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[AMPS] Dollars per dB

To: <>
Subject: [AMPS] Dollars per dB
From: (Larry L. Ravlin)
Date: Thu, 31 Dec 1998 17:29:11 -0800
What this all boils down to (and by the way you are absolutely correct in
your figures) is "you are better off to sink you bucks into a GOOD antenna
than a amplifier.  
this does not mean that I am against power, far from it, but there is More
to gain from a good antenna than there is from a good amp.

Larry K0AEY

> From: DavidC <>
> To: Ham -; Ham -
> Cc: Ham - Jim Cunningham - AXS <>
> Subject: [AMPS] Dollars per dB
To: <>
> Date: Thursday, December 31, 1998 5:18 PM
> I am interested in reactions to this presentation (below)by K2UVG.
> It sounds logical on the face of it ... though I'll have to rerun his
> numbers for used solid state and tube amplifiers and see how
> they look.  Since I recently acquired a used Cushcraft A3S w/40m
> I appreciate that illustration ... used is more cost efficient!  :-)
> 73 & Happy New Year to All!  DavidC  K1YP
> Dollars per dB
> or...or so you want to improve your station! 
> ------------------------------------------------------------------------
> If I held up a dollar bill, you all would recognize it for what it is. If
> wrote "dB" on the blackboard, you would probably tell me that you herd
> about it but that you don't quite understand it. Well let's work on that.

> When I talk about station improvement, I am really talking about signal
> inprovement. It is useful to appraise signal strengths in terms of
> loudness as registered by the human ear. For example, if a person
> that a signal is "twice as loud" when the transmitter power is increased
> from 10 watts to 40 watts, he will also estimate that a 400 watt signal
> twice as loud as a 100 watt signal. 
> The human ear has a logarithmic response. Dont let that word throw you.
> Well have it licked in short order. This fact is the basis for the use of
> relative power unit called the decibel (dB). A change of one decibel in
> power level is just dectable as a change in loudness under ideal
> conditions. The number of decibels corresponding to to a given power
> is given by the equation: 
> db = 10 log P2/P1 
> There is that nasty word log again.... dont worry we will slay that
> Lets create some rules of thumb. First lets calculate a power ratio of
> .. 
> db = 10 log P2/P1 = 10 log 2/1 = 10 log 2 
> It turns out the log of 2 = .3010299957. So the power ratio of 2 is equal
> to 3.010299957 dB. Well just call it 3 dB. Another ratio to remember is
> P2/P1 = 10. 
> dB = 10 log 10 
> The log of 10 is 1. So a power ratio of 10 is also 10 dB. Knowing these
> rules and the fact that since by the definition of logs we are talking
> about exponents... and when we multiply numbers with exponents we just
> exponents... so when multiplying power ratios we just add decibles. Lets
> look at an example: 
> Suppose we have a power ratio of 8. How many dB is that? Well we know
> our 2 rules that its greater than 3dB and less than 10 db. We also know
> that a power ratio of 8 is also equal to 2 X 2 X 2. Using the last rule
> have 3 dB + 3 dB + 3 dB = 9 dB. Every time you double the power you add 3
> dB. Evey time you reduce the power by 2 (half) you loose 3 dB. 
> The S-unit and dB are used as references on receiver signal-strength
> meters. No particular standard has been adopted by the industry at this
> time, as a S meter is a relative reading instrument on most amateur
> However, during WWII at least one receiver manufacturer used 50 micro
> for S9 and each S unit below S9 was supposed to be equal to 6 dB. The
> above S9 are already in dB. I will use this "standard" convention that a
> unit is equal to 6 dB. 
> Pop quiz...what is the power ratio associated with 6 dB ? Well 3 dB is 2
> and another 3 dB is another 2... thats 6 dB and 2 time 2 or 4. 
> Lets go back to $ per dB. You all knew what a $ was. Now you are dB
> and "per" is just the arithmetic operator of division. Miles per hour
> ...miles divided by hours...$ per dB ... dollars divided by dB. This
> us a Figure of Merit or Measure (FOM) that we can use to look at several
> ways of improving our station. 
> Lets now use this new found knowledge to improve a typical start-up
> station. This station will consis of the following: 
> Power out - 100 watts
> Antenna - dipole
> Coax - 100 ft of RG-58
> You notice that when I described this station, I am only talking about
> business end. I make certain assumptions like you are not using a crystal
> radio to receive. We will also make use of the fact that an improvement
> the antenna system (coax and antenna) on transmit will also improve the
> received signal. 
> Lets tackle the transmitter. How do we improve the power out. Well 100
> watts makes a good exciter for a linear amp. Lets use that approach. We
> also going to compare apples to apples or use CW figures of power out.
> a recent catalog: 
> Ameritron ALS-500M - solid state linear - 400 watts CW - Price $679.95 
> To go from 100 watts to 400 double 100 to 200 (3dB) and you
> double 200 to 400(another 3 dB). Adding the dB we have a 6dB improvement.
> Now just divide dollars by dB or in this case 679.95/6 = $113.33/dB. For
> every $113 we get a 1 dB improvement in our signal. What is this total
> improvement going to do at the received end ? Remember that 6 dB is equal
> to 1 S-unit. If your are S8 with 100 watts your now S9. If you were S9
> are S9+6dB. Note: To keep it simple, I did not include the 12 volt supply
> in this calculation. When you consider cost it should be TOTAL cost. 
> Lets look at a bigger amp. 
> Alpha ETO - 91 Beta - 1500 watts - Price $2300 
> Double 100 = 200, double 200 = 400, double 400 = 800, double 800 = 1600.
> Each double is 3 dB or 1600 watts is 12 db. We also know that 10 times
> or 1000 watts is 10 dB. If we guess 11 dB for 1500 watts we would be
> on. Our FOM would be $2300/11 dB or $209.09/dB. Note that the improvement
> on the received side would be almost 2 S-units. Note: Again I did not
> include the cost of putting in 220 volts to the shack. 
> Now lets look at the antenna and take down that dipole and put up a beam.

