# Proposed Electronic Calculator/Chapter 15

​15. The Design of Valve-elements.
(i) Outline of the problem.- To design valve-elements with properties as described in § 5 and to work at a frequency of say 30 or 100 kilocycles would be very straightforward. When the pulse recurrence frequency is as high as a megacycle we shall have to be more careful about the design, but we need not fear any real difficulties of principle about working at these frequencies, and with such band widths. The successful working of television equipment gives us every encouragement in this respect. A word of warning might perhaps be in order at this point. One is tempted to try and carry the argument further and try to infer something from the success of R.D.F. at frequencies of several thousands of megacycles. Such an analogy would however not be in order for although these very high frequencies are used the bandwidth of intelligence which can be transmitted is still comparatively small, and it is not easy to see how the band width could be greatly increased.
In this chapter I shall discuss the limitations inherent in the problem, and shall also show very tentative circuit diagrams by way of illustration. These circuits have not yet been tried out, and I have too much experience of electronic circuits to believe that they will work well just as they stand. (This does not represent a superstitious belief in the cussedness of circuits and the inapplicability of mathematics thereto. Rather it means that normally the amount of mathematical argument required to get a reliable prophecy of the behaviour of a circuit is out of proportion to the small trouble required to try it out, at any rate if one is in an electrical laboratory. In practice one compromises with a rough mathematical argument and then follows up with experiment. The apparent ‘cussedness’ of electronic circuits is due to the fact that it is necessary to make rather a lot of simplifying assumptions in these arguments, and that one is very liable to make the wrong ones, by false analogy with other circuits one has dealt with on previous occasions. The cussedness lies more in the minds dealing with the problem than in the electronic circuits themselves.)
(ii) Sources of delay.- There are two main reasons why vacuum tubes should cause delays, viz. the input capacity and the transit time. Of these perhaps the first is in practice the more serious, the second the more theoretically unavoidable.
The delay due to the input capacity, when the valves are driven to saturation or some other limiting arrangement is used, is of the order of C/g$_m$, where C is the input capacity and g$_m$ is the mutual conductance of the valve. We may, for instance consider the idealised circuit Fig. 44. (Coupling with a battery is of course not practical politics, but it produces essentially the same effects as more practical circuits, and is more easily understood). If I is the saturation current then the grid swing required to produce it is I/g$_m$ and the charge which must flow into the grid to produce this voltage is CI/g$_m$. If the whole saturation current is available the time required is C/g$_m$. This argument is only approximate, and omits some small purely numerical factors. However it illustrates the more important points. In particular we can see that Miller effect is not a very serious matter because of the limiting, which reduces the effective amplification factor to 1. On the other hand, if one valve is used to serve several inputs the delay will be correspondingly increased because the capacity has become multiplied by the number of grids served.
This connecting of several grids to one anode, and a number of other practical points will tend to make the actual delay due to input capacity several times greater than C/g$_m$, e.g. 10 C/g$_m$.
​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/g$_m$ 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/g$_m$ and transit time can be seen by calculating C/(g × Transit time), where C is the grid-cathode capacity and g is the actual conductance, i.e., the ratio of current to V.
${\begin{aligned}{\frac {C}{g\times {\text{Transit time}}}}&={\frac {CV}{I\times {\text{Transit Time}}}}\\&={\frac {\text{Charge on grid}}{\text{Charge in transit}}}\end{aligned}}$
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.
​In order to give an idea of the effect of these delays we have shown in Fig. 45 a pulse of width 0.2 μs and the same pulse delayed, after the manner of Fig. 44a, by 0.03 μs, this representing our calculated value of 0.003 multiplied by 10 to allow for numerous grids, etc. etc. It will be seen that the effect is by no means to be ignored, but nevertheless of a controllable magnitude.
(iii) Use of cathode followers.- In order to try and separate stages from one another as far as possible we shall make considerable use of cathode followers. This is a form of circuit which gives no amplification, and indeed a small attenuation (e.g. 0.5 dB); but has a very large input impedance and a very low output impedance. This means chiefly that we can load a valve with many connections into cathode followers without its output being seriously affected.
