The circuit shown in Fig. P7.99 is known as an astable multivibrator and finds wide

Chapter 23, Problem 99

(choose chapter or problem)

The circuit shown in Fig. P7.99 is known as an astable multivibrator and finds wide application in pulse circuits. The purpose of this problem is to relate the charging and discharging of the capacitors to the operation of the circuit. The key to analyzing the circuit is to understand the behavior of the ideal transistor switches and The circuit is designed so that the switches automatically alternate between ON and OFF. When is OFF, is ON and vice versa.Thus in the analysis of this circuit, we assume a switch is either ON or OFF. We also assume that the ideal transistor switch can change its state instantaneously. In other words, it can snap from OFF to ON and vice versa.When a transistor switch is ON, (1) the base current is greater than zero,(2) the terminal voltage is zero, and (3) the terminalvoltage is zero. Thus, when a transistorswitch is ON, it presents a short circuit between theterminals b,e and c,e. When a transistor switch isOFF, (1) the terminal voltage is negative, (2) thebase current is zero, and (3) there is an open circuitbetween the terminals c,e. Thus when a transistorswitch is OFF, it presents an open circuit betweenthe terminals b,e and c,e. Assume that T has beenON and has just snapped OFF, while has been OFFand has just snapped ON. You may assume that atthis instance, is charged to the supply voltageand the charge on is zero. Also assumeanda) Derive the expression for during the intervalthat is OFF.b) Derive the expression for during the intervalthat is OFF.c) Find the length of time is OFF.d) Find the value of at the end of the intervalthat is OFF.e) Derive the expression for during the intervalthat is OFF.f) Find the value of at the end of the intervalthat is OFF.g) Sketch versus t during the interval thatis OFF.h) Sketch versus t during the interval thatis OFF.