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electronics fundamentals circuits, devices, and applications THOMAS L. FLOYD DAVID M. BUCHLA วงจร RC Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 การตอบสนองต่อสัญญาณไซน์ของวงจร RC เมื่อมีท้งั ค่าความต้านทานและค่าการเก็บประจุอยูใ่ นวงจรอนุกรม มุมของเฟสระหว่าง แรงดันที่ป้อนและกระแสรวมจะอยูร่ ะหว่าง 0 และ 90 ขึ้นอยูก่ บั ค่าของความ ต้านทานและค่ารี แอคแตนซ์ VR VC V R leads VS V C lags V S R C VS I I leads V S Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 อิมพีแดนซ์ในวงจรอนุกรม RC ในวงจรอนุกรม RC ค่าอิมพีแดนซ์รวมมีค่าเท่ากับผลรวมของเฟสเซอร์ของ R และ XC R จะพล็อตตามแนวแกน x ซีกบวก. XC พล็อตตามแนวแกน y ซีกลบ XC R tan 1 R R Z เป็ นเส้นทะแยงมุม XC XC Z Z เปลี่ยนตาแหน่งของเฟสเซอร์ให้เป็ นสามเหลี่ยม อิมพีแดนซ์. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 จงวาดภาพสามเหลี่ยมอิมพีแดนซ์ และแสดงค่าของ R = 1.2 kW และ XC = 960 W Z 1.2 kW 2 + 0.96 kW 1.33 kW tan 1 0.96 kW 1.2 kW 39 Electronics Fundamentals 8th edition Floyd/Buchla 2 R = 1.2 kW 39o Z = 1.33 kW XC = 960 W © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 การวิเคราะห์วงจรอนุกรม RC ใช้กฎของโอห์ม โดยใช้ Z, V, I V IZ V I Z V Z I เนื่องจากในวงจรอนุกรม I มีค่าเท่ากันในทุก ๆ ที่ของวงจร จึงสามารถหาแรงดัน ตกคร่ อมอุปกรณ์ต่าง ๆ ด้วยค่าอิมพีแดนซ์ของอุปกรณ์ตวั นั้นกับค่าของกระแส Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 จากตัวอย่างที่ผา่ นมา สมมติให้กระแสมีค่า 10 mArms จงวาดเฟสเซอร์ไดอะแกรม ของแรงดัน แรงดันของเฟสเซอร์ไดอะแกรมหาได้จากกฎของโอห์ม ด้วยการคูณอิมพีแดนซ์เฟส เซอร์แต่ละตัวด้วย 10 mA R = 1.2 kW 39o Z = 1.33 kW Electronics Fundamentals 8th edition Floyd/Buchla x 10 mA = XC = 960 W VR = 12 V 39o VS = 13.3 V VC = 9.6 V © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 การเปลี่ยนแปลงของมุมเฟสเมื่อเทียบกับความถี่ เมื่อความถี่เปลี่ยน สามเหลี่ยม อิมพีแดนซ์ของวงจรอนุกรม RC ก็จะ เปลี่ยนไปด้วยดังภาพ เนื่องจาก XC จะมีค่าน้อยลง ถ้าเพิ่มความถี่ f ลักษณะแบบนี้เรี ยกว่า การตอบสนอง ต่อความถี่ของวงจร RC R 3 Increasing f 2 1 Z3 f3 XC 2 f2 XC 1 f1 Z2 Z1 Electronics Fundamentals 8th edition Floyd/Buchla XC 3 © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 การนาไปใช้งาน ถ้ากาหนดความถี่ให้ วงจรอนุกรม RC สามารถใช้ในการสร้างเฟสล้าหลังได้ดว้ ยการ กาหนดปริ มาณของแรงดันอินพุต และเอาต์พตุ ที่ได้จากแรงดันตกคร่ อมตัวเก็บประจุ วงจรนี้เรี ยกว่าวงจร low-pass filter เป็ นวงจรที่ยอมให้ความถี่ต่าผ่านไปได้เท่านั้น V R Vin C Vout VR f (phase lag) Vout Electronics Fundamentals 8th edition Floyd/Buchla Vout f Vin Vin (phase lag) © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 ในทานองเดียวกัน ถ้ากลับอุปกรณ์ในวงจร ก็จะได้วงจร high-pass filter วงจรที่ ยอมให้ความถี่สูงผ่านไปได้ จากความถี่ที่กาหนด (cutoff frequency) C V Vout Vin (phase lead) Vin R Vout Vout VC Electronics Fundamentals 8th edition Floyd/Buchla Vin (phase lead) © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 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 Electronics Fundamentals 8th edition Floyd/Buchla R R © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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. G 1 R 1 BC XC 1 Admittance is the reciprocal of impedance. Y Z Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 Y G2 + BC 2 BC G From the diagram, the phase angle is tan 1 BC Y VS G BC Electronics Fundamentals 8th edition Floyd/Buchla G © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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. BC G tan 1 Y is the diagonal BC Y VS G BC Electronics Fundamentals 8th edition Floyd/Buchla G © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 Summary Sinusoidal response of parallel RC circuits Draw the admittance phasor diagram for the circuit. The magnitude of the conductance and susceptance are: G 1 1 1.0 mS R 1.0 kW Y G 2 + BC 2 BC 2 10 kHz 0.01 mF 0.628 mS 1.0 mS + 0.628 mS 1.18 mS 2 2 BC = 0.628 mS VS f = 10 kHz R 1.0 kW C 0.01 mF Y= 1.18 mS G = 1.0 mS Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 Summary Analysis of parallel RC circuits Ohm’s law is applied to parallel RC circuits using Y, V, and I. V I Y I VY Y I V 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 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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. BC = 0.628 mS Y= 1.18 mS G = 1.0 mS Electronics Fundamentals 8th edition Floyd/Buchla x 10 V = IC = 6.28 mA IS = 11.8 mA IR = 10 mA © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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: BC 2 fC As frequency increases, BC and IC must also increase, so the angle between IR and IS must increase. Electronics Fundamentals 8th edition Floyd/Buchla IC IS IR © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 Z Electronics Fundamentals 8th edition Floyd/Buchla XC(eq) = Z sin © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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. Z1 Z2 For example, the R1 C1 components in the R2 C2 green box are in series: Z1 R12 X C21 The components in the yellow box are R2 X C 2 in parallel: Z 2 R22 X C2 2 Electronics Fundamentals 8th edition Floyd/Buchla 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. © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 20 μs T 8.0 div 160 μs div Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 5 μs t 4.9 div 24.5 μs div The phase shift is calculated from t 24.5 μs o 360 360 55 T 160 μs Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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: R = 1.2 kW 39o Z = 1.33 kW Electronics Fundamentals 8th edition Floyd/Buchla x 10 mA = XC = 960 W VR = 12 V 39o VS = 13.3 V VC = 9.6 V © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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. The rms current in the earlier example was 10 mA. Show the power triangle. VR = 12 V x 10 mA = 39o VS = 13.3 V Electronics Fundamentals 8th edition Floyd/Buchla VC = 9.6 V Ptrue = 120 mW 39o Pa = 133 mVA Pr = 96 mVAR © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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. Some components such as transformers, motors, and generators are rated in VA rather than watts. Electronics Fundamentals 8th edition Floyd/Buchla Ptrue (W) Pa (VA) Pr (VAR) © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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. Vin 10 V dc Vout 10 10VVrms rms 10 V rms 0 10 V dc 100 100W W W 100 20 kHz ƒƒƒ == 110 kHz kHz V 8.46 rms V rms 10 V dc 1.57 0.79V rms 0 11 mm mFF F Vout (V) 9.98 Plotting the response: 8.46 1.57 0.79 9 8 7 6 5 4 3 2 1 0.1 Electronics Fundamentals 8th edition Floyd/Buchla 1 10 20 100 f (kHz) © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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. Vin 10 V dc Vout 10V V rms rms 10 10 V rms 0 10 V dc m F 11mm mF F 1 F ƒ = 100 Hz ƒ = 1 kHz ƒ = 10 kHz 9.87V rms 5.32 V rms 0.63 V rms 100 W W 100 100 100 W 0 V dc Vout (V) 9.87 Plotting the response: 5.32 0.63 Electronics Fundamentals 8th edition Floyd/Buchla 10 9 8 7 6 5 4 3 2 1 0 0.01 0.1 1 10 f (kHz) © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 Selected Key Terms Impedance The total opposition to sinusoidal current expressed in ohms. Phase angle The angle between the source voltage and the total current in a reactive circuit. Capacitive The ability of a capacitor to permit current; suceptance (BC) the reciprocal of capacitive reactance. The unit is the siemens (S). Admittance (Y) A measure of the ability of a reactive circuit to permit current; the reciprocal of impedance. The unit is the siemens (S). Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 Selected Key Terms Power factor The relationship between volt-amperes and true power or watts. Volt-amperes multiplied by the power factor equals true power. Frequency In electric circuits, the variation of the output response voltage (or current) over a specified range of frequencies. Cutoff The frequency at which the output voltage of frequency a filter is 70.7% of the maximum output voltage. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 Quiz 5. Admittance is the reciprocal of a. reactance b. resistance c. conductance d. impedance Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 Quiz 9. The maximum power factor occurs when the phase angle is a. 0o b. 30o c. 45o d. 90o Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 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 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 10 Quiz Answers: Electronics Fundamentals 8th edition Floyd/Buchla 1. a 6. a 2. b 7. d 3. c 8. d 4. c 9. a 5. d 10. b © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved.