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วงจร RC

electronics fundamentals. circuits, devices, and applications. THOMAS L. FLOYD DAVID M. BUCHLA. วงจร RC. การตอบสนองต่อสัญญาณไซน์ของวงจร RC.

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วงจร RC

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  1. electronics fundamentals circuits, devices, and applications THOMAS L. FLOYD DAVID M. BUCHLA วงจร RC

  2. การตอบสนองต่อสัญญาณไซน์ของวงจรRCการตอบสนองต่อสัญญาณไซน์ของวงจรRC เมื่อมีทั้งค่าความต้านทานและค่าการเก็บประจุอยู่ในวงจรอนุกรม มุมของเฟสระหว่างแรงดันที่ป้อนและกระแสรวมจะอยู่ระหว่าง 0 และ 90 ขึ้นอยู่กับค่าของความต้านทานและค่ารีแอคแตนซ์

  3. อิมพีแดนซ์ในวงจรอนุกรมRCอิมพีแดนซ์ในวงจรอนุกรมRC ในวงจรอนุกรมRCค่าอิมพีแดนซ์รวมมีค่าเท่ากับผลรวมของเฟสเซอร์ของRและXC Rจะพล็อตตามแนวแกนxซีกบวก. XCพล็อตตามแนวแกนyซีกลบ R R Zเป็นเส้นทะแยงมุม XC XC Z Z เปลี่ยนตำแหน่งของเฟสเซอร์ให้เป็นสามเหลี่ยมอิมพีแดนซ์.

  4. Example จงวาดภาพสามเหลี่ยมอิมพีแดนซ์ และแสดงค่าของR = 1.2 kWและXC = 960 W R = 1.2 kW 39o XC = 960 W Z = 1.33 kW

  5. การวิเคราะห์วงจรอนุกรมRCการวิเคราะห์วงจรอนุกรมRC ใช้กฎของโอห์ม โดยใช้Z, V, I เนื่องจากในวงจรอนุกรมIมีค่าเท่ากันในทุก ๆ ที่ของวงจร จึงสามารถหาแรงดันตกคร่อมอุปกรณ์ต่าง ๆ ด้วยค่าอิมพีแดนซ์ของอุปกรณ์ตัวนั้นกับค่าของกระแส

  6. x 10 mA = Example จากตัวอย่างที่ผ่านมา สมมติให้กระแสมีค่า 10 mArmsจงวาดเฟสเซอร์ไดอะแกรมของแรงดัน แรงดันของเฟสเซอร์ไดอะแกรมหาได้จากกฎของโอห์ม ด้วยการคูณอิมพีแดนซ์เฟสเซอร์แต่ละตัวด้วย 10 mA VR = 12 V R = 1.2 kW 39o 39o XC = 960 W VC = 9.6 V VS = 13.3 V Z = 1.33 kW

  7. การเปลี่ยนแปลงของมุมเฟสเมื่อเทียบกับความถี่การเปลี่ยนแปลงของมุมเฟสเมื่อเทียบกับความถี่ เมื่อความถี่เปลี่ยน สามเหลี่ยมอิมพีแดนซ์ของวงจรอนุกรมRCก็จะเปลี่ยนไปด้วยดังภาพเนื่องจากXCจะมีค่าน้อยลง ถ้าเพิ่มความถี่ f ลักษณะแบบนี้เรียกว่า การตอบสนองต่อความถี่ของวงจรRC

  8. การนำไปใช้งาน ถ้ากำหนดความถี่ให้ วงจรอนุกรมRCสามารถใช้ในการสร้างเฟสล้าหลังได้ด้วยการกำหนดปริมาณของแรงดันอินพุต และเอาต์พุตที่ได้จากแรงดันตกคร่อมตัวเก็บประจุ วงจรนี้เรียกว่าวงจรlow-pass filterเป็นวงจรที่ยอมให้ความถี่ต่ำผ่านไปได้เท่านั้น R VR Vout Vin Vout C Vin Vout Vin

