DELAY LINE WITH MAGNETIC CONTROL

L. M. ANAN'EV, Ya. S. PEKKER

(Presented by the scientific seminar of the Department of Industrial Electronics)

In various radio-engineering devices, artificial delay lines are used to form rectangular pulses of short duration and to obtain a constant delay of pulse signals from tenths of a microsecond to tens of microseconds. Such lines are usually made of inductive-capacitive elements connected in series, each of which is an \(LC\) low-pass filter.

The widespread use of artificial delay lines is due to their simplicity, low cost, and practically unlimited service life, which is an indisputable advantage over various electronic circuits intended for the same purposes.

In a number of radio-engineering devices it is necessary to obtain a controlled signal delay; this is achieved by using appropriate electronic circuits, the replacement of which by controlled delay lines (CDL) can substantially increase the reliability of these devices.

A delay line is characterized by its basic parameters: wave impedance — \(\rho_0 = \sqrt{\dfrac{L}{C}}\) and the magnitude of the delay — \(\tau_{\text{d0}} = n\sqrt{LC}\) (\(n\) is the number of sections of the line). It is obvious that, in order to obtain a controllable delay, it is necessary to vary at least one of the line elements—\(L\) or \(C\), or the number of its sections.

When developing controlled delay lines, it is necessary to take into account the features of the devices in which the CDL is to operate. The principal and general requirements imposed on a CDL should be considered to be: low weight and dimensions, simplicity of the control circuit, a wide range of variation of the delay time, and also matching of the CDL with the load over the entire control range.

At present, for regulating the delay time, stepwise variation is most often used either of the number of line sections [3] or of the line capacitance [4]. Such regulation is carried out by a mechanical switch. The simplicity of the control circuit and the possibility of varying the delay time over wide limits are advantages of these lines. However, the electrical noise arising during switching, as well as the abrupt change in delay time by switching, are substantial disadvan-

...disadvantages that make the use of this type of DL difficult in a number of devices, for example, in stabilization and modulation circuits, etc. DLs with contactless and smooth delay adjustment are free of these disadvantages.

To implement a smooth change in the delay time of an artificial line, it is necessary to provide for the possibility of appropriately regulating the parameters of the elements comprising it.

Preliminary studies have shown that the most promising approach is magnetic control of the DL, whose time characteristics are regulated by changing the inductance of the cells (Fig. 1, a). The inductance of the sections of such a DL is made on toroidal magnetic cores. On each core, in addition to the winding \(L\), a control winding \(L_y\) is placed. In order to decouple

Fig. 1. \(a\)—circuit of a delay line with magnetic control; \(b\)—placement of the control winding for an odd number of line sections;
\(U_{\mathrm{in}}\)—input signal, \(L\)—section inductance,
\(C\)—section capacitance, \(L_y\)—control winding,
\(R_{\mathrm{load}}\)—load resistance, \(\Phi_y\)—control magnetic flux

the signal and control circuits, the windings \(L_y\) are connected in opposed pairs when the number of sections is even; when it is odd, the control winding is placed on the core as shown in Fig. 1, b. Such an arrangement of the winding \(L_y\) prevents pulses from passing through the control circuit, but makes fabrication of the line more difficult.

The principle of control in this case is based on the fact that, when the magnetizing current of the core changes, its magnetic permeability changes and, consequently, the inductance of the sections and the delay time of the line change.

As the core material in this case it is most expedient to use ferrites, whose magnetic permeability [1, 2] depends strongly on the magnitude of the magnetizing current. Moreover, this dependence is expressed the more sharply, the greater the initial permeability of the ferrite, \(\mu_n\). The dependence of the effective permeability of the ferrite \(\mu_d\) on the magnitude of the magnetizing current is exponential in character and, neglecting hysteresis, is approximated by the expression

\[ \mu_d = \mu_n e^{-\alpha I_y}, \tag{1} \]

where \(\alpha\) is a coefficient depending on the composition of the ferrite.

Taking this into account, let us determine the dependence of the delay time of the line, its characteristic impedance, and the output voltage on the degree of magnetization.

The inductance of the toroidal winding is determined by the known formula

\[ L=\frac{0.4\pi\,10^{-8}\,\mu_d\,\omega^2 S_c}{l_c}\,|2n|, \tag{2} \]

where \(\omega\) is the number of turns of the winding,
\(S_c\) and \(l_c\) are, respectively, the cross section and the mean length of the magnetic line of force of the core.

