Starting current law

The starting current law describes the behavior of vacuum - electron tubes with hot cathode at negative grid voltages ; The term grid here means any cold electrode such as a control grid , screen grid or anode .

description

At 0 V grid voltage, a small grid current can be measured. The cause is the negatively charged electrons ejected from the cathode . ${\ displaystyle I_ {0}}$

If the electrons have to run against a repulsively polarized grid, the current is even smaller, because electrons with less energy than (- e is the charge of the electron and U <0 the voltage of the grid in relation to the cathode) cannot reach the grid and fall back on the cathode. ${\ displaystyle eU}$

The proportion of electrons with higher electrical energy than (and thus the grid current ) decreases exponentially with the grid tension: ${\ displaystyle eU}$ ${\ displaystyle I}$

{\ displaystyle I = I_ {0} \ cdot e ^ {\ frac {eU} {k _ {\ mathrm {B}} T}}}

With

the Boltzmann factor ${\ displaystyle e ^ {\ frac {eU} {k _ {\ mathrm {B}} T}}}$ ${\ displaystyle e ^ {\ frac {eU} {k _ {\ mathrm {B}} T}}}$
- the elementary charge ${\ displaystyle e}$
- the grid tension ${\ displaystyle U <0}$
- the Boltzmann constant ${\ displaystyle k _ {\ mathrm {B}}}$
- the absolute temperature ${\ displaystyle T}$

( is the thermal energy ).

{\ displaystyle k _ {\ mathrm {B}} T}

example

For an oxide cathode with a temperature of 1100 K, the following applies:

Grid voltage and current
at 1100 K.
U	I.
0 V	100% I ₀
−0.1 V	35% I ₀
−0.2 V	12% I ₀
−1 V	0.003% I ₀

The powerless control of electron tubes is therefore only given at grid voltages below −1 V. The usual amplifier circuits with tubes work with such small grid voltages. An exception is the grid audion , where the grid voltage is approximately 0 V.

Connection with the space charge law

The starting current law is supplemented by the space charge law for positive grid voltages. For U = 0 V, both laws contradict each other: according to the starting current law the current is equal to I ₀ and according to the space charge law it is 0. The real characteristic of an electron tube shows an overlay. Before the maximum negative grid current is reached at 0 V according to the starting current law, the characteristic curve bends in the direction of positive grid current.

At a certain grid voltage greater than −2 V, the grid current is therefore again 0. This operating point results in the lowest load on the resonant circuit during a grid audion . The operating point depends on the tube: for the triode UX199 it is −1.1 V, for the triode KC1 it is −0.6 V and for the triode RE134 it is −0.03 V.

literature

H. Barkhausen: Textbook of electron tubes, 1st volume General Basics , S. Hirzel Verlag, Leipzig 1965, 11th edition, page 41ff.
Alexander Potchinkov: Simulation of tube amplifiers with SPICE: PC simulations of electron tubes in audio amplifiers , Vieweg + Teubner, 2009, ISBN 3834806420