  9. ในทำนองเดียวกัน ถ้ากลับอุปกรณ์ในวงจร ก็จะได้วงจรhigh-pass filterวงจรที่ยอมให้ความถี่สูงผ่านไปได้ จากความถี่ที่กำหนด (cutoff frequency) C Vout Vin Vin Vout R Vout VC Vin

  10. Summary Applications An application showing how the phase-shift network is useful is the phase-shift oscillator, which uses a combination of RC networks to produce the required 180o phase shift for the oscillator. Amplifier Rf Phase-shift network C C C R R R

  11. Summary Sinusoidal response of parallel RC circuits For parallel circuits, it is useful to introduce two new quantities (susceptance and admittance) and to review conductance. Conductance is the reciprocal of resistance. Capacitive susceptance is the reciprocal of capacitive reactance. Admittance is the reciprocal of impedance.

  12. Summary Sinusoidal response of parallel RC circuits In a parallel RC circuit, the admittance phasor is the sum of the conductance and capacitive susceptance phasors. The magnitude can be expressed as From the diagram, the phase angle is BC Y BC VS G G

  13. Summary Sinusoidal response of parallel RC circuits Some important points to notice are: G is plotted along the positive x-axis. BC is plotted along the positive y-axis. Y is the diagonal BC Y BC VS G G

  14. Summary Sinusoidal response of parallel RC circuits Example Draw the admittance phasor diagram for the circuit. The magnitude of the conductance and susceptance are: BC= 0.628 mS Y = 1.18 mS VS R 1.0 kW C 0.01 mF f = 10 kHz G = 1.0 mS

  15. Summary Analysis of parallel RC circuits Ohm’s law is applied to parallel RC circuits using Y, V, and I. Because V is the same across all components in a parallel circuit, you can obtain the current in a given component by simply multiplying the admittance of the component by the voltage as illustrated in the following example.

  16. x 10 V = Summary Analysis of parallel RC circuits Example If the voltage in the previous example is 10 V, sketch the current phasor diagram. The admittance diagram from the previous example is shown for reference. The current phasor diagram can be found from Ohm’s law. Multiply each admittance phasor by 10 V. BC= 0.628 mS IC= 6.28 mA Y = 1.18 mS IS = 11.8 mA IR = 10 mA G = 1.0 mS

  17. IC IS q IR Summary Phase angle of parallel RC circuits Notice that the formula for capacitive susceptance is the reciprocal of capacitive reactance. Thus BC and IC are directly proportional to f: As frequency increases, BC and IC must also increase, so the angle between IR and IS must increase.

  18. Summary Equivalent series and parallel RC circuits For every parallel RC circuit there is an equivalent series RC circuit at a given frequency. The equivalent resistance and capacitive reactance are shown on the impedance triangle: Req= Z cos q XC(eq)= Z sin q Z

  19. Z1 Z2 R1 C1 R2 C2 Summary Series-Parallel RC circuits Series-parallel RC circuits are combinations of both series and parallel elements. These circuits can be solved by methods from series and parallel circuits. For example, the components in the green box are in series: The components in the yellow box are in parallel: The total impedance can be found by converting the parallel components to an equivalent series combination, then adding the result to R1 and XC1 to get the total reactance.

  20. Summary Measuring Phase Angle An oscilloscope is commonly used to measure phase angle in reactive circuits. The easiest way to measure phase angle is to set up the two signals to have the same apparent amplitude and measure the period. An example of a Multisim simulation is shown, but the technique is the same in lab. Set up the oscilloscope so that two waves appear to have the same amplitude as shown. Determine the period. For the wave shown, the period is

  21. Summary Measuring Phase Angle Next, spread the waves out using the SEC/DIV control in order to make an accurate measurement of the time difference between the waves. In the case illustrated, the time difference is The phase shift is calculated from 55o

  22. x 10 mA = Summary The power triangle Recall that in a series RC circuit, you could multiply the impedance phasors by the current to obtain the voltage phasors. The earlier example is shown for review: VR = 12 V R = 1.2 kW 39o 39o XC = 960 W VC = 9.6 V VS = 13.3 V Z = 1.33 kW

