Linear Amplifiers in DSB/AM Operation

John, KD7DO, in Benson , AZ suggested I include the comments I made to him about running a linear amplifier behind a low-power, AM transmitter -- in his case a Harvey-Wells Bandmaster driving a homebrew amplifier running a single 813...

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 If you have a real
rock-crusher linear amplifier for SSB, say a pair of 3-500Z's or 3CX800's that provides a total plate dissipation of 1000 to 1600 watts, then driving it with 20 to 30 watts out of the Bandmaster would give you a very healthy 200 to 300 watts of carrier power. On the other hand, an amplifier running a single 813 with its 125 watts of plate dissipation would only be capable of giving you, at best, a 42-watt carrier, hardly better than the Bandmaster barefoot.

Here's how that works -----

First, two assumptions:

(1) Any amplifier
you use has to be capable of a peak-envelope power output of 4 times the desired carrier level power output.  This is a fundamental fact of double-sideband, full-carrier AM operation.   At 100% positive modulation, the RF output voltage doubles and so, by P = V^2 / R, the output power is quadrupled.

(2) From experience we know that vacuum-tube
linear amplifiers achieve approximately 25% efficiency at carrier level -- quite a ways off from their theoretical efficiency of 67% at maximum PEP.

Now, a little bit of algebra to solve for the maximum carrier
power output  (Po)  obtainable for a give plate dissipation  (Wd) .

(Also, let me use * for multiply rather
than x)

efficiency  =  eff  =  (power out)  /  (power in)  =  Po  /  Pi   ; (by definition)

Transposing to get plate power input:  

         Pi = Po / eff

Plate dissipation power  Wd :    (that which is not output, is dissipated)

        Wd  =  Pi  -  Po 

Substituting for Pi in the above expression for Wd:

       Wd  =  ( Po  /  eff )  -  Po   =   Po  *  ( 1  /  eff  -  1 )

Solving for desired output power by transposing Po and Wd:  

         Po  =  Wd  /  ( 1  /  eff  -  1 )    ; ;    <-----<<<<

In the 813 case with   Wd  =  125 watts   and  eff  =  25%  =  0.25

Carrier Output Power is:
        Po  =  125  /  ( 1  /  0.25  -  1 ) 
                =  125  /  ( 4 - 1 )
                = 125  /  3 
                = 41.67 watts     

Of course, at that power level, you'd better have a fan blowing on the 813 because you will definitely be showing color on the plate. The PEP output will be about 167 watts, very doable for this amp.

Another example is my own, a pair of 3-500's dissipating 600 watts, or 300 watts / tube:

  Wd  =  600 W,   eff  =  0.25

       Po  =  600  /  ( 1  /  0.25  -  1 )
              =  600 / 3
              =  200  watts carrier output power

There's a reason why I don't crank it up higher. The power supply, running off of 110 volts, limits the amp to about 800 watts PEP output. That's the real limiting factor. But 200 watts of carrier is enough to be heard through the fades and over the urban electronic din.

As you can see, AM isn't kind to linear amplifiers at all. This was the lesson the broadcasters learned back in the late 20's and early 30's that caused them to adopt plate modulation almost universally. However, for ham-radio use, low-level modulation still works OK, but tends to heat up the shack during long, "old-buzzard" transmissions.

Regarding audio quality being degraded going through a linear amplifier -- as long as the '4 times carrier power' rule is observed for the amplifier's PEP output capability, there shouldn't be a problem. Violating that rule is easy because, as one cranks up the carrier level, the amplifier efficiency also increases, so the plate dissipation remains pretty much the same, the amplifier doesn't burn up, but the positive modulation peaks become severely flat-topped and the received audio sounds horrible.

I guess the bottom line on a linear amplifier "afterburner" is that unless you can see at least a 6 dB boost in output power, with 10 dB actually being the preferred figure, it really isn't worth it to build or buy the beast.

            For similar view on this subject, click here for  a note by George Grammer, W1DF. (~300K)