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Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2002 The McGraw-Hill Companies Grob Schultz.

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Presentation on theme: "Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2002 The McGraw-Hill Companies Grob Schultz."— Presentation transcript:

1 Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2002 The McGraw-Hill Companies Grob Schultz

2 Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2003 The McGraw-Hill Companies 23 CHAPTER RC and L/R Time Constants

3 Topics Covered in Chapter 23  High Voltage Produced by Opening an RL Circuit  RC Time Constant  RC Charge and Discharge Curves  High Current Produced by Short- circuiting RC Circuit  RC Waveshapes

4 Topics Covered in Chapter 23 (continued)  Long and Short Time Constants  Charge and Discharge with Short RC Time Constant  Long Time Constant for RC Coupling Circuit  Universal Time Constant Graph  Comparison of Reactance and Time Constant

5 The transient response of an inductor has a time constant T = L / R.  T is in seconds  L is in henries  R is in ohms The time (T) required for a change in current of 63 % is one time constant, T. Inductor current reaches its steady-state value in five time constants. Transient Response of an Inductor

6 L R Transient Response of an Inductor (charge) 10 V T in ms i C in mA 1 k  1 H T = L/R = 1/1 x 10 3 = 1 ms Steady state circuit current (I SS ) = 10 mA I SS = 10 V/1 k  = 10 mA

7 Interrupting Inductor Current Opening the circuit causes a rapid decrease in current. In an inductive circuit, the faster the rate of change of current, the higher the amount of induced voltage: v L = L(di/dt). The instant an inductive circuit is opened, a high voltage is generated across the inductor.

8 10 V Interrupting Current Flow in an Inductive Circuit Large di/dt generates a very high voltage.

9 Shorting a Charged Capacitor Shorting the capacitor causes a rapid decrease in capacitor voltage. In a capacitor circuit, the faster the rate of change of voltage, the higher the amount of current: i C = C(dv/dt). The instant a charged capacitor is shorted with a very low resistance, considerable discharge current flows through the short.

10 Shorting a charged capacitor With large capacitors, this can be dangerous!

11 The transient response of a capacitor has a time constant T = RC.  T is the time in seconds  C is the capacitance in farads  R is the resistance in ohms The time required for a change in voltage of 63 % is one time constant, T. Capacitor voltage reaches its steady-state value in five time constants. Transient Response of a Capacitor

12 T in ms R C 1 k  1  F 10 V v C in Volts Transient Response of a Capacitor (charge) T = RC = 1 x10 3 x 1 x = 1 ms Initial charge = 0 V

13 T in ms R C 1 k  1  F v C in Volts Transient Response of a Capacitor (discharge) T = RC = 1 x10 3 x 1 x = 1 ms Initial charge = 10 V

14 Short Time Constants A short time constant is 1/5 or less of the pulse width of the applied voltage. RC Circuits: Produces sharp voltage spikes for v R and rounded edges for v C at the leading and trailing edges of an applied rectangular wave. L/R Circuits: Produces rounded edges for v R and sharp voltage spikes for v L.

15 VSVS vCvC VSVS vRvR R C Short Time Constant in an RC Circuit 100 Hz 1 k  1  F Pulse width = 5 ms T = RC = 1 ms

16 Long Time Constants A long time constant is 5 or more times longer than the pulse width of the applied voltage. RC Circuits: v R is very nearly the same as the applied waveform, and the capacitor blocks the average dc level of the applied waveform. L/R Circuits: v R resembles the average dc level of the applied waveform.

17 VSVS vCvC VSVS vRvR R C Long Time Constant in an RC Circuit 2.5 kHz 1 k  1  F Pulse width = 0.2 ms T = 1 ms

18 Output Waveshapes With long time constants:  v C and i L rise slowly to the steady-state value.  The output waveform is said to be integrated. With short time constants:  v C and i L rise rapidly to the steady-state value.  The output waveform is said to be differentiated.

19 VSVS R C Integrators and Differentiators v OUT Integrators use a relatively long time constant. VSVS R C v OUT Differentiators use a relatively short time constant.

20 Universal Time Constant Graphs Rising curve: Value increases 63% with each time constant. Can represent:  Capacitor charging voltage, v C  Rising inductor current, i L Falling curve: Value decrease 63% with each time constant. Can represent:  Capacitor discharging voltage, v C  Decaying inductor current, i L

21 T % % % % % % % % % % % 40 % 60 % 80 % 100 % 0 % Universal Rising Curve T

22 T % % % % % % % % % % % % 40 % 60 % 80 % 100 % 0 % Universal Falling Curve T


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