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In dieser Arbeit wird die Fortpflanzung sinusoidaler Druckschwankungen in einem porösen Körper mit complexer Struktur betrachtet.
OF S I N U S O I D A L
(UDC 621.374) R. L. K r i n i t s k i i
A. A. M u r a k h i n
Translated from Izmeritel'naya Tekhnika, No. 9, pp. 69-72, September, 1966
In certain instances it is necessary to produce a train of pulses, which starts at an instant corresponding to a definite phase of a sinusoidal input voltage. This task is performed by comparison devices which produce pulses at the instant the sinusoidal voltage equals the threshold voltage. It is obvious that the value and the sign of the threshold voltage which serves as a comparison level determine the recorded phase. The comparison devices used for these purposes should meet the following basic requirements. They should operate over a wide frequency range of input voltages with a stable comparison instant and output pulse parameters of the required precision; they should not tend to oscillate and they should have a simple design. It can be stated on the basis of an analysis of existing comparators that the most suitable devices from the point of view of the above requirements consist of diode-regenerative circuits . In using these circuits over a wide frequency range of input voltages, the following conditions are normally met. 1. A zero threshold voltage is used. By meeting at the instant of comparison this condition, for which the input voltage has a maximum rate of change, the possibility of repeated operations is reduced and the position with respect to time of the output pulses is made independent of the sinusoidal voltage amplitude. 2. Pronounced positive feedback is used in order to preserve constant pulse parameters and precise locking-in when the input voltage frequency is changed. Normal diode-regenerative circuits with a pronounced positive feedback and a zero threshold voltage tend to oscillate in the absence of an input signal, which in certain cases is completely inadmissible. Below we examine a comparator which operates with a transformer feedback over a wide frequency range with a sufficiently precise locking in of the pulse leading edges, and does not tend to oscillate in the absence of input signals. The particular feature of the device (Fig. 1) consists of using a high-frequency pentode which has a cathode grid and operates in this case as a tube with a variable transconductance. Let us examine the purposes for which the basic elements of the circuit are intended. The input cathode follower with a transformer output decouples the comparison circuit from the source of sinusoidal oscillations. The regenerative part of the circuit uses tube 6Zh20P. The positive feedback is obtained by connecting pulse transformer Tr into the cathode-grid circuit of the tube. A positive feedback factor larger than unity is attained in this circuit by selecting a corresponding vatue for ratio n of transformer Tr. A shaping two-terminal network consisting of a shock-excitation circuit made up of inductance L and stray capacitances is included in the anode circuit. Damping diode D shunts this circuit. The control grid is connected through a high resistance to the anode voltage source. In such a condition (Fig. 2), the tube transmits an anode current, the slope of its grid-plate characteristic is equal to zero, and the tube does not approach an oscillatory condition. Let us examine briefly the operation of this circuit (Fig. 3). When the negative half-wave of the sinusoidal voltage appears at the output of the cathode follower (Fig. 3a), the control grid voltage of tube 6Zh20P attains a certain negative value Ug.cr and the transconductance of the tube rises to Scr,* thus producing an avalanche-type *Ug.cr and Scr are the negative control-grid voltage and the corresponding transconductance at which the avalanchetype process starts in the circuit.
process which blocks the tube. A voltage pulse is generated in the windings of the positive feedback transformer Tr and superposed on the input signal (Fig. 3b). The blocking of the tube produces a negative rise in the anode current (Fig. 3c) and the shock-excitation circuit bursts into oscillations whose first half-period is used as an output pulse (Fig. 3d). Damping diode D is connected in such a manner that its forward resistance shunts the circuit during the second halfperiod, thus choking the oscillations.
As soon as the control grid voltage attains in the positive half-wave of the input signal the cutoff value of Eg0,the anode current rises in a cumulative manner. The phase of the oscillations induced by the conducting tube in the shockexcitation circuit is such that the oscillations are choked from their first half-period by the damping effect of the shunting $, m A / V diode D. 9 2o
i~ ,mA *0
On the basis of the simplified circuit (Fig. 4), let us determine the conditions of the avalanche-type blocking of tube 6Zh20P. We shall consider the pulse transformer to be ideal and neglect its inertia. It follows from Fig. 4 that
C~=Cout + Cc.h,
-3 -Z -I -0 b
where Cou t is the output capacitance, Cc. h is the capacitance between the cathode and the heater. For an insulated heater capacitance Cc.h is not taken into consideration. For a given direction of voltages and currents during the blocking of the tube, their variations can be represented by the following equations:
9uin~ @ ~ ~ ~ ~ ~ - ' - - g
ia - ~ - s U g J r
Ua ~ Ea -4" U1;
U~ : Ut 7~Ug., U~ -: nUL;
i c , - - Ct
dU1 dt '
dU~ C2 - , dl
Fig. 3 where n = U2/U 1 is the transformation ratio, S is the tube transconductance, Ri is the internal resistance of the tube, C z = Cin is the input capacitance of the tube, Ug is the voltage between the control grid and the cathode, U1 is the voltage across the primary winding of the transformer, U2 is the voltage across the secondary winding of the transformer, it is the current in the primary winding of the transformer, i 2 is the current in the secondary winding of the transformer, i Ct is the current through capacitance C1, and icz is the current through capacitance C2.
