Trailing-Edge Response

At instant b in Fig. 226, it is assumed that the switch S in Fig. 233 is opened suddenly. The equivalent circuit now reverts to that shown in Fig. 235, in which L_e is the OCL, and C_D is total capacitance referred to the primary.

Fig. 235. Interpolation chart for pulse transformer backswing. (Click on the image to get a closer view)

Figure 235 illustrates the decline of pulse voltage after instant b (Fig. 226), the equation for which is:

[129]

where m₁,m₂ =, m = 1/2R_IC_D, and other terms are defined in Fig. 235. Abscissas are time in terms of the time constant determined by OCL and capacitance C_D. Ratio k₃ on these curves has a different meaning, and time constant T is greater than in Fig. 230, but with low capacitance k₃ is high and the curves with higher values of k₃ drop rapidly. The slope of the trailing edge can be kept within tolerable limits, provided that the capacitance of the transformer is small enough. Accurate knowledge of this capacitance is therefore important. Measurement and evaluation of transformer capacitance should be made as in Chapters 5 and 7.

If the transformer has appreciable magnetizing current, the shape of the trailing edge is changed. The greater the magnetizing current, the more pronounced the negative voltage backswing. The ordinates at the left of Fig. 235 are given in terms of the voltage E_a, at instant a, as if there were no droop at the top of the pulse. These curves apply when there is droop, but then the ordinates should be multiplied by the fraction of E_a to which the voltage has fallen at the end of the pulse.

Magnetizing current at the end of the pulse is

[130]

where

m = R₁R₂/(R₁ + R₂)L (see Fig. 233)

τ = pulse duration in seconds

L = primary OCL in henrys

Magnetizing current can be expressed as a fraction Δ of the primary load current I, or Δ = i_M/I. For any R₁/R₂ ratio, Δ = [(R₁ + R₂)/R₁] · voltage droop at point b (Fig. 226), or

[131]

where E_a = voltage at point a (Fig. 226), and E' = voltage at point b. This equation gives the multiplier for finding the actual trailing-edge voltage from the backswing curve parameters in Fig. 235. With increasing values of A the backswing is increased, especially for the damped circuits corresponding to values of k₃ ≥ 1.0. The same is also true for lower values of k₃, but with diminishing emphasis, so that in Fig. 235 exciting current has less influence on the oscillatory backswings. These afford poor reproduction of the original pulse shape, but occasionally large backswing amplitudes are useful, as mentioned in Line-Type Radar Pulsers.

Equation 129 is plotted at the left of Fig. 235 for Δ = 0, and at the right of Fig. 235 for Δ = 3. Instructions are given under Fig. 235 for finding the backswing in terms of E_a by interpolation for 0 < Δ < 3, and for given values of k₃ and t/T. This chart eliminates the labor of solving equation 129 for a given set of circuit conditions. Elements L_e, C_D, and R₁ in Fig. 235 sometimes include circuit components in addition to the transformer, as will be explained later. For linear resistive loads, the terms are interchangeable with L and R₂ of Fig. 233, and with C₂ of Fig. 229, all referred to the primary winding.

In transformers with oscillatory constants the backswing becomes positive again on the first oscillation. In some applications this would appear as a false and undesirable indication of another pulse. The conditions for no oscillations arc all included in the real values of the equivalent circuit angular frequency, i.e., by the inequality