   35.83     524.2    970.7
  XMTR  2-30 IONCAP #23[omat\48-8m.ant       ] Az=150.0 OFFaz= 75.3   0.070kW
  RCVR  2-30 2-D Table [default\SWWHIP.VOA   ] Az=  0.0 OFFaz= 35.8
  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

  18.0  6.8  6.2  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0 FREQ
        1F2  1F2   -    -    -    -    -    -    -    -    -    -  MODE
       35.9 29.6   -    -    -    -    -    -    -    -    -    -  TANGLE
        4.2  3.9   -    -    -    -    -    -    -    -    -    -  DELAY
        392  308   -    -    -    -    -    -    -    -    -    -  V HITE
       0.50 0.76   -    -    -    -    -    -    -    -    -    -  MUFday
        123  119   -    -    -    -    -    -    -    -    -    -  LOSS
         20   23   -    -    -    -    -    -    -    -    -    -  DBU
       -104 -101   -    -    -    -    -    -    -    -    -    -  S DBW
       -158 -157   -    -    -    -    -    -    -    -    -    -  N DBW
         54   56   -    -    -    -    -    -    -    -    -    -  SNR
         36   30   -    -    -    -    -    -    -    -    -    -  RPWRG
       0.06 0.04   -    -    -    -    -    -    -    -    -    -  REL
       0.00 0.00   -    -    -    -    -    -    -    -    -    -  MPROB
       0.11 0.12   -    -    -    -    -    -    -    -    -    -  S PRB
       20.3 17.1   -    -    -    -    -    -    -    -    -    -  SIG LW
        9.4  5.4   -    -    -    -    -    -    -    -    -    -  SIG UP
       22.2 19.4   -    -    -    -    -    -    -    -    -    -  SNR LW
       10.9  7.8   -    -    -    -    -    -    -    -    -    -  SNR UP
       -2.5 -4.6   -    -    -    -    -    -    -    -    -    -  TGAIN
       -0.7 -0.3   -    -    -    -    -    -    -    -    -    -  RGAIN
         31   37   -    -    -    -    -    -    -    -    -    -  SNRxx

Please note that for the circuit calculation we have assumed some power losses so that only 70% of the transmitting power goes to the antenna. That explains the power of 0.070kW in the above example. The same "70% rule" applies to our second example below.

As we can see, the required SNR (67) is greater than the predicted SNR (56) for that hour. The poor performance of this circuit is mainly due to the low transmitting power. Furthermore, the broadcast frequency (6.17 MHz, or 6.2 as given above) is too close to the MUF (6.8 MHz). The MUF is defined as the median maximum usable frequency for a given path, month, SSN and hour. On each day of the month at this hour, there is a maximum observed frequency (MOF) for this mode (1F2). The median of this distribution is called the MUF for that mode. In other words, the MUF is the frequency for which ionospheric support is predicted on 50% of the days of the month.

The required SNR is greater than the predicted SNR, so we need to use the formula 2:

(2) z = ABS(SNR - REQ.SNR) / (ABS(SNR UP) / 1.28)

where z = ABS(56 - 67) / (ABS(7.8) / 1.28) = 1.805

Now, look up the z value of 1.805 in Table 2. The percentage value will be around 3.6% which corresponds to just about 1 day. By the way, if the power to the antenna would have been 100 watts instead of 70 watts, we could have got 7% (2 days) as the result. Looking back now to the circuit results, you will see that the value of REL, the Circuit Reliability Factor, is 0.04, ie. 4%. This is the same answer VOACAP gives us without any laborous calculations from our part!

This is the SNR distribution as a chart:

The Answer

If the required SNR is 67, then the circuit reliability is predicted to be about 3.6% (REL 0.04 ie. 4%). That means you can maintain a reasonable grade of broadcasting service between Virrat and Copenhagen only on one day out of 30 days in December 2001 on the frequency of 6170 kHz at 1800 UTC.

2. Case YLE Radio Finland

In December 2001, YLE Radio Finland transmits from Pori (Finland) to Africa on 15.520 MHz with a transmitter power of 500 kW between 17-18 UTC. Calculate the number of days in a month to achieve a 67-dB circuit reliability at these hours in Johannesburg (South Africa).

This circuit is almost 10,000 kms so we are using Method 30, Short/Long Path Smoothing:

  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

  17.0 20.4 15.5  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0 FREQ
       F2F2 F2F2   -    -    -    -    -    -    -    -    -    -  MODE
        7.0  7.2   -    -    -    -    -    -    -    -    -    -  TANGLE
       14.0  7.2   -    -    -    -    -    -    -    -    -    -  RANGLE
       35.0 34.1   -    -    -    -    -    -    -    -    -    -  DELAY
        462  281   -    -    -    -    -    -    -    -    -    -  V HITE
       0.50 0.87   -    -    -    -    -    -    -    -    -    -  MUFday
        143  140   -    -    -    -    -    -    -    -    -    -  LOSS
         47   49   -    -    -    -    -    -    -    -    -    -  DBU
        -87  -85   -    -    -    -    -    -    -    -    -    -  S DBW
       -172 -167   -    -    -    -    -    -    -    -    -    -  N DBW
         85   83   -    -    -    -    -    -    -    -    -    -  SNR
          9    2   -    -    -    -    -    -    -    -    -    -  RPWRG
       0.81 0.88   -    -    -    -    -    -    -    -    -    -  REL
       0.00 0.00   -    -    -    -    -    -    -    -    -    -  MPROB
       0.40 0.47   -    -    -    -    -    -    -    -    -    -  S PRB
       25.0 15.1   -    -    -    -    -    -    -    -    -    -  SIG LW
       20.4  5.5   -    -    -    -    -    -    -    -    -    -  SIG UP
       26.7 17.5   -    -    -    -    -    -    -    -    -    -  SNR LW
       21.2  7.2   -    -    -    -    -    -    -    -    -    -  SNR UP
       21.8 21.9   -    -    -    -    -    -    -    -    -    -  TGAIN
       -0.5 -2.4   -    -    -    -    -    -    -    -    -    -  RGAIN
         58   65   -    -    -    -    -    -    -    -    -    -  SNRxx

Now the REQ.SNR is lower than the predicted SNR (83) so we'll apply

(1) z = (SNR - REQ.SNR) / (ABS(SNR LW) / 1.28)

where z = (83 - 67) / (ABS(17.5) / 1.28) = 1.17

The z value of 1.17 (now from Table 1) translates approximately to 88%, which corresponds to 26 days. Again, we will note that VOACAP has already calculated the same value for us in REL (0.88 = 88%).

  18.0 17.4 15.5  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0 FREQ
       F2F2 F2F2   -    -    -    -    -    -    -    -    -    -  MODE
        4.0  4.0   -    -    -    -    -    -    -    -    -    -  TANGLE
       12.0 12.0   -    -    -    -    -    -    -    -    -    -  RANGLE
       34.4 34.2   -    -    -    -    -    -    -    -    -    -  DELAY
        350  317   -    -    -    -    -    -    -    -    -    -  V HITE
       0.50 0.84   -    -    -    -    -    -    -    -    -    -  MUFday
        143  137   -    -    -    -    -    -    -    -    -    -  LOSS
         45   51   -    -    -    -    -    -    -    -    -    -  DBU
        -87  -81   -    -    -    -    -    -    -    -    -    -  S DBW
       -170 -168   -    -    -    -    -    -    -    -    -    -  N DBW
         83   87   -    -    -    -    -    -    -    -    -    -  SNR
         11    7   -    -    -    -    -    -    -    -    -    -  RPWRG
       0.77 0.83   -    -    -    -    -    -    -    -    -    -  REL
       0.00 0.00   -    -    -    -    -    -    -    -    -    -  MPROB
       0.37 0.42   -    -    -    -    -    -    -    -    -    -  S PRB
       25.0 25.0   -    -    -    -    -    -    -    -    -    -  SIG LW
       20.9  9.5   -    -    -    -    -    -    -    -    -    -  SIG UP
       26.7 26.6   -    -    -    -    -    -    -    -    -    -  SNR LW
       21.6 10.8   -    -    -    -    -    -    -    -    -    -  SNR UP
       19.7 19.7   -    -    -    -    -    -    -    -    -    -  TGAIN
       -0.9 -0.9   -    -    -    -    -    -    -    -    -    -  RGAIN
         56   60   -    -    -    -    -    -    -    -    -    -  SNRxx

Here, z = (87 - 67) / (ABS(26.6) / 1.28) = 0.962, which is approximately 83% or 25 days (see Table 1). Note again the REL of 0.83 (83%) given by VOACAP.

The Answer

YLE Radio Finland is predicted to maintain a reasonable grade of broadcasting service to Johannesburg (South Africa) on 26 days out of 30 days in December 2001 on the frequency of 15.520 MHz at 1700 UTC, and on 25 days out of 30 days at 1800 UTC.