107_34 - 1 Electrical Engineering Technology EET 107...

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Unformatted text preview: 1 Electrical Engineering Technology EET 107 Introduction to Circuit Analysis # 34 Professor Robert Herrick Purdue University © EET 107 - 34 Introduction to Circuit Analysis 2 Overview u Capacitive Coupler and Filter u Qualitative RC Transient Response u Switched RC Transient Response Purdue University © EET 107 - 34 Introduction to Circuit Analysis 3 Capacitive Reactance 1 XC = 2π f C c XC = capacitive reactance f = frequency C = capacitance Purdue University © EET 107 - 34 Introduction to Circuit Analysis 4 Capacitive Reactance – Ideal Extremes 1 XC = 2π f C Low frequency High frequency DC f = 0 Hz f = ∞ Hz XC = ∞ Ω XC = 0 Ω OPEN SHORT Purdue University © EET 107 - 34 Introduction to Circuit Analysis 5 Capacitive Reactance – Ideal Models C dc open C ac short Purdue University © EET 107 - 34 Introduction to Circuit Analysis 6 Reactance – Ideal Signal Effects 16 Vdc + 10 V dc − Idc= 0 6 Vdc Blocks DC current dc open 0 V rms Passes AC current i ac short Purdue University © EET 107 - 34 Introduction to Circuit Analysis 7 Ideal Quick Look Frequency Effects C Sine wave f + esupply(t) + vC(t) − R + vR(t) − DC or Ideally for AC low frequency AC open Low f + esupply(t) short R Purdue University © + vR(t) − High f EET 107 - 34 + esupply(t) 0V R + vR(t) − Introduction to Circuit Analysis 8 Reactance – Ideal Signal Effects 10 Vdc 2 Vrms 1 kHz DC C Rload AC +10 Vdc− 10 V open C 0 Vrms + Rload 0Vdc 2 Vrms − Purdue University © + C Rload 2 Vrms − EET 107 - 34 Introduction to Circuit Analysis 9 BJT Amplifier – Coupling Capacitors +Esupply R1 + VR1 − RC + VRC − 0V 0V ein AC coupling capacitor R2 + VR2 − Purdue University © 0V Q RE vout 0V + VRE − EET 107 - 34 AC coupling capacitor Introduction to Circuit Analysis 10 Single Supply Op Amp: 9 V Portable Radio Assume 1 V head room. 1 Vp 0V 1V < vout < 8 V 9V ein + 0V − 2 Vp vout LM741 1V 2 Vp 0V a Ri 1k Purdue University © Rf actual output waveform 0V 1k EET 107 - 34 desired output waveform Introduction to Circuit Analysis 11 Single Supply Op Amp: 4.5 Vdc Offset 5.5 V +9 V 0V −1 V + ein 1Vp 1 kHz 6.5V 4.5 V 1V X C 3.5 V R1 100 k 4.5V +9 V 3 7 + 0V LM741 − 4 R2 100 k 2V 2.5V 6 X + vout 0V C 2 −2V Rf 1 k DC Voltage Divider Ri 1k X Purdue University © C DC open creates a 4.5 Vdc voltage follower EET 107 - 34 Introduction to Circuit Analysis 12 Single Supply Op Amp – AC Signal 5.5 V +9 V 0V −1 V + ein 1Vp 1 kHz 6.5V 4.5 V 1V C 3.5 V R1 100 k R2 100 k 4.5V +9 V 3 2V 2.5V 7 + 0V LM741 − 4 6 vout + C 2 Rf 1 k AC coupling capacitor Purdue University © Ri 1k C AC short AC amplifies EET 107 - 34 0V −2V AC coupling capacitor Introduction to Circuit Analysis 13 Power Supply with Filter Capacitor D e supply DC with ripple Rload Filter capacitor Purdue University © D esupply EET 107 - 34 Vout C Rload Introduction to Circuit Analysis 14 Overview u Capacitive Coupler and Filter u Qualitative RC Transient Response u Switched RC Transient Response Purdue University © EET 107 - 34 Introduction to Circuit Analysis 15 Capacitor key Characteristics - know these ! C • Natural open to fixed DC • Stores charge • Stores voltage V = Q / C • Resists change in voltage • Retains voltage • Returns charge like E source Purdue University © EET 107 - 34 Introduction to Circuit Analysis 16 RC Circuit – switch nomenclature t=0 SW E 10 V • • • • + vR(t) − R 1k t<0 t = 0− t = 0 or t = 0+ t>0 Purdue University © iR( t) iC(t) C 1µ + vC(t) − switch open just before switch closes switch just closed switch closed EET 107 - 34 Introduction to Circuit Analysis 17 RC Circuit for t < 0 for Uncharged cap +10V− t=0 SW E 10 V Purdue University © VC = Q / C = 0C / 1µF = 0V 0V + vR(t) − R 1k iR(t) 0A uncharged capacitor iC(t) C 1µ EET 107 - 34 + vC(t) − 0V Introduction to Circuit Analysis 18 Initial RC Circuit for t = 0 for 0V +10V− t=0 + v R(0) − SW E 10 V R 1k iR(0) 10mA iC(0) + vC(0) = 0 Vdc − C 1µ + 0V short − IC = IR = 10V / 1kΩ = 10mA Purdue University © EET 107 - 34 Introduction to Circuit Analysis 19 Steady State RC Circuit for t >> 0 for 0V +0V− tè∞ + vR(∞) − SW R 1k E 10 V iR(∞) 0mA iC(∞ ) C 1µ + + vC(∞) = 10 Vdc − 10V OPEN − Capacitor is fully charged – acts open ! Purdue University © EET 107 - 34 Introduction to Circuit Analysis 20 RC Circuit - C Voltage vc(t) exponentially increases from 0V to 10V in 5 ms vC(V) 10 0 1 2 3 4 5 t(ms) Exponential growth curve Purdue University © EET 107 - 34 Introduction to Circuit Analysis 21 RC Circuit - R Voltage vR(t) exponentially decreases from 10V to 0V in 5 ms vR(V) 10 0 1 2 3 4 5 t (ms) Exponential decay curve Purdue University © EET 107 - 34 Introduction to Circuit Analysis 22 RC Circuit - R and C Current iC(t)=iR(t) exponentially decrease from 10mA to 0mA in 5 ms iC(mA)=iR(mA) 10 0 1 2 3 4 5 t (ms) Exponential decay curve Purdue University © EET 107 - 34 Introduction to Circuit Analysis 23 RC Circuit - Time Constant t=0 + vR(t) − SW E 10 V • • • • R 1k iR(t) iC(t) C 1µ + vC(t) − τ = RC τ = 1kΩ × 1µF = 1ms Long time = 5τ Cap 99% charged 5τ = 5 × 1ms = 5ms Purdue University © EET 107 - 34 Introduction to Circuit Analysis 24 Overview u Capacitive Coupler and Filter u Qualitative RC Transient Response u Switched RC Transient Response Purdue University © EET 107 - 34 Introduction to Circuit Analysis 25 RC Circuit - exponential function Calculator Key x e 2nd Purdue University © LN EET 107 - 34 Introduction to Circuit Analysis 26 RC Circuit - exponential function Negative Key −x e (−) Purdue University © EET 107 - 34 Unary negative Introduction to Circuit Analysis 27 RC Circuit - exponential function Try it ! e−0 = 1.00 e−1 = 0.37 e−5 = 0.01 e−100 = 0.00 Purdue University © EET 107 - 34 Introduction to Circuit Analysis 28 RC Circuit - exponential sketch with τ = RC e−t/τ 0 1τ 2τ 3τ 4τ 5τ ∞ value e− 0 e−1 e−2 e−3 e−4 e−5 1.00 0.37 0.13 0.05 0.02 0.01 e− ∞ t 0.00 e-t/τ 1.0 0.0 0 τ 2τ 3τ 4τ 5τ t Exponential Decay Curve lll Purdue University © EET 107 - 34 Introduction to Circuit Analysis 29 RC Circuit - exponential function e−t/τ Decaying exponential t goes from 0 e−t/τ As goes from 1 Purdue University © EET 107 - 34 to to ∞ 0 Introduction to Circuit Analysis 30 RC Circuit - exponential sketch