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Q. Use necessary circuit and waveforms to explain the working of a Bootstrap sweep generator
The bootstrap circuit illustrated in figure given below is a commonly used method for achieving a constant charging current. Here, transistor Q1 acts as a switch and Q2 as an emitter follower which is connected across capacitor C. Therefore, the output voltage V0 will be approximately equal to the voltage across C. The transistor, therefore, provides a low resistance output terminal for the saw-toothed generator.
Initially, Q1 is ON and Q2 is OFF. Hence, C1 is charged to the supply voltage Vcc through diode D and the output voltage V0 is zero. When a negative pulse, as shown in waveform figure, is applied to the base of Q1 and Q1 is turned OFF. Now, capacitor C1 discharges and capacitor C starts charging through resistor R. As a result, the base voltage of Q2 and V0 start increasing from zero volts. Therefore, diode D becomes reverse biased. The value of capacitor C1 is much larger than that of capacitor C. The voltage across R remains substantially constant throughout the charging process and thus the charging current (iR) is maintained constant. So, capacitor C is charged with a constant current which causes the voltage across C, i.e. the output voltage V0 to increase linearly with time with the relation, V0 = Vcct/RC.
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Q. Determine the Laplace transform for each of the following functions from the basic de?nition of Equation. (a) f 1 (t) = u(t) (b) f 2 (t) = e-at (c) f 3 (t) = df (t) dt,
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