Total Response

By means of the curves we can now construct the pulse shape delivered to load R₂. Suppose that a transformer with the following properties is required to deliver a flat top pulse of 15 microseconds' duration.

Primary leakage inductance (secondary short-circuited)	= 1.89 · 10-4 henry
Primary open-circuit inductance	= 0.1 henry
Primary/secondary turns ratio Np/Ns	= 1:3
Source resistance R1	= 800 ohms
Load resistance (primary equivalent) R2	= 5,000 ohms
Primary effective capacitance C2	= 448 μμf

From the expressions given in Fig. 230

m = 2.34 · 10⁶

T = 1.8 microseconds

k₁ = 0.68

The front of the wave follows a curve between those marked k₁ = 0.4 and k₁ = 0.8 in Fig. 230. Value E_a is reached in 0.5T or 0.85 microsecond, and an overshoot of about 10 per cent occurs in 1.2 microseconds.

The top of the wave slopes down to a voltage determined by the product τR₁/L_e = 0.12, and by a curve between those for R₂ = ∞ and R₂ = 2R₁ in Fig. 234. Voltage E' at b is evidently 0.9E_a.

The trailing edge is found from Fig. 235. Here

Load voltage reaches zero in 0.05T or 2.11 microseconds. The negative loop has maximum amplitude of 33 per cent E' at 0.2T or 8.44 microseconds beyond the pulse edge b. The pulse delivered to load R₂ is shown in Fig. 236, in terms of E instead of E_a.

Fig. 236. Output voltage of pulse transformer.

So far we have assumed that the pulse source is disconnected at the end of the pulse. In some applications the source remains connected.

This would result if switch S (Fig. 233) were left closed, and battery E were short-circuited. Under these conditions the leakage inductance remains in the circuit, and an additional transient occurs. The transient has a shape similar to one of the curves of Fig. 231 but is inverted and superposed on the backswing voltage due to OCL. In the example just given, this superposed oscillation has an amplitude of 10 per cent of E, with a total result similar to the oscillogram of Fig. 237.

Fig. 237. Oscillogram of voltage pulse.

Superposed backswing oscillations are discussed more fully in Design of Pulse Transformers. Because of the distributed nature of leakage inductance and capacitance, higher-frequency superposed oscillations may sometimes occur even when the load is disconnected at the end of a pulse. By their very nature, the conditions for these oscillations are difficult to state with certainty, but if oscillations occur on the front edge they are likely to appear on the trailing edge, superposed on the voltage back-swing.