> Cushcraft A3S - 3 elm tri-bander - Gain 8 dBd - $349.95 
> Whoops, what is that "d" behind the dB ? Well in antennas they use 2
> references when describing the gain of an antenna. The ideal or perfect
> antenna that radiates equally in all directins is called an isotropic
> antenna. Gain measured against this fictious antenna is labeled dBi. Gain
> measured relative to a dipole is dBd. The difference between them is that
> dipole has a gain of 2.14 dBi or 0 dBd. Since we have a dipole and the
> beam is rated in dBd, we are all set. All we have to do is take the cost
> and divide by the gain. $349.95/8 = $43.74/db. Note: Here again I did not
> include a rotor or tower/mast. 
> Finally lets look at the coax. Here we must introduce attenuation. Coax
> never gives us anything like the linear or antenna did. It always takes
> something away from us. To improve our system we must insure that it
> away the least amount. The amount it takes away is called attenuation.
> can go to the Handbook or Antenna Book and look up the attenuation
> of various coaxial cables. They are measured in db per 100 ft at a
> particular frequency. The higher the frequency the higher the
> Here is a sample table: 
> Coax4 MHz30 MHz150 MHzRG-58.82.77RG-8 foam.27.927/8 in hardlineless than
> .1.25.7
> Since we have been talking about HF in our past examples, we will stick
> HF here and use the 30 MHz figures. This is a worst case for HF.
> we have an attenuation of 2.7 dB if we go to RG-8 foam filled coax, we
> improve that by 1.8 dB (2.7 - .9 = 1.8). The cost of 100 foot of Belden
> 8214 which is RG-8 foam is $49.95. Doing the now familar math $49.95/1.8
> $27.75/dB. 
> An aside...42 feet of RG-58 at 2 meters takes that 50 watt rig and makes
> a 25 watt rig! 
> By now it should be obvious that I chose the order of improvements to
> a point. Use the best coax you can, use the best antenna you can and then
> worry about the power or $113/dB > $43/dB > $27/dB. 
> The Moral of this story is NEVER use RG-58!
> ------------------------------------------------------------------------
> If you would like to use this document, feel free to do so. All I ask is
> that you give proper credit and drop me an e-mail telling me what you are
> doing with it.
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