Electrical Engineering Homework Help

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IntroductionThe 555 timer integrated circuit (IC) has become a mainstay in electronics design.A 555 timer will produce a pulse when a trigger signal is applied to it. The pulselength is determined by the amount of time it takes to charge and discharge acapacitor connected to a 555 timer. A 555 timer can be used to denounce switches,Modulate signals, create accurate clock signals, create pulse width modulated(PWM) signals, etc. A 555 timer can be obtained from various manufacturersincluding Fairchild Semiconductor and National Semiconductor.The 555 timer can operate in 3 different modes:i. Monostable Modeii. Astable Mode or free runningiii. Bistable Mode or Schmitt TriggerDesignsHere is a simple oscillator circuit that varies the duty cycle over a wide rangewithout affecting the frequency. It is a variation of the simple 555 astableoscillator. Initially, I told a reader that there was no standard 555 circuit that coulddo this, but then the grey matter started working. The use of an air-variable
capacitor for frequency control is a mind-blower—nothing short of a time warp!555 Duty Cycle Control SchematicOverviewWhen potentiometer R1 is centered, operation is obvious and the duty cycle is50%. However, as R1 is rotated in either direction the charge time and dischargetimes vary accordingly. The two sides of R1 have independent steering diodes (D1& D2). C1 & C2 make up the timing capacitor. Pins 2 & 6 of the 555 are the upperand lower thresholds of the input comparators. The charge /discharge voltage is
taken from pin 3 because it has rail-to-rail voltage swing, and the open collectoroutput (pin 7) cannot do this. The rectangular waveform output is taken from pin 7instead. R3 is the pull-up resistor.If constant frequency is desired, C1 could be padded for the correct frequency.However, most experimenters also want variable frequency. Since R1 cannot bevaried in total resistance, it cannot vary the frequency. R2 could vary thefrequency, but would also affect the duty cycle ratio limits as well. The onlypractical means of obtaining variable frequency is to vary C1.Mathematical proofQ = I * T – where Q is the charge, I is charge current and T is charge timeQ = C * V – where Q is charge, C is capacitance, and V is voltage across thecapacitorI * T = C * VE = I * R – where E is voltage I is current and R is resistanceI * T = C * I * R – because E is simply another expression for VT = C * R – dividing by I—we have now proved that charge time is directlyproportional to R
So we have a charge resistance and a discharge resistance, the sum of which isconstant and equal to the R1 potentiometer total resistance (1 to 3). Therefore, thesum of the charge and discharge times is also constant. Since F = 1/T, thefrequency is also be constant.In other words, the two resistances are complementary and the two time periodsare likewise complementary.The Air Variable CapacitorThe old-fashioned air variable capacitor is old and klunky. While DigiKey offersno such product, these devices remain available on eBay as used or old stock.Every serious experimenter should have one of these. The one I would buy is a 3-gang 440pf. Wired in parallel the total capacitance is 1320pf. Physical sizelimitations prevent higher capacitances.Actually, it is fun to play with air variable capacitors.High impedancesTo obtain a reasonably low frequency, R1 had to be selected to have as high aresistance as possible. 2M is the highest value pot I had on hand. A 5M would alsobe a good selection. To function under such high impedance conditions, I selected
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