  23. VR = 12 V x 10 mA = 39o VC = 9.6 V VS = 13.3 V Summary The power triangle Multiplying the voltage phasors by Irms gives the power triangle (equivalent to multiplying the impedance phasors by I2). Apparent power is the product of the magnitude of the current and magnitude of the voltage and is plotted along the hypotenuse of the power triangle. Example The rms current in the earlier example was 10 mA. Show the power triangle. Ptrue = 120 mW 39o Pr = 96 mVAR Pa = 133 mVA

  24. Summary Power factor The power factor is the relationship between the apparent power in volt-amperes and true power in watts. Volt-amperes multiplied by the power factor equals true power. Power factor is defined mathematically as PF = cos  The power factor can vary from 0 for a purely reactive circuit to 1 for a purely resistive circuit.

  25. Summary Apparent power Apparent power consists of two components; a true power component, that does the work, and a reactive power component, that is simply power shuttled back and forth between source and load. Ptrue (W) Some components such as transformers, motors, and generators are rated in VA rather than watts. Pr (VAR) Pa (VA)

  26. Summary Frequency Response of RC Circuits When a signal is applied to an RC circuit, and the output is taken across the capacitor as shown, the circuit acts as a low-pass filter. As the frequency increases, the output amplitude decreases. Plotting the response:

  27. Summary Frequency Response of RC Circuits Reversing the components, and taking the output across the resistor as shown, the circuit acts as a high-pass filter. As the frequency increases, the output amplitude also increases. Plotting the response:

  28. Selected Key Terms The total opposition to sinusoidal current expressed in ohms. Impedance Phase angle Capacitive suceptance (BC) Admittance (Y) The angle between the source voltage and the total current in a reactive circuit. The ability of a capacitor to permit current; the reciprocal of capacitive reactance. The unit is the siemens (S). A measure of the ability of a reactive circuit to permit current; the reciprocal of impedance. The unit is the siemens (S).

  29. Selected Key Terms The relationship between volt-amperes and true power or watts. Volt-amperes multiplied by the power factor equals true power. Power factor Frequency response Cutoff frequency In electric circuits, the variation of the output voltage (or current) over a specified range of frequencies. The frequency at which the output voltage of a filter is 70.7% of the maximum output voltage.

  30. Quiz 1. If you know what the impedance phasor diagram looks like in a series RC circuit, you can find the voltage phasor diagram by a. multiplying each phasor by the current b. multiplying each phasor by the source voltage c. dividing each phasor by the source voltage d. dividing each phasor by the current

  31. Quiz 2. A series RC circuit is driven with a sine wave. If the output voltage is taken across the resistor, the output will • be in phase with the input. • lead the input voltage. • lag the input voltage. • none of the above

  32. Quiz 3. A series RC circuit is driven with a sine wave. If you measure 7.07 V across the capacitor and 7.07 V across the resistor, the voltage across both components is a. 0 V b. 5 V c. 10 V d. 14.1 V

  33. Quiz 4. If you increase the frequency in a series RC circuit, a. the total impedance will increase b. the reactance will not change c. the phase angle will decrease d. none of the above

  34. Quiz 5. Admittance is the reciprocal of a. reactance b. resistance c. conductance d. impedance

  35. Quiz 6. Given the admittance phasor diagram of a parallel RC circuit, you could obtain the current phasor diagram by a. multiplying each phasor by the voltage b. multiplying each phasor by the total current c. dividing each phasor by the voltage d. dividing each phasor by the total current

  36. Quiz 7. If you increase the frequency in a parallel RC circuit, a. the total admittance will decrease b. the total current will not change c. the phase angle between IR and IS will decrease d. none of the above

  37. Quiz 8. The magnitude of the admittance in a parallel RC circuit will be larger if a. the resistance is larger b. the capacitance is larger c. both a and b d. none of the above

  38. Quiz 9. The maximum power factor occurs when the phase angle is a. 0o b. 30o c. 45o d. 90o

  39. Quiz 10. When power is calculated from voltage and current for an ac circuit, the voltage and current should be expressed as a. average values b. rms values c. peak values d. peak-to-peak values

  40. Quiz Answers: 1. a 2. b 3. c 4. c 5. d 6. a 7. d 8. d 9. a 10. b

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