Fig. 46 shows a design of cathode follower in which the input capacity effect has been reduced by arranging that the anode is screened from the grid and that the screen voltage as well as that of the cathode moves with the grid. If one could ignore transit time effects this would have virtually zero input capacity.
(iv) The ‘limiting amplifier’ circuit.- When low frequencies are used the limiter circuit can conveniently be nothing more nor less than an amplifier, the limiting effect appearing at cut-off and when grid and cathode voltages are equal. At high frequencies we cannot get a very effective limiting effect at cathode voltage, owing to the fact that the grid must be supplied from a comparatively low impedance source to avoid a large delay arising from input capacity, but on the other hand, in order to get a limiting effect we need a high impedance, high compared with the grid conduction impedance (about 2000 ohms probably).
At high frequencies it is probably better to use a ‘Kipp relay’ circuit. This is nothing more than a multivibrator in which one leg has been made infinitely long (and then some), i.e. one of the two semi-stable states has been made really stable. An impulse will however make the system occupy the other state for a time and then return, producing a pulse during the period in which it occupies the less stable state. This pulse can be taken in either polarity. It is fairly square in shape and its amplitude is sensibly independent of the amplitude of the tripping pulse, although its time may depend on it slightly. These are all definite advantages.
A suggested circuit is shown in Fig. 47, and the waveforms associated with it at various points in Fig. 48.
(v) Trigger circuit.- The trigger circuit need only differ very little from the limiter or Kipp relay. It needs to have two quite stable states, and we therefore return both of the grids of the 6SN7 to -15 volts instead of returning one to ground. Secondly the inhibitory connection is different. In the case of the limiter it simply consists of an opposing or negative voltage on the cathode follower; in the case of the trigger circuit it must trip the valve back, and therefore we need a second cathode follower input connected to the other grid of the 6SN7.
(vi) Unit delay.- The essential part of the unit delay is a network, designed to work out of a low impedance and into a high one. The response at the output to a pulse at the input should preferably be of the form indicated in Fig. 50, i.e. there should be a maximum response at time 1 μs after the initiating pulse, and the response should be zero by a time 2 μs after it, and should remain there. It is particularly important that the response should be near to zero at the integral multiples of 1 μs after the initiating pulse (other than 1 μs after it).
​A simple circuit to obtain this effect is shown in Fig. 51a. The response is shown in Fig. It differs from the ideal mainly in having its maximum too early. It can be improved at the expense of a less good zero at 2 μs by using less damping, i.e. reducing the 500 ohm resistor. It is also possible to obtain altogether better curves with more elaborate circuits.
The 1000 ohm resistors at input and output may of course be partly or wholly absorbed into the input and output circuits. Further the whole impedance scale may be altered at will.
The fact that the pulse has become greatly widened in passing through the delay network does not signify. It will only be used to gate a clock pulse or to assist in tripping a Kipp relay, and therefore will give rise to a properly shaped pulse again.
(vii) Trigger limiter.- We can build up a trigger limiter out of the other elements, although we cannot replace it by such a combination in the circuit diagrams because we are not putting a legitimate form of input into all of them. The circuit is (Fig. 52).
The valve P is merely a frequency divider. It can be used to supply all the trigger limiters. The trigger circuit Q should be tripped by the combination of pulse from P and continuous input, and will itself trip R. The arrangement of two trigger circuits prevents any danger of half-pulse outputs, which we are most anxious to avoid. In order that there might be a half-pulse output the trigger circuit Q would have to remain near its unstable state of equilibrium for a period of time of 1 μs. In order that this may happen the magnitude of the continuous input voltage has to be exceedingly finely adjusted; the admissible range is of the form Ae$^{−tgm/C}$ where A might be say 100 volts (it doesn't matter really) and t is the time between pulses, C and g$_m$ the input capacity and mutual conductance of the valves used in the trigger circuit; C/g$_m$ might be 0.002 μs (we do not need to allow for Miller effect), so that the admissible voltage range is about 10$^{−200}$ volts which is adequately small.