By solving the system of equations (1) with respect to Ug, we find g
By adopting notations
C2 - - ~ n--I B-
R i (n - C --
e_gg +BUg= c. dt
T h e solution of differential equation (8) with the i n i t i a l conditions t = 0 and Ug = Ug.c r taken into consideration has the form of B
The solution thus obtained serves to find the conditions at which the a v a l a n c h e - t y p e process arises in the c i r cuit, to evaluate the optimum transformation ratio n and to d e t e r m i n e the d e l a y A of the pulse leading edges with respect to the instants which correspond to the various sinusoidal-signal phases of rr(2k + 1), where k = 0,1,2 .... It will be seen from (6) that the a v a l a n c h e - t y p e process arises when B --A > o.
By substituting in (7) for A and B their values from (2) and (3), we obtain SRi (n
l) - - 1 >0 Ri (n~ C~ - - CD -
Since n > 1 and C 2 > C1. the denominator of the expression is larger than zero. Therefore, (7) is met when SRi (n - - l)
1 > O.
n > ! + $R-~"
Inequality (8) is the condition for the a v a l a n c h e - t y p e process arising. Let us now d e t e r m i n e the transformation ratio nop t for which the tube will be blocked in the shortest possible time
By expanding (6) into a Taylor series about t = 0, and by neglecting terms of a higher order than one, we o b tain
and neglecting 1/SRi as compared with unity, we obtain
n~--2n-I---~2=O. From (8) we find that
c, hop t = 1 +
(9) For this transformation coefficient n the blocking process of the tube will last a m i n i m u m time. Let us now provide a quaiitative determination of the optimum transformation coefficient and the critical transconductance Scr for which the avalanche-type process starts. We find that nop t = 1.85 and Scr = 0.40
for C1 = Cout = 2.45 pF, Ca = Cin = 8.6 pF, and ri.av --- 3 k a .
The delay A of the pulse leading edges with respect to the instants corresponding tothe sinusoidal signal phases rr(2k + 1) consists of the delay r b of the beginning of the excitation current drop with respect to these instants, and the delay r due to the finite duration of the excitation current drop. The anode current drop begins to form at the instant when the control grid voltage attains the value of Ug.c r. Assuming (Fig. 2) that Ug.c r = Scr/tanlS, we find that Scr = 0.40 m A / V , tanl5 = 30 inV. The v a l u e of r b is determined from t h e condition
and Ug.c r = 13.3
arc sin - - Um
It has been established experimentally that the input signal amplitude should be at least 7.5 V for a single operation of the circuit in the low-frequency range. Then, 1 13.,q ~ b = - - arc sin - - l0 - 3 ~ 0,00026T. o~ 7.5
Let us evaluate the duration of the avalanche-type process in the circuit with r g .
It follows from (6) that
1-- Ug'crB C 1 -- UgB C
The a v a l a n c h e - l i k e process ends when the control grid voltage attains the value of Ug = Eg0, and
= - - In Eg o g B 1---- B C
The actual time r is increased due to the inertia of the pulse transformer. In such a case the duration of the avalanche-type process is calculated from the formula
~__ I// ,~+ 2 s
where ~"tr is the duration of the transient-function leading edge in the pulse transformer. Provided that ~-b is insignificant, and the duration of r is made small enough by selecting appropriate values for the circuit components, the delay A of the output-pulse leading edge in the comparator will be small and the locking-in instant will correspond to the sinusoidal signal phases sufficiently close to the values of ~r(2k + 1). An experimental verification of the comparator was made with a 6Zh20P tube, a type MIT-2 transformer (with a transformation ratio of n = 2) in the positive feedback circuit, and a high-quality (Q = 100-180) induction coil in the anode circuit. The comparator was fed with a 7.5-V sinusoidal signal. The circuit operated in the range of 2.5-750 kHz. The duration of output pulses was 0.4/2sec with an amplitude of 20 V. Oscillograms of the input and output voltages were photographed on oscillograph type"DUOSKOP" (TPW). A study of the oscillograms has shown that the delay of the output pulse leading edges is at a maximum in the low-frequency range (A ~ 0.5 vsec) and it drops at higher frequencies to A ~ 0.1 gsec. Ttle delay varies with respect to the period from 0.001 T at ~ = 2.5 kHzto about OAT at f = 750 kHz.
LITERATURE 1. 2. 3.
Z. Ya. Milman and G. Taub, Pulse and Digital Devices, Gose~nergoizdat (1960). R.L. Krinitsldi and V. K. Knyazev, Author's Certificate No. 166731, Bull. of Inventions, No. 23 (1964). L.A. Meerovich and L. G. Zelichenko, Pulse Technology, Izd. "Sovetskoe radio," Moscow (1954).