Electronics Fundamentals 8 th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. วงจร RC electronics fundamentals circuits, devices, and applications THOMAS L. FLOYD DAVID M. BUCHLA

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. การตอบสนองต่อสัญญาณไซน์ของ วงจร RC เมื่อมีทั้งค่าความต้านทานและค่าการเก็บประจุอยู่ในวงจร อนุกรม มุมของเฟสระหว่างแรงดันที่ป้อนและกระแสรวม จะอยู่ระหว่าง 0  และ 90  ขึ้นอยู่กับค่าของความต้านทาน และค่ารีแอคแตนซ์

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. อิมพีแดนซ์ในวงจรอนุกรม RC ในวงจรอนุกรม RC ค่าอิมพีแดนซ์รวมมีค่าเท่ากับผลรวมของ เฟสเซอร์ของ R และ X C R จะพล็อตตามแนวแกน x ซีกบวก. R X C พล็อตตามแนวแกน y ซีกลบ XCXC Z เปลี่ยนตำแหน่งของเฟสเซอร์ให้เป็น สามเหลี่ยมอิมพีแดนซ์. R XCXC Z Z เป็นเส้นทะแยง มุม

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. R = 1.2 k  X C = 960  จงวาดภาพสามเหลี่ยมอิมพีแดนซ์ และแสดงค่า ของ R = 1.2 k  และ X C = 960  Z = 1.33 k  39 o

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. การวิเคราะห์วงจรอนุกรม RC ใช้กฎของโอห์ม โดยใช้ Z, V, I เนื่องจากในวงจรอนุกรม I มีค่าเท่ากันในทุก ๆ ที่ของ วงจร จึงสามารถหาแรงดันตกคร่อมอุปกรณ์ต่าง ๆ ด้วยค่าอิมพีแดนซ์ของอุปกรณ์ตัวนั้นกับค่าของกระแส

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. จากตัวอย่างที่ผ่านมา สมมติให้กระแสมีค่า 10 mA rms จง วาดเฟสเซอร์ไดอะแกรมของแรงดัน V R = 12 V V C = 9.6 V แรงดันของเฟสเซอร์ไดอะแกรมหาได้จากกฎของโอห์ม ด้วยการคูณอิมพีแดนซ์เฟสเซอร์แต่ละตัวด้วย 10 mA x 10 mA = R = 1.2 k  X C = 960  Z = 1.33 k  39 o V S = 13.3 V 39 o

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. การเปลี่ยนแปลงของมุมเฟสเมื่อเทียบกับ ความถี่ เมื่อความถี่เปลี่ยน สามเหลี่ยมอิมพีแดนซ์ ของวงจรอนุกรม RC ก็จะ เปลี่ยนไปด้วยดังภาพ เนื่องจาก X C จะมีค่า น้อยลง ถ้าเพิ่มความถี่ f ลักษณะแบบนี้เรียกว่า การตอบสนองต่อความถี่ ของวงจร RC

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. การนำไปใช้ งาน R VRVR V out C V in V out V in ถ้ากำหนดความถี่ให้ วงจรอนุกรม RC สามารถใช้ในการ สร้างเฟสล้าหลังได้ด้วยการกำหนดปริมาณของแรงดัน อินพุต และเอาต์พุตที่ได้จากแรงดันตกคร่อมตัวเก็บประจุ วงจรนี้เรียกว่าวงจร low-pass filter เป็นวงจรที่ยอมให้ ความถี่ต่ำผ่านไปได้เท่านั้น

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. R VCVC V out C V in V out V in ในทำนองเดียวกัน ถ้ากลับอุปกรณ์ในวงจร ก็จะได้วงจร high-pass filter วงจรที่ยอมให้ความถี่สูงผ่านไปได้ จาก ความถี่ที่กำหนด (cutoff frequency)

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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 180 o phase shift for the oscillator. Amplifier RfRf R R R CCC Phase-shift network

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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. Admittance is the reciprocal of impedance. Capacitive susceptance is the reciprocal of capacitive reactance.

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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 VSVS G BCBC Y G BCBC From the diagram, the phase angle is

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Summary Sinusoidal response of parallel RC circuits VSVS G BCBC Y G BCBC G is plotted along the positive x-axis. B C is plotted along the positive y-axis. Y is the diagonal Some important points to notice are:

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Summary Sinusoidal response of parallel RC circuits VSVS C 0.01  F Y = 1.18 mS G = 1.0 mS B C = mS Draw the admittance phasor diagram for the circuit. f = 10 kHz R 1.0 k  The magnitude of the conductance and susceptance are:

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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.

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Summary Analysis of parallel RC circuits 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. x 10 V = Y = 1.18 mS G = 1.0 mS B C = mS I R = 10 mA I C = 6.28 mA I S = 11.8 mA

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Summary Phase angle of parallel RC circuits Notice that the formula for capacitive susceptance is the reciprocal of capacitive reactance. Thus B C and I C are directly proportional to f: IRIR ICIC ISIS  As frequency increases, B C and I C must also increase, so the angle between I R and I S must increase.

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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: Z R eq = Z cos  X C(eq) = Z sin 

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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: R1R1 C1C1 R2R2 C2C2 Z1Z1 Z2Z2 The total impedance can be found by converting the parallel components to an equivalent series combination, then adding the result to R 1 and X C1 to get the total reactance.

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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 55 o

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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: V R = 12 V V C = 9.6 V x 10 mA = R = 1.2 k  X C = 960  Z = 1.33 k  39 o V S = 13.3 V 39 o

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Summary The power triangle Multiplying the voltage phasors by I rms gives the power triangle (equivalent to multiplying the impedance phasors by I 2 ). 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. The rms current in the earlier example was 10 mA. Show the power triangle. P true = 120 mW P r = 96 mVAR x 10 mA = 39 o P a = 133 mVA V R = 12 V V C = 9.6 V V S = 13.3 V 39 o

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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.

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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. P true (W) P r (VAR) Some components such as transformers, motors, and generators are rated in VA rather than watts. P a (VA)

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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:

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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:

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Impedance Phase angle Capacitive suceptance (B C ) Admittance (Y) The total opposition to sinusoidal current expressed in ohms. Selected Key Terms The ability of a capacitor to permit current; the reciprocal of capacitive reactance. The unit is the siemens (S). The angle between the source voltage and the total current in a reactive circuit. A measure of the ability of a reactive circuit to permit current; the reciprocal of impedance. The unit is the siemens (S).

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Power factor Frequency response Cutoff frequency The frequency at which the output voltage of a filter is 70.7% of the maximum output voltage. In electric circuits, the variation of the output voltage (or current) over a specified range of frequencies. The relationship between volt-amperes and true power or watts. Volt-amperes multiplied by the power factor equals true power. Selected Key Terms

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Quiz 2. A series RC circuit is driven with a sine wave. If the output voltage is taken across the resistor, the output will a.be in phase with the input. b.lead the input voltage. c.lag the input voltage. d.none of the above

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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 V

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Quiz 5. Admittance is the reciprocal of a. reactance b. resistance c. conductance d. impedance

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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 I R and I S will decrease d. none of the above

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Quiz 9. The maximum power factor occurs when the phase angle is a. 0 o b. 30 o c. 45 o d. 90 o

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. 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

Electronics Fundamentals 8 th edition Floyd/Buchla Chapter 10 © 2010 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Quiz Answers: 1. a 2. b 3. c 4. c 5. d 6. a 7. d 8. d 9. a 10. b