6.002x circuits and electronics€¦ · 2 n sinusoidal steady state (sss) reading 13.1, 13.2 + –...
TRANSCRIPT
![Page 1: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/1.jpg)
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6.002x CIRCUITS AND ELECTRONICS
The Impedance Model !!!
Reading: Section 13.3 from text
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n Sinusoidal Steady State (SSS) Reading 13.1, 13.2
+
–
vtVv iI cos+ –
RC
Review
n Focus on sinusoids. n Focus on steady state, only care about vP as vH dies away.
SSS
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3
3
4
Hv
total
Review
Vp contains all the information we need:
p
p
V
V
Amplitude of output cosine
Phase
sneak in Vi e jωt
drive
complex algebra
take real part
The Sneaky Path
Vp
tVi cos Vp cos wt +ÐVpéë ùû
set up DE
usual circuit model
nightmare trig.
1
tj
p eV
RCj
Vi
1
2
Sinusoidal Steady State SSS Approach
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4
transfer function
jHRCjV
V
i
p
1
1
Review Frequency response - magnitude RCj
VV i
p
1
pp VtVv cos
The Frequency View
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5
RC
1
4
2
0
i
p
V
V
1
RCtan 1
The Frequency View
Review
CvOv
BIASV
+ –
+ –
GSC
R
SVFrequency response - phase
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6
Is there an even simpler way to get Vp ?
RCj
VV i
p
1
t
agony
sneaky
approach
Eff
ort
easy
Usual
diff eqn.
approach
? Is there
any even
simpler
way
without
DEs?
RCj
VV i
p
1
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The Impedance Model
Is there an even simpler way to get Vp ?
Consider resistor:
R
Ri+
– RvResistor
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8
The Impedance Model -- Capacitor Consider capacitor:
C
Ci+
– CvCapacitor
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9
The Impedance Model -- Inductor Consider Inductor:
L
Li+
– LvInductor
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10
The Impedance Model -- Inductor Consider Inductor:
L
Li+
– Lv
ts
lL eIi
ts
lL eVv
dt
diLv L
L
Inductor
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inductor resistor capacitor
The Impedance Model -- Summary
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Back to RC example…
+
– Cv
Iv + –
R
C
capacitor
sCZC
1
cCc IZV
impedance
cI
+
– cV CZ
Is there an even simpler way to get Vp ?
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13
Impedance model:
Back to RC example…
+
– Cv
Iv + –
R
C
+
– cViV +
–
RZR
sCZC
1
cI
capacitor
sCZC
1
cCc IZV
impedance
cI
+
– cV CZ
Is there an even simpler way to get Vp ?
![Page 14: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/14.jpg)
14
t
sneaky
approach
Eff
ort
agony
easy
Usual
diff eqn.
approach
There you have it
super
sneaky… no DEs!
Impedance method Today
![Page 15: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/15.jpg)
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Signal Notation
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Impedance Method Summary
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17
Another example, recall series RLC Remember, we want only the steady-state response to sinusoid (SSS)
![Page 18: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/18.jpg)
18
Another example, recall series RLC Remember, we want only the steady-state response to sinusoid (SSS)
![Page 19: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/19.jpg)
19
The Big Picture… Vi coswt Vp cos wt +ÐVpéë ùû
set up DE
usual circuit model
nightmare trig.
Vi e st
drive complex algebra
take real part
complex algebra
impedance-based circuit model
No D.E.s, No trig!
t
agony
sneaky
approach
Eff
ort
easy
Usual
diