Page:Alan Turing - Proposed Electronic Calculator (1945).pdf/45

 The delay due to transit time may be calculated, in the case of a plane structure, to be 3d(m/2eV)½ where m, e are respectively the mass and charge of the electron, V is the voltage of the grid referred to cut-off and d is the grid-cathode spacing. In other words the transit time may be calculated on the assumption that the average velocity of the electrons between cathode and grid is one-third of the velocity when passing the grid. This time may be compared with C/gm which, if C is calculated statically, has the value $$\frac{3}{2}d(m/2eV)^\frac{1}{2}$$, i.e. half of the transit time. That there should be some such relation between C/gm and transit time can be seen by calculating C/(g x Transit time), where C is the grid-cathode capacity and g is the actual conductance, i.e., the ratio of current to V.

$$\frac{C}{g \times \mbox{Transit time}} = \frac{CV}{I \times \mbox{Transit Time}}$$

$$= \frac{\mbox{Charge on grid}}{\mbox{Charge in transit}}$$

Let us now calculate actual values. The voltage V by which the grid exceeds cut-off might be 10 volts which corresponds to a velocity about 1/300 of velocity of light (Note: annihilation energy of electron is half a million volts) or one metre per microsecond. If d is 0.2 cm. the transit time is 0.006 μs. A typical value for C/gm is 0.002 μs.

The relation between C/gm and transit time brings up an important point, viz. that these two phenomena of time delay are really inseparable. The input capacity of the tube when ‘hot’ really consists largely of a capacity to the electrons. When the motion of the electrons is taken into account the capacity is found to become largely resistive (Ferris effect).

Before proceeding further I should try to explain the way I am using the word ‘delay’. When I say that there is a delay of so many microseconds in a circuit I do not mean to say that the output differs from the input only in appearing that much later. I wish I did. What I mean is something much less definite, and also less agreeable. Strictly speaking I should specify very much more than a single time. I should specify the waveform of the output for every input waveform, and even this would be incomplete unless it referred both to voltages and currents. We have not space to consider these questions, nor is it really necessary. I should however give some idea of what kind of distortion of output these ‘delays’ really involve. In the case of the input capacity the distortion may be taken to be of the form that an ideal input pulse of unit area is converted into a pulse of unit area with sharp leading edge and exponentially decaying trailing edge, the time constant of the delay being the ‘delay’, thus Fig. 44a. In the case of the transit time the curve is probably more nearly of the ‘ideal’ form (Fig. 44b).

To give the word ‘delay’ a definite meaning, at any rate for networks, I shall understand it to mean the delay for low frequency sine waves. This is equal to the displacement in time of the centre of gravity in the case of pulses. by