On the Application of Self-Oscillators in Pulse Mode
Abstract Generated abstract
This paper examines the use of pulsed self-oscillators as transmitters in meter-band radar stations, focusing on the causes and consequences of carrier-frequency instability. Using a two-stroke, two-circuit common-anode oscillator as an example, it analyzes frequency setting errors, the dependence of feedback on line tuning, and transient effects arising during pulse formation, including changes in tube dynamic capacitance and noise-initiated oscillation buildup. The discussion indicates that practical frequency-setting errors and pulse-to-pulse delays can exceed requirements for precise radar applications, especially distance measurement and moving-target selection. It concludes that although pre-excitation can reduce settling time, pulsed self-oscillators are of limited suitability where high frequency stability and timing accuracy are required.
Full Text
On the Application of a Self-Oscillator in Pulse Mode
F. I. Peregudov
(Presented by Professor V. N. Kessenikh, Doctor of Physical and Mathematical Sciences)
In meter-band radar stations, the principal type of transmitter is the pulsed self-oscillator. Self-oscillators have found such wide application owing to the simplicity of their construction and operation.
A characteristic feature of such a transmitter is its multi-circuit nature, practically unavoidable in the meter band. In multi-circuit systems, smooth adjustment of the generator’s operating mode is facilitated.
Most self-oscillators are built according to a push-pull circuit. Owing to the joint operation of two tubes, it is possible to obtain a power of self-oscillation twice as great as in a single-ended circuit.
As oscillatory systems in push-pull circuits, two-wire lines are used, which facilitates coupling to a symmetrical load.
However, despite all their advantages, self-oscillators have a number of serious shortcomings. The most important of these is insufficiently high frequency stability.
In the operation of meter-band radar stations, instability of the carrier frequency is observed, caused by changes in the operating mode of the transmitter (for example, during circular search), replacement of tubes, etc. As is known, the total frequency instability of a generator depends not only on the accuracy with which the frequency is maintained over time, but also on the accuracy with which the required frequency can be set. The reduction of pulse emission of the generator tubes during operation necessitates periodic retuning of the transmitter in order to increase the radiated power. As a result of retuning, not only the power but also the frequency changes.
The pulse mode of operation of a self-oscillator causes additional instability of the carrier frequency. The presence in the circuit of several natural frequencies, as well as changes in the dynamic capacitances of the tubes, gives rise, during the establishment of the pulse amplitude, to a transient process in frequency.
In connection with the crowding of the meter band and the expansion of the range of tasks solved by radar technology, the requirement for frequency stability of radar transmitters is increasing both over long intervals of time and during the radiation of a single pulse.
This makes it necessary to examine in greater detail the causes of frequency instability in pulsed self-oscillators.
For analysis one may use the circuit of a pulsed two-stroke, two-circuit self-oscillator, built according to the common-anode circuit with two tubes of the GI-17 type (Fig. 1). As is known, in a common-anode circuit
Fig. 1. Circuit of a two-stroke pulsed self-oscillator with grounded anode
Fig. 2. Equivalent oscillatory system of the self-oscillator
operation takes place at the upper coupling frequency according to the circuit of a three-point self-oscillator with capacitive feedback. In powerful self-oscillators strong coupling between the circuits is used, when the capacitances \(C_1\), \(C_2\), and \(C_3\) are of the same order; therefore the circuits are strongly detuned relative to the self-oscillation frequency. With strong detuning of a circuit, its active losses may be neglected, and therefore the natural frequencies of the system (Fig. 2) are determined from the condition:
\[ x_1 + x_2 + x_3 = 0, \tag{1} \]
where \(x_1\) and \(x_3\) are the reactances of circuits 1 and 3;
\(x_2\) is the coupling resistance.
Replacing \(x_1\), \(x_2\), and \(x_3\) by the admittances \(y_1\), \(y_2\), and \(y_3\), and introducing the admittances of the partial circuits \(y'_1\) and \(y'_3\)¹), we obtain
\[ y'_1 y'_3 - y_2^2 = 0, \tag{2} \]
¹) A partial circuit is a circuit remaining in the system when another circuit is short-circuited.
where
\[ y'_1=\omega C'_1-\frac{1}{\rho_1}\operatorname{ctg}\frac{\omega l_1}{c}, \]
\[ y'_3=\omega C'_3-\frac{1}{\rho_3}\operatorname{ctg}\frac{\omega l_3}{c}, \]
\[ C'_1=C_1+C_3, \]
\[ C'_3=C_2+C_3, \]
\(c\) — speed of light;
\(\omega\) — frequency of the self-oscillations;
\(\rho_1, \rho_3\) — characteristic impedance of the cathode and grid lines;
\(l_1, l_3\) — length of the cathode and grid lines.
Using the method for calculating two-circuit generators on lines proposed by S. I. Evtyanov [1], let us estimate the accuracy of frequency setting when the feedback coefficient is varied.
Fig. 3. Dependence of the self-oscillation frequency and the feedback coefficient on the length of the cathode line \((l_1)\), at constant length of the grid line \((l_3)\)
The family of curves shown in Fig. 3 gives the dependence of the self-oscillation frequency and of the feedback coefficient on the length of the cathode line. The length of the grid line has been chosen as the parameter. It follows from the graph that, in order to regulate the feedback coefficient at constant frequency, it is necessary to retune both lines simultaneously.
For example, at the frequency \(f = 62.5\) MHz, in order to change the feedback coefficient \(k\) from 0.15 to 0.45 it is necessary to change the length of the cathode line \(l_1\) by 0.10 m, and the length of the grid line \(l_3\) by 0.06 m.
