130CHAPTER 3. DIODES AND RECTIFIERSpared with 5 ms for previous circuits. It required 40 msec for the voltages to rise to a terminalvalue for this circuit. The netlist in Figure 138,3.49 has a “.tran 0.010m 50m” command to extendthe simulation time to 50 msec; though, only 40 msec is plotted.The Cockcroft-Walton multiplier serves as a more efﬁcient high voltage source for photo-multiplier tubes requiring up to 2000 V. 181, Moreover, the tube has numerous dynodes, ter-minals requiring connection to the lower voltage “even numbered” nodes. The series string ofmultiplier taps replaces a heat generating resistive voltage divider of previous designs.An AC line operated Cockcroft-Walton multiplier provides high voltage to “ion generators”for neutralizing electrostatic charge and for air puriﬁers.• REVIEW:• A voltage multiplier produces a DC multiple (2,3,4, etc) of the AC peak input voltage.• The most basic multiplier is a half-wave doubler.• The full-wave double is a superior circuit as a doubler.• A tripler is a half-wave doubler and a conventional rectiﬁer stage (peak detector).• A quadrupler is a pair of half-wave doublers• A long string of half-wave doublers is known as a Cockcroft-Walton multiplier.3.9Inductor commutating circuitsA popular use of diodes is for the mitigation of inductive “kickback:” the pulses of high voltageproduced when direct current through an inductor is interrupted. Take, for example, thissimple circuit in Figure 139,3.50 with no protection against inductive kickback.+−+−−+−+−+Vonoffoff(a)(b)(c)(d)Figure 3.50:Inductive kickback: (a) Switch open. (b) Switch closed, electron current ﬂowsfrom battery through coil which has polarity matching battery. Magnetic ﬁeld stores energy.(c) Switch open, Current still ﬂows in coil due to collapsing magnetic ﬁeld. Note polarity changeon coil. (d) Coil voltage vs time.When the pushbutton switch is actuated, current goes through the inductor, producinga magnetic ﬁeld around it. When the switch is de-actuated, its contacts open, interruptingcurrent through the inductor, and causing the magnetic ﬁeld to rapidly collapse. Because thevoltage induced in a coil of wire is directly proportional to the rate of changeover time ofmagnetic ﬂux (Faraday’s Law: e = NdΦ/dt), this rapid collapse of magnetism around the coilproduces a high voltage “spike”.