Front-Edge Response

The step-up transformer is illustrated by Fig. 229.

Fig. 229. Circuit for step-up transformer.

When the front of the wave (Fig. 226) is suddenly impressed on the transformer, it is simulated by the closing of switch S. At this initial instant, voltage e across R₂ is zero, and the current from battery E is also zero. This furnishes two initial conditions for equation 128, which expresses the rate of rise of voltage e from zero to its final steady value E_a = ER₂/(R₁ + R₂):

[128]

where m₁, m₂ = -m(1 ± ).

Fig. 230. Influence of transformer constants on front edge of pulse (R1 = 0). For equivalent circuit see Fig. 229.

Figure 230 shows the rate of rise of the transformed pulse for R₁ = 0 and Fig. 231 for R₁ = R₂. In hard-tube modulators, source resistance is comparatively small and approaches R₁ = 0. Line-type modulators are usually designed so that R₁ = R₂.

The scale of abscissas for these curves is not time but percentage of the time constant T of the transformer. The equation for this time constant is given in Figs. 230 and 231.

Fig. 231. Influence of transformer constants on front edge of pulse (R1 = R2).

It is a function of leakage inductance and of capacitance C₂. The rate of voltage rise is governed by another factor k₁, which is a measure of the extent to which the circuit is damped. The relation of this factor k₁ and the various constants of the transformer is given directly in Figs. 230 and 231.

The greater the transformer leakage inductance and distributed capacitance, the slower is the rate of rise, although the effect of R₁ and R₂ is important, for they affect the damping factor k₁. If a slight amount ofoscillation can be tolerated, the wave rises up faster than if no oscillation is present. Yet, if the circuit is damped very little, the oscillation may reach a maximum initial voltage of twice steady-state voltage E_a, and usually such high peaks are objectionable. The values for k₁ given in these figures are those which fall within the most practicable range. Time required for pulse voltage to reach 90 per cent of E_a is given in Fig. 232.

Fig. 232. Time required to reach 90 per cent of final voltage.