In practice, transmitter tuning is carried out by means of a wavemeter and a power-level indicator. The accuracy of frequency setting will be determined by the accuracy of the wavemeter used, the width of the spectrum of the radio pulse radiated by the transmitter, and the accuracy with which the line shorting jumpers are set.
The relative effective error of frequency setting may be determined as
\[ \delta = \sqrt{ \left( \frac{\dfrac{\partial f}{\partial l_1}\Delta l_1}{f} \right)^2 + \left( \frac{\dfrac{\partial f}{\partial l_3}\Delta l_3}{f} \right)^2 + \left(\frac{\Delta f_1}{f}\right)^2 + \left(\frac{\Delta f_2}{f}\right)^2 }, \tag{3} \]
where \(\Delta l_1,\ \Delta l_3\) are the inaccuracies in setting the shorting jumpers;
\(\Delta f_1\) is the absolute error of the wavemeter measurement;
\(\Delta f_2\) is the additional absolute measurement error due to the presence of a frequency spectrum.
For real conditions, \(\delta\) is of the order of \(0.2\text{–}0.6\%\). It should be noted that, in accordance with the international radio regulations, since 1953 the permissible frequency deviations for fixed, mobile, and radionavigation stations in the range \(30\text{–}100\) MHz have been set equal to \(0.02\%\).
Consequently, the frequency stability of self-oscillators on long lines is insufficient.
In pulsed two-circuit self-oscillators an additional instability of the carrier frequency is observed, caused by nonstationary processes at the beginning and at the end of the pulse. In the work of M. V. Blagoveshchenskii [2] it is indicated that the relative change in frequency during the transient process reaches several percent. However, that work does not take into account the influence of the capacitance caused by the space charge of the tube (dynamic capacitance). The magnitude of the dynamic capacitance of the tube is related in a definite way to the steepness of the tube characteristic [3]. During the establishment of the voltage amplitude in the self-oscillator, as the voltage on the tube grid changes, the steepness will change and, consequently, so will the dynamic capacitance of the tube.
A change in the dynamic capacitance causes a transient process in frequency.
When radar stations are used for the precise determination of distances and for the selection of moving targets, the use of pulsed self-oscillators as transmitters is limited because of the unstable delay that occurs in the front of the high-frequency pulse relative to the front of the modulating pulse.
This phenomenon occurs not only in the decimeter range [4], but also on meter waves [5].
With strong coupling between the circuits, a two-circuit self-oscillator may be regarded approximately as a single-circuit one. In this case, the solution of the nonlinear differential equation describing the transient process in the self-oscillator, by the method of slowly varying amplitudes with approximation of the tube characteristic by a shortened polynomial of the third degree, makes it possible to determine the settling time to the level 0.9 of the stationary value [6]
\[ t_{\text{set}}=\frac{Q}{\omega}\,\frac{1}{kS_0R_{oe}-1}\ln\left[\,4\left(\frac{A_{\text{st}}}{A_0}\right)^2-4\,\right], \tag{4} \]
where
\(\omega\) — frequency of self-oscillations;
\(Q\) — quality factor of the circuit;
\(R_{oe}\) — equivalent resistance of the circuit;
\(S_0\) — tube transconductance at the operating point;
\(A_{\text{st}}\) — steady-state amplitude of self-oscillations;
\(A_0\) — initial amplitude of self-oscillations;
\(k\) — feedback coefficient.
It follows from formula (4) that the settling time, other conditions being equal, depends on the initial amplitude of the self-oscillations.
Depending on the circuit and the operating conditions of the self-oscillator, self-oscillations in the circuit arise either from electrical jolts when the power supplies are switched on, or as a result of electrical fluctuations in the circuit. For the circuit considered by us, the amplitude of the natural oscillations in the grid circuit at the instant self-oscillations arise, for a frequency \(f=60\) MHz and a leading-edge duration of the modulating pulse \(\tau_f=0.5\ \mu\text{s}\), is \(50\)–\(100\) mV [4].
The effective noise voltage in the grid circuit may be determined as
\[ U_{\text{n eff}}=\frac{3.56}{C_{ag}}\sqrt{\frac{I_g}{\Delta f}}\ [\text{mV}], \tag{5} \]
where
\(I_g\) — current of the grid circuit in mA;
\(\Delta f\) — noise passband of the circuit in MHz;
\(C_{ag}\) — capacitance of the circuit in pF.
For the case when \(I_g=5.0\) A, \(C_{ag}=5\) pF, \(\Delta f=0.5\) MHz,
\[ U_{\text{n eff}}=70\ \text{mV}. \]
The maximum noise peaks may considerably exceed the effective voltage [4]. Thus, in the case considered by us, self-oscillations in the generator may arise under the influence of the noise voltage. When the self-oscillator is started by the noise voltage, the settling time of the steady-state amplitude of oscillations in pulsed operation will fluctuate around its most probable value.
It is shown in [7] that the scatter of the settling time amounts to more than twice the value of the circuit time constant (taking into account the shunting of the circuit by the tube).
According to [5], because of the presence of a nonstationary delay in the settling time, the self-oscillator proves unsuitable for measuring the drift velocity of meteor trails (the case in which an accurate measurement of distance is required).
A reduction of the settling time is achieved by applying high-frequency pre-excitation of the self-oscillator. Pre-excitation is also possible by pulses of constant voltage beginning somewhat earlier than the principal modulating pulse [4].
Thus, in cases where increased frequency stability and high accuracy are required of a radar station,
distance measurement, pulsed self-oscillators prove to be of little use as transmitters for radar stations.
References
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