Substituting the value of \(\mu_d\) into expression (2), we obtain

\[ L_{\mathrm{mag}} = L e^{-a I_y}. \tag{3} \]

Whence

\[ \tau_{z\mathrm{mag}}=\tau_{z0} e^{-\frac{a}{2} I_y} \tag{4} \]

and

\[ \rho_{\mathrm{mag}}=\rho_0 e^{-\frac{a}{2} I_y}. \tag{5} \]

Thus, the delay time \(\tau_{z\mathrm{mag}}\) and the characteristic impedance of the line \(\rho_{\mathrm{mag}}\) under magnetization vary according to an exponential law. The change in characteristic impedance when regulating the delay time leads to a violation of the matching conditions of the line with the load, which causes a change in the amplitude of the output signal according to a law that is not difficult to obtain by using the equivalent replacement circuit of the device in Fig. 2.

Fig. 2. Equivalent replacement circuit of the delay line:
\(U_{\mathrm{in}}\) — generator of input pulses, \(U_{\mathrm{out}}\) — output signal, \(R_i\) — internal resistance of the input-pulse generator, \(\rho\) — characteristic impedance of the DL, \(R_L\) — load resistance

From Fig. 2 it is seen that the output voltage is

\[ U_{\mathrm{out}}=U_{\mathrm{in}}\frac{R_L}{R_L+R_i+\rho_{\mathrm{mag}}}, \tag{6} \]

where \(R_i\) is the internal resistance of the source of input pulses,
\(\rho_{\mathrm{mag}}\) is the characteristic impedance of the UDL,
\(R_L\) is the load resistance.

Taking into account that \(\rho_{\mathrm{bias}}=\rho_0 e^{-\frac{\alpha}{2}I_y}\), one may write

\[ U_{\mathrm{out}}=U_{\mathrm{in}}\, \frac{1}{ 1+\dfrac{R_i}{R_{\mathrm{L}}}+\dfrac{\rho_0}{R_{\mathrm{L}}}\,e^{-\frac{\alpha}{2}I_y} }. \tag{7} \]

To verify the dependences obtained, experimental samples of a controlled delay line (CDL) were fabricated; the experimental characteristics of one of them are shown in Fig. 3 and are in good agreement with the theoretical ones.

In the figure: vertical axis—\(\tau_z\) (nsec), \(U_{\mathrm{out}}/U_{\mathrm{in}}\); horizontal axis—\(I_y\) (mA). Curve labels: \(R=2.5\), \(R=1.6\), \(R=1.2\), \(R=0.8\); dashed curve: \(\tau_z=f(I_y)\).

Fig. 3. Experimental characteristics of a CDL for various load resistances.
CDL parameters: core type \(\Phi\)-2000, \(G_{\mathrm{n}}=10\) mm,
\(W_L=110\) turns, \(W_{I_y}=110\) turns, \(C=750\) pF, \(n=10\).

Experimental investigations of prototype CDL samples confirmed the possibility of smooth adjustment of the delay time over a wide range, which can be extended by introducing additional switching of the line sections.

However, variation of the line output signal under biasing is not always acceptable.

Let us consider the conditions under which the output signal from the CDL remains constant. It is obvious that, in order to obtain a constant output signal, the change in the characteristic impedance of the CDL must be fully compensated by a change in at least one of the quantities entering expression (7). For structural reasons, the internal resistance of the signal source \(R_i\) is not

always possible to vary according to a definite law. Therefore it is expedient to connect a matching element to the load resistance \(R_{\mathrm{n}}\), which makes it possible to vary \(Z_{\mathrm{n}}\) according to the required law. In the present case, the use of a purely active resistance as the matching element is undesirable, since this lowers the efficiency of the device and, moreover, requires the creation of potentiometers with a specified dependence \(R=f(\gamma)\) (\(\gamma\) is the angle of rotation of the potentiometer slider); in this case only mechanical adjustment is possible.

To vary the load resistance, an electron tube or a transistor may be used as matching elements, but this leads to complication of the circuit and to a reduction in its reliability.

It is most convenient to obtain \(Z_{\mathrm{n}}=f(I_y)\) with a series or parallel connection of \(R_{\mathrm{n}}\) with a matching controlled inductive reactance \(x_L(I_y)\).

Let us consider the case of a parallel connection of a matching controlled inductance with \(R_{\mathrm{n}}\), which, in our opinion, is the most suitable for stabilizing the output voltage from the ULZ. Expression (7) in this case is written in the form

\[ U_{\mathrm{out}}=U_{\mathrm{in}}\frac{Z_{\mathrm{n}}(I_y)}{Z_{\mathrm{n}}(I_y)+R_i+\rho(I_y)} . \tag{8} \]

To obtain a constant output signal, the second factor in expression (8) must remain unchanged over the entire control range and equal to some value

\[ A=\frac{Z_{\mathrm{n}_0}}{Z_{\mathrm{n}_0}+R_i+\rho_0}, \tag{9} \]

where

\[ Z_{\mathrm{n}_0}=\frac{x_{L_0}R_{\mathrm{n}}}{x_{L_0}+R_{\mathrm{n}}} \]

is the load resistance at \(I_y=0\).

