电路分析英文ecte170-lecture

1、 ECTE170 Lecture 9/111Chapter 15 Boylestad Impedance and phasor diagramsSeries and Parallel AC Circuits2Impedance and Phasor DiagramsResistorBoylestad, Prentice Hall 2007VIVoltage and current are in phase3Impedance and Phasor DiagramsInductorVIBoylestad, Prentice Hall 2007Current lags the voltage by

2、 90 degrees9004Impedance and Phasor DiagramsCapacitorIVBoylestad, Prentice Hall 2007Current leads the voltage by 90 degrees9005Impedance and Phasor DiagramsAn important note on phasor diagrams: Any phasor diagram can be rotated in either direction as long as the relative phase angles (and the magnit

3、udes) of the various phasors are maintained. For example, for the capacitor following can be done.IVIVIV9009009006Example 17Example 28Example 39Example 410Series Connection of ImpedancesResistors, inductors and capacitors can be connected in series to form complex circuits. Since each component can

4、be represented as an impedance, we can draw the following circuit:Z1Z2Z3Total impedance = ZT = Z1 + Z2 + Z3Z1 = R, Z2= jwL, Z3 = 1/jwC11Series Connection of ImpedancesFor a series connection of R, L and CTotal impedance = ZT = R + jwL+1/jwC =R + jXL - jXCRjwL1/jwCZTRjXL-jXCRjXL-jXCZTImpedance diagra

5、m12Series Connection of ImpedancesRjwL1/jwCSupply voltage = VT = VR + VL + VC = IR + I(jXL) + I(- jXC)VTVRVRVLVRVCIRI(jXL)I(-jXC)VTIq- angle between voltage current (power factor angle of the total circuit)I has been selected to be the reference I13Example 5: Series Connection of Impedances14Example

6、 6: Series Connection of Impedances15Voltage Divider RuleExample 15.9,Using the voltage divider rule find the voltage across each element of the circuit16Voltage Divider continued17Voltage Divider RuleVoltage divider rule states:Vx - voltage across one or more elements connected in series that have

7、a total impedance of ZxZT total impedance of all series connected elements VT total voltage across all series connected elements18Example 7: Voltage Divider19Example 7 continued20Example 7 Continued21Example 8: Series Connection of Impedances22Example 8 continued23Example 8 Continued 24Example 8 Con

8、tinued25Example 8 Continued26Example 8 Continued27Frequency response of series circuitsThe behaviour of a series connected R, L and C circuit will depend on the frequency response of the individual components added together using a phasor approach28Frequency response of series circuits at low freque

9、ncies L is less effective and impedance is governed by R and C at high frequencies C is less effective and impedance is governed by R and L29Frequency response of a series R-C circuitFig 15.48, p 655, Bolylestad at low frequencies XC dominates (XC R) and at high frequencies its dominance decreases (

10、XC R)30Frequency response of a series R-C circuitVariation of the magnitude of ZT with frequencyVariation of the angle of ZT with frequency31Frequency response of a series R-L circuitExample 15.12, p 661, Boylestad(a) Determine the frequency at which R = XL(c) Find the total impedance for f =100Hz a

11、nd 40kHz (d) Plot VL vs frequency (e) Find the phase angle of ZT at f = 40kHz. Can the circuit be considered inductive? Why?32Frequency response of a series R-L circuitExample 15.12, p 661, Boylestad.33Example Continued34Example Continued35Example Continued36Parallel AC CircuitsIn general impedances

12、 can be connected in parallel. If Z1, Z2 . ZN are connected in parallel we can write:Fig 15.58, p 664, Bolylestad37Parallel AC CircuitsFor a resistance:For an inductor:For a capacitor:38Parallel AC CircuitsExample 15.13, p 666, Boylestad(a) Calculate the input impedance (b) Draw the impedance diagra

13、m (c) Find the admittance of each element (d) Determine the input admittance and draw the admittance diagram39Example Continued40Example Continued41Parallel AC CircuitsExample 15.14, p 666, Boylestad(a) Calculate the input impedance (b) Draw the impedance diagram (c) Find the admittance of each elem

14、ent (d) Determine the input admittance and draw the admittance diagram42Example Continued43Example Continued44Parallel AC Circuits, more examples45Current Divider Rule46Current Divider Rule47Another Example48Frequency separation Amplifier drives the speakers all connected in parallel through R-L-C c

15、ircuits Each speaker is able to reproduce a range of frequencies only, so divert those frequencies to appropriate speaker Send low frequencies to the woofer and high frequencies to the tweeter and the mid range frequencies to the mid range speaker49Frequency separation Assuming the amplifier to be a voltage source (12V) in series with an internal resistance (8W) (commonly known as the output impedance of the amplifier) the voltage that appear across the 8W speaker can be found out as the frequency varies in the audible range50Frequency separationEquations used to calculate the voltag