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Discussion Starter #1 (Edited)
In Post #44 of this thread I described that a station on a VHF-LO channel will have a lower power requirement than a station on a VHF-HI or UHF channel to cover the exact same area.

Anyone have the formula handy showing that as the frequency rises, the wavelength decreases correspondingly, and the power needed to broadcast the signal at a constant field strength also rises?

Ideally I'd like to use the formula to put together a reference table listing the frequency, wavelength, and relative power efficiency of each TV channel.
 

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google search for VHF vs UHF propagation models
came up with this as an example hit...and a bunch more

http://www.tapr.org/ve3jf.dcc97.html

to show how path losses vary with frequency.
and to show that wavelength decreases with increasing frequency
just use:

c = f x λ

c= speed of light, meters/sec
f frequency in hz
λ= wavelength in meters

p.s. - wish i could draw greek symbols:)
 

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Yep, 300 (rounded speed of light) divided by the frequency in megahertz will give you the wavelength in meters of a wire with zero diameter.


As for power, the simple way I look at it is you need to generate a lesser number of wavelengths at lower frequencies to go from point A to point B than at high frequencies.
 

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Anyone have the formula handy showing that as the frequency rises, the wavelength decreases correspondingly
Wavelength (in metres) = 300/frequency (in MHz)

So, a 1 MHz signal would have a 300M wavelength and 100 MHz, 3M etc.

BTW, it's actually 299.792458, but 300 is close enough. The speed of light is 299,792,458 metres per second in a vacuum and slightly less in air.

Not sure what the speed of dark is. ;-)
 

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Discussion Starter #6
I'm trying to remember the equation that includes frequency, wavelength (which are simply inverse proportions) and power ouput, with field strength as the constant, which yields a relative value of power efficiency with an ideal antenna. Dagnabbit I just can't seem to find it.

In layman's terms that equation says "All things being equal, on TV channel x you would need y watts of power to cover area z".
 

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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
 

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The speed of light is 299,792,458 metres per second in a vacuum and slightly less in air.

Not sure what the speed of dark is. ;-)
Dark is faster than light, that much is known. When you open a closet door, you can see the light flood in, but never can you see the dark leave! ;)
Bad news is faster than dark. Nothing travels faster than bad news. If my memory is right, in The Hitchhiker's guide to the Galaxy, they mention powering spaceship with bad news, but then there is no point getting anywhere because you are not welcome there as you come with bad news...

:D
 

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I couldnt find that quote in the script, but found this little gem, heh. :p

FORD : Brace yourself. This is a bit like being drunk.

ARTHUR : What's so bad about being drunk?

FORD : Ask a glass of water.
 

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That does it...

Seeing this thread now ... I've definitly got the bug now.

I'm back in Kingston right now - Tuesday evening - on my few days off ... online in the Eng Library of my University (Skool is back in session - woo hoo), and I'm about to go deep down into the "STACKS" to explore abit in the old EE books.

And I'm gonna dig out my EE notes from SKOOL ... in boxes in the basement.

I'll need therapy soon.
 

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Yes ... most everyone associates Kingston with the various Correctional Instituitions in the area. Pennitentiaries, Jails, Prisons.

(ex. Kingston Penitentiary - "The Big House" - is the most notoriously famous - the maximum security PENN, near the lake, right in Kingston, keeps/has kept some of the worst offenders. SCARY.)

(ex. also, the former P4W - Prison for Women - nearby to Kingston PENN. Closed down for some time now. P4W was really scary. Perhaps you remember some of the news reports on the P4W)

Not so sure if I would trust some of those guys in the PENN with long metal antenna parts ... you'd soon end up with alot of hidden deadly weapons.

And yet ... they do have work programs like that for "The Boys Inside" in some institutions.

No ... I did my "TIME" in a different sort of Institution in Kingston. It's called a University. Trust me ... I payed my dues to society there. Four years hard time (luckily, more than 4 years time was not required, to complete my sentence. But for some others ... poor souls ... YES ... more time was required).

But I would not give up my University Education for anything.

Good Lessons learned ... "On the Inside" ....

LOL.
 

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Back on topic.

We knew the formula relating frequency and wavelength as:

Velocity = Frequency x Wavelength

v = f x λ

v = the velocity of the wave (meters per second) m/s
f = frequency of the wave (the units are Hertz / hz / cycles per second) 1/s
λ = the wavelength of the wave (in meters) m

In free space, like in outer space/vacuum, or in air, the velocity of EM waves, or radio waves, is the speed of light. It can be a different speed ... if the wave is traveling in different materials, or in different confines, ex. like in a coax cable, or in a wave guide.

Speed of Light in free space is usually rounded off to:
c = 3.0 x 10^8 meters per second.

That's 300,000,000 metres per second.

Sample calculation:

What's the wavelength at 900 Mhz?
(Mega = 10^6)

v = f x λ

3x10^8 = 900x10^6 x λ

300000000 = 900000000 x λ

w = 300000000 / 900000000 = 1/3 meter = 0.333 meters.

900 Mhz frequency has a 33.3 cm wavelength in free space / air.

(knowing your Metric prefixes and what they mean in terms of powers of ten, helps quite a bit in doing these sorts of calculations.)
 

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The power present in an EM sine waves / radio waves, is another formula.

Don't remember that formula from memory ... but for a given amplitude, I think I remember that the power increases as frequency increases.

Yes, I've had that formula too ... somewhere in my notes / in my University EE or Physics studies.

If I find it ... I'll post it up sometime.

(Amplitude = peak size of sine wave. Thats' the key point in all this - if you're trying to compare power. Same size peak / same voltage peak / the higher frequency signal has more power ... I think.)
 

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Discussion Starter #16
Tip: putting HTML symbols for Engineers in your posts

Tip for everyone: you should be able to find most HTML symbols used in engineering in this set of tables:

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and a variety of other HTML characters in this one:

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The post editor at this site allows you to copy and paste any of those symbols into your messages here.
 
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