By J. A. Coekin
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Extra info for High-Speed Pulse Techniques
E. the discharge current iR will not change sig nificantly from its value IR immediately after the transient. The storage time is therefore determined by exactly the same procedure as produced eqn. 6). Hence /, = rln[l + IF/IR] HIGH-SPEED PULSE TECHNIQUES 50 but with specific expressions for IF and IR as given above. Substitution and rearrangement produces the relationship which is clearly less than the value obtained without the capacitance. 7 provides an exercise to discover just how significant the reduction may be.
TRANSIENTS AND WAVESHAPING IN LINEAR CIRCUITS '-TO* (a) R21 33 =f= L I Yo (b) FIG. 14. Series and parallel RLC circuits. (1) When (RJ2L)2 > 1/LC or Ri > 2VL/C, the bracket is posi tive, the roots are real and the circuit is overdamped. The current rises slowly, more or less sinusoidally and then decays exponentially. 17). (2) When (Ä,/2L)2 = 1/LC or Rt = VlL/C, the square bracket disappears. 17) simplifies to 1 L (s +a) in which a = —Rxj2L, the circuit is critically damped with the current given by i(s) = ζ (Vt/L) expi-Rs/U).
3RC) when the criterion is met. When the stated criterion is not met, the output wave becomes triangular and attenuated, progressively as the time constant exceeds RC small (a) RC large (b) FIG. 8. Low-pass response to rectangular pulses. TRANSIENTS AND WAVESHAPING IN LINEAR CIRCUITS 27 tp. The effect on a pulse train is shown in Fig. 9. As the converse of the high-pass circuit we would expect the low-pass to perform an approximate integration. The transient block certainly predicts it. When RC is large, v0 is small compared with vs so that vs = iR and v0 = (RC)'1 I vsdt.
High-Speed Pulse Techniques by J. A. Coekin