The node in the 555 timer at which the voltage is VTH (i.e., the inverting input

Chapter 18, Problem 18.48

(choose chapter or problem)

The node in the 555 timer at which the voltage is VTH (i.e., the inverting input terminal of comparator 1) is usually connected to an external terminal. This allows the user to change VTH externally (i.e., VTH no longer remains at 2 3 VCC). Note, however, that whatever the value of VTH becomes, VTL always remains 1 2VTH . (a) For the astable circuit of Fig. 18.31, rederive the expressions for TH and TL, expressing them in terms of VTH and VTL. (b) For the case C = 1 nF, RA = 7.2 k, RB = 3.6 k, and VCC = 5 V, find the frequency of oscillation and the duty cycle of the resulting square wave when no external voltage is applied to the terminal VTH . (c) For the design in (b), let a sine-wave signal of a much lower frequency than that found in (b) and of 1-V peak amplitude be capacitively coupled to the circuit node VTH . This signal will cause VTH to change around its quiescent value of 2 3 VCC, and thus TH will change correspondinglya modulation process. Find TH , and find the frequency of oscillation and the duty cycle at the two extreme values of VTH .