with τ = RC 10V ss v(t) Capacitor 10V init v(t) Resistor Exponentially Rising 0V init 1ms 0 τ Curve 0V ss 2τ 3τ 4τ 5τ t Rising Curve Purdue University © EET 107 - 34 (up 63% in τ) τ 2τ 3τ 4τ 5τ (up 99%Curve) in 5 τ Falling 0 t Introduction to Circuit Analysis 31 RC Circuit - exponential sketch with τ = RC v(t) Capacitor 10VExponentially 10V init ss v(t) Resistor Falling Curve 1ms (down 63% in τ) 0V init 0V ss τ 2τ 3τ 4τ 5τ (down 99% in 5 τ) 0 t Rising Curve Purdue University © EET 107 - 34 1ms 0 τ 2τ 3τ 4τ 5τ t Falling Curve Introduction to Circuit Analysis 32 RC Circuit – transient vC(t) t=0 SW Universal expression for Capacitor voltage E 10 V + vR(t) − iR(t ) i C( t) R 1k C 1µ + vC(t) − vC (t) = Vss + (Vinit − Vss) e−t/τ vC (t) = 10V + (0V − 10V) e−t/1ms vC (t) = 10V − 10V e−t/1ms Purdue University © EET 107 - 34 Introduction to Circuit Analysis 33 RC Circuit – transient vC(t) t=0 SW + vR(t) − iR(t ) i C( t) R 1k E 10 V C 1µ + vC(t) − Capacitor voltage values vc(0) = 10V − 10V e−0/1ms = 0V vc(1ms) = 10V − 10V e−1ms/1ms = 6.32V vc(2ms) = 10V − 10V e−2ms/1ms = 8.65V vc(5ms) = 10V − 10V e−5ms/1ms = 9.93V Purdue University © EET 107 - 34 Introduction to Circuit Analysis 34 RC Circuit - C Voltage vc(t) exponentially increases from 0V to 10V in 5 ms vC(V) 10 ∆ = 10V 8.6 6.3 ∆ 0.63 of ∆ 0.63 of ∆ 0 0 1 2 3 4 5 t(ms) Exponential growth curve Purdue University © EET 107 - 34 Introduction to Circuit Analysis 35 Quick Sketch - rising curve Rising Curve Over τ Start at INIT value then and Up 63% of remaining change and plot the point. Repeat from each new point. Purdue University © EET 107 - 34 Introduction to Circuit Analysis 36 RC Circuit − transient iC(t) t=0 SW E 10 V Universal expression for Capacitor current + vR(t) − iR(t ) i C( t) R 1k C 1µ + vC(t) − ic(t) = Iss + (Iinit − Iss) e−t/τ ic(t) = 0mA + (10mA − 0mA) e−t/1ms ic(t) = 10mA e−t/1ms Purdue University © EET 107 - 34 Introduction to Circuit Analysis 37 RC Circuit – transient iC(t) t=0 SW E 10 V + vR(t) − iR(t ) i C( t) R 1k C 1µ + vC(t) − Capacitor current values iC(0) = 10mA e−0 /1ms = 10mA iC(1ms) = 10mA e−1ms/1ms = 3.68mA iC(2ms) = 10mA e−2ms/1ms = 2.33mA iC(5ms) = 10mA e−5ms/1ms = 0.07mA Purdue University © EET 107 - 34 Introduction to Circuit Analysis 38 RC Circuit - R and C Current iC(t)=iR(t) exponentially decrease from 10mA to 0mA in 5 ms iC(mA)=iR(mA) 10 0.63 of ∆ ∆= 10mA 3.7 2.3 0 ∆ 0.63 of ∆ 0 1 2 3 4 5 t (ms) Exponential decay curve Purdue University © EET 107 - 34 Introduction to Circuit Analysis 39 Quick Sketch - falling curve Falling Curve Over τ Start at INIT value then and Down 63% of remaining change and plot the point. Repeat from each new point. Purdue University © EET 107 - 34 Introduction to Circuit Analysis 40 Overview u Capacitive Coupler and Filter u Qualitative RC Transient Response u Switched RC Transient Response Purdue University © EET 107 - 34 Introduction to Circuit Analysis ...
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This note was uploaded on 02/22/2012 for the course ECET 107 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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