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Chapter 2 -  THE EQUATIONS
 

THE BASIC EQUATION

  Although  the  equations  describing  the  operation of  the  vacuum  tube
are derived in many text books, the derivation  is  repeated  here  so  that
a form more suitable  for  use  with  G-Curves  can  be  shown.  With  these
equations and the  G-Curves,  the  performance  of  a  vacuum  tube  in  its
circuit may be calculated at any point within the operating area.

  The total instantaneous value  of  the  plate  current  in  a  tube  is  a
function of the tube parameters and can be expressed as:

                     i_b = f ( e_b, e_c1, e_c2, . . . )

  The  unspecified  parameters are  functions  of such  things  as  filament
voltage,  tube  geometry,  temperature,  and  many  other  factors.  Holding
the unspecified  parameters  constant,  a  series  expansion  of  the  above
equation in terms of partial derivatives of ‘f ‘ can  be  written. These par-
tial derivatives  are  the  commonly  used  conductance  parameters  in  the
following equation:

                i_p = ( g_m1* e_g1 ) + ( g_m2* e_g2 ) + . . . + ( g_p* e_p )                 (3)

where the g's are the values of the partial derivatives.  This is  the  basic
equation from which  equations  for  use  with  the  G-Curve  technique  are
derived.  For triodes, it reduces to:

                         i_p = ( g_m* e_g ) + ( g_p* e_p )                                  (4)
 

RESISTANCE-COUPLED AMPLIFIER EQUATIONS

  The triode R-C amplifier circuit is shown in  Fig. 2-1.  For  the  present
analysis R_k1 may be assumed equal to  zero,  or  a  short  circuit.  Because
supply voltage E_bb is  constant,  plate  voltage  change  e_p  is  equal  but
opposite in polarity to the output voltage change, i.e. :

                          e_p = -e_L = -i_p* R_L

  Using this to eliminate i_p from Equation 4 gives:

                          e_p = ( -g_m* R_L* e_g ) / [ 1 + ( g_p* R_L )]

  and the equation for amplification follows  immediately:

                      K =  e_p / e_g  = ( -g_m* R_L ) / [1 + ( g_p* R_L )]               (5)
 
 
 
 
 
 

6
 
 

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Copyright 2008 for Phyllis K. Pullen, M.D.,
by Robert J. Legg