After transformations we obtain

\[ Z_{\mathrm{n}}(I_y)=\frac{x_L(I_y)\cdot R_{\mathrm{n}}}{x_L(I_y)+R_{\mathrm{n}}} =\frac{AR_i}{1-A}+\frac{A}{1-A}\rho_0 l^{-\alpha I_y}. \tag{10} \]

Solving (10) with respect to \(x_L(I_y)\), we obtain

\[ x_L(I_y)= \frac{ R_{\mathrm{n}}\left(\dfrac{AR_i}{1-A}+\dfrac{A}{1-A}\rho_0 l^{-\alpha I_y}\right) }{ R_{\mathrm{n}}-\dfrac{AR_i}{1-A}-\dfrac{A\rho_0}{1-A}l^{-\alpha I_y} }. \tag{11} \]

For \(R_i=0\) and \(R_{\mathrm{n}}\gg 1\), the value of the matching controlled inductance is

\[ x_L(I_y)=\frac{A}{1-A}l^{-\alpha I_y} =\frac{R_{\mathrm{n}}x_{L_0}}{R_{\mathrm{n}}+x_{L_0}}e^{-\alpha I_y}, \tag{12} \]

Such a dependence \(x_L=f(I_y)\) is easy to realize if an inductance on ferrite with bias is used. The initial value \(x_{L_0}\) at \(I_y=0\) is determined from the condition of matching the ULZ with the load. Thus, for example, under the best matching,

\[ \rho_0=Z_{\mathrm{n}_0}=\frac{x_{L_0}R_{\mathrm{n}}}{R_{\mathrm{n}}+x_{L_0}} . \tag{13} \]

Whence

\[ x_{L_0}=\frac{\rho_0 R_{\mathrm{l}}}{R_{\mathrm{l}}-\rho_0}. \tag{14} \]

Thus, the introduction of a matching controlled inductance in parallel with the load resistance makes it possible simply to stabilize the output signal from the DLU.

The possibility of practical application of a DL with magnetic control depends on its dimensions and power consumption. The dimensions of a DLU without switching of sections are determined mainly by the sizes of the ferrite cores, while the power consumed is determined by the value \(AW_y\) of the control. In this connection we shall determine the minimum core volume and the optimum value of \(AW_y\) of the control.

For complete utilization of the magnetic-core material, it is necessary that the core operate on the limiting minor loop. In this case, during the action of the pulse an induction is produced in the core

\[ \Delta B=B_s-B_r=\frac{100\,U_{\mathrm{i}}\tau_{\mathrm{i}}}{W_L S_c}, \tag{15} \]

where \(B_s\) and \(B_r\) are the saturation induction and the residual induction of the core, respectively,

\(U_{\mathrm{i}}\) is the amplitude of the input pulse,

\(\tau_{\mathrm{i}}\) is the duration of the input pulse, and the field strength is

\[ \Delta H=H_m=\frac{0.4\pi\omega I_{\mathrm{i}}}{l_c}, \tag{16} \]

where \(H_m\) is the field strength at which saturation of the core occurs;

\(I_{\mathrm{i}}\) is the current in the pulse.

From expressions (15) and (16) we find the minimum core volume

\[ V_{c\min}=S_c\cdot l_c=\frac{40\pi\,U_{\mathrm{i}}I_{\mathrm{i}}\tau_{\mathrm{i}}}{\Delta B H_m}. \tag{17} \]

For regulation of the delay time over the greatest range, the bias field strength must vary from zero to \(H_m\), i.e.,

\[ AW_y=\frac{H_m l_c}{0.4\pi}. \tag{18} \]

Solving equations (17) and (18) accordingly, we obtain the optimum value

\[ AW_y=\frac{100\,U_{\mathrm{i}}I_{\mathrm{i}}\tau_{\mathrm{i}}}{\Delta B S_c}. \tag{19} \]

It should be noted that the expressions obtained are valid for rectangular pulses. It can be shown that \(V_{c\min}\) and \(AW_y\) depend strongly on the shape of the signal applied to the input of the line. For example, for the frequently encountered parabolic pulse, the minimum core volume decreases by approximately a factor of 2, and \(AW_y\) by a factor of 5, all other conditions being equal.

Thus, a delay line with magnetic control is a simple and reliable device that makes it possible to obtain a smoothly adjustable delay. Owing to these qualities, such DLs may find wide application in various radio-engineering devices.

References

1. L. I. Rabkin. High-Frequency Ferrimagnetics. Moscow, Fizmatgiz, 1960.
2. L. I. Rabkin, B. Sh. Epshtein. Nonmetallic Ferrimagnetics in Communications Equipment. Svyazizdat, 1952.
3. Elektronika, 1963, No. 3, 11, 40.
4. L. M. Znamenskii. Adjustable Artificial Lines. Svyazizdat, 1961.