The writer considers in the present paper the jumping phenomena or the so-called "Zie herscheinungen" such as are observed in the two mutually coupled circuits comprising a triode valve oscillator.
In order to explain the jumping phenomena, it is necessary to consider the variation of a certain effective constant of the oscillatory system, that is dependent upon the amplitude of ossillation. The writer refers to the well-known falling oscillation characteristic for the case of electrostatically coupled circuits, and to the lumped voltage characteristic of a triode valve for the inductively coupled circuits.
For the former case, the condition of the existence of jumping phenomena is given by
α'/h1>1+β/σ……(eq. 24)
and the oscillation constant for the point J, at which the two jumping points coincide, is riven by
(x)J=(ω2/ω1)2 J=1/σ(1+d2/β)……(eq. 22)
These theoretical considerations are verified with some experimental results.
For the latter case, the condition of tie jnmping phenomena is
Nω12>ρ(1+β)……(eq.54, )
and the point J is simply given by x=1, i. e.. ω1=ω2•
There are three cases which may be considered concerning the magnitude of the product of the damping constants of respective oscillation circuits. When the damping constants are small, the jumping phenomena generally take place, and when they are a little higher, there is a "silent interval", within which no oscillation can exist. When the damping constant is still larger and exceeds a certain limit, an oscillation can always exist without any jumping phenomenon. This condition of imaginary coupling-so the writer will call it -is considered mathematically and the following results are obtained for the case of'inductively coupled circuits. The critical point C is given by
kc2=k'Mg-L1/ρ•R2/L2……(eq. 67, )
xc=1-kc2=σc……(eq. 68, )
and the range of imaginary coupling is given by the interval between the two intersecting. points of two curves represented by the equations
x/σ=q°2……(eq. 69, )
and q°=2x/1-ε+x……(eq. 70, )
The above results are fairly well verified by experiments. This paper includes the following topics.
Introduction,
Part I. Electrostatically coupled circuits.
I Falling oscillation-characteristic,
II Coupling frequencies and the amplitudes of oscillating voltages,
III Jumping phenomena,
IV Effect of changing the oscillation constant of the primary circuit. Part II. Inductively coupled circuits.
V Effective internal resistance of a vacuum tube,
VI Coupling frequencies and .amplitudes of oscillating currents,
VII Jumping phenomena,
VIII Critical coupling coefficient,
IX Effect of changing the oscillation constant of the primary circuit. Conclusions.