[Amps] Line Sections As Plate Lines

[jeff millar]

The line is not physically 1/2 wave long because it's loaded at both 
ends by capacitance.  I use the RF Dude's smith chart program (or the 
Linux one by Lapo Pieri, IK5NAX) and enter some starting values.  Then 
just tune the values with the keys until you get a match, change the 
length of the line, readjust tune and load C and repeat.  A few minutes 
of playing will show how to move the values to get closer to the 50 Ohm 
center point.  

You stated 74 Ohms of stray C, which corresponds to 15 pF at 144 MHz, 
allocate 9 pF to the tube and 6 pF to the other end to keep the tune and 
load flapper small.

    144.2 MHz Frequency
    100000 Ohm open circuit impedance (dummy hi-z starting point)
    Parallel Plate impedance 2000 Ohms ( 3600V / (1.8 * 1 Amp))
    Parallel Plate output C   9 pF (GS-35 has 4.4 pf Cout plus 4.6 pF stray)
    Series Transmision line of 87 Ohms and 114 degrees long
    Parallel tune C of 4.3 pF
    Series load C of 3.4 pF
This produces a nice match to 50 Ohms

The length of the line is computed directly from  length in degrees, 
assuming velocity factor of 1 for air coax, for example
    (113 degrees /360) * 300 M meters_per_sec / 144.2 MHz = 66 cm = 26 
inches. 

Other combinations work as well
75  Ohm line
    Tline of 75 Ohms, 116 degrees long
    Tune C of 6 pF
    Load C of 3.6 pF
100 Ohm line
    T line of 100 Ohms, 92 degrees
    Tune C of 8.4 pF
    Load C of 4.2 pF
More Tune C, shorter line
    T line of 50 Ohms, 105 degrees
    Tune C of 24 pF
    Load C of 5.5 pF
Less tune C, longer line
    T line of 50 Ohms, 140 degrees
    Tune C of 3.7 pF
    Load C of 3.4 pF

This calculation can be done with transmission line formulas and math, 
but its complex numbers with real and imaginary impedances...lots of 
opportunity for silly math errors.  The smith chart program lets you 
enter approximate components and then tune all the values with up/down 
keys on the computer until the end point of the arcs lands on the 50 Ohm 
point in the middle. 

The length of the anode can get modeled as either a lumped capacitance 
of about 5 pF or as a short section of lower impedance transmission line.

The impedance of the transmission line depends on the diameter of center 
conductor and the dimensions of the box.  I don't have the formulas 
handy.  The process basically is to decide how big you want the outer 
box and how small you're willing to go for the center without skin 
effect losses becoming too much.  Using high impedance lines make for a 
shorter overall design but risk heating and possible detuning due to 
thermal effects.  The web designs you pointed to look like about 50 
Ohms.  Knowing the impedance helps to ensure the model works correctly.

hope this helps,

jeff, wa1hco

JMLTINC at aol.com wrote:

>Hi again guys-
>
>Sorry if I was not clear about my question. Let me try it from a different angle. Specifically:
>
>How do you calculate the length for a 1/2wl plate line????
>That is, what is the formula?
>
>I already know:
>Freq = 144Mhz
>Zo = 87 ohms
>Ctotal (tube, strays, tune) = 74 ohms
>
>Thanks-
>John, N9RF
>
>
>
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