Receive Power (dBm) = Transmit Power (dBm) - Total Path Loss + Antenna Gain

where:

Total Path Loss (dB) = Line-Of-Sight Path Loss + Other Losses

and:

Other Losses = Indoor Loss + Tree Loss + WhateverOtherExternal Losses

**Free Space Loss (dB) = 32.4 dB + 20 * log(frequency in MHz) + 20 * log(distance in miles)**
[For distance in kilometers, substitute 36.6 for 34.2.]

So, for "idealized" line-of-sight to outdoor antenna, No Preamp and -83 dBm (CECB) Tuner Sensitivity:

**Required Transmit Power (dBm ERP) =**

-83 dBm - Antenna Gain + Balun/Cable/Splitter Loss + 32.4 dB + 20*log(freq) + 20 * log(distance)
Add 60 dB to convert from dBm ERP to dBkW ERP and do an antilog:

Required Transmit Power (kW ERP) = 10 ^ (dBm ERP + 60)
===================================================

FCC OET-69 "assumes" fol. antenna gains, downlead cable losses & System Noise Figures,

presuming a 30-foot high, outdoor antenna and NO Preamp (use dBi in formulas):

Lo-VHF = 4 dBd = 6.2 dBi and Downlead Cable Loss = 1 dB and System NF = 10 dB

Hi-VHF = 6 dBd = 8.2 dBi and Downlead Cable Loss = 2 dB and System NF = 10 dB

UHF = 10 dBd = 12.2 dBi and Downlead Cable Loss = 4 dB and System NF = 7 dB

Note that improved UHF NF is cancelled out by extra Downlead Cable Loss and that the

extra antenna boost at UHF freqs is overwhelmed by the frequency loss factor:

20 * log(Ch 6) = 38.6 dB

20 * log(Ch10) = 45.8 dB

20 * log(Ch33) = 55.4 dB

Free Space Path Loss on Hi-VHF is nominally 10 dB lower than at UHF and

even less in Lo-VHF Band....

===================================================

To approximate FCC's power allocation rules, plug in the above numbers and below System Sensitivity,

but bear in mind there are several other terrain, interference reduction and max power (UHF = 1 MW) rules

and OET-69 uses a somewhat mysterious "Dipole Factor" method with no freq correction across VHF Bands:

http://www.fcc.gov/Bureaus/Engineering_Technology/Documents/bulletins/oet69/oet69.pdf
**Allocated Transmit Power (dBm ERP) =**

System Sensitivity (dBm) - Antenna Gain (dBi) + Balun/Cable/Splitter Loss + Free Space Path Loss
where:

System Sensitivity (dBm) = -106 dBm (Thermal Noise Power) + 15 dB (ATSC SNR) + System Noise Figure

so:

FCC System Sensitivity (VHF) = -81 dBm

FCC System Sensitivity (UHF) = -84 dBm

hence:

**Lo-VHF Allocated Transmit Power (dBm ERP) =**

-81 dBm Sensitivity - 6.2 dBi Gain + 1 dB Downlead Loss + Free Space Path Loss
**Hi-VHF Allocated Transmit Power (dBm ERP) =**

-81 dBm Sensitivity - 8.2 dBi Gain + 2 dB Downlead Loss + Free Space Path Loss
**UHF Allocated Transmit Power (dBm ERP) =**

-84 dBm Sensitivity - 12.2 dBi Gain + 4 dB Downlead Loss + Free Space Path Loss
======================================================

Fortunately, we can do better than the FCC Planning Factors if a Preamp is suitable for the location:

Without Preamp: System Noise Figure (dB) = Balun/Cable/Splitter Loss + Tuner Noise Figure (typ. 5-10 dB).

With Preamp: System Noise Figure (e.g. "Signal Loss") is illustrated here (for excl. 6 dB NF Tuner):

http://www.digitalhome.ca/forum/showthread.php?p=888368
https://spreadsheets.google.com/ccc?key=phsRNZNCpKqgbqKCH6hFmLw&hl=en#gid=0