(McGraw-Hill) (Instructors Manual) Electric Machinery Fundamentals 4th Edition Episode 1 Part 5 ppsx

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(Note: The above discussion assumes that transformer T3 is never in either state long enough for it to

saturate.)

3-8. Figure P3-3 shows a relaxation oscillator with the following parameters:

R1 = variable R2 = 1500Ω

1.0 F C = µ VDC = 100 V

BO V = 30 V 0.5 mA HI =

(a) Sketch the voltages v t C ( ) , v t D ( ) , and v t o ( ) for this circuit.

(b) If R1 is currently set to 500 kΩ, calculate the period of this relaxation oscillator.

SOLUTION

(a) The voltages vC(t), vD(t) and vo(t) are shown below. Note that vC(t) and vD(t) look the same during

the rising portion of the cycle. After the PNPN Diode triggers, the voltage across the capacitor decays with

time constant τ2 = R1R2

R1 + R2

C, while the voltage across the diode drops immediately.

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(b) When voltage is first applied to the circuit, the capacitor C charges with a time constant τ 1 = R1 C =

(500 kΩ)(1.00 µF) = 0.50 s. The equation for the voltage on the capacitor as a function of time during the

charging portion of the cycle is

( ) 1

t

R C

Cv t A Be−

= +

where A and B are constants depending upon the initial conditions in the circuit. Since vC(0) = 0 V and

vC(∞) = 100 V, it is possible to solve for A and B.

A = vC(∞) = 100 V

A + B = vC(0) = 0 V ⇒ B = -100 V

Therefore,

( ) 0.50 100 100 V

t

Cvt e−

= −

The time at which the capacitor will reach breakover voltage is found by setting vC(t) = VBO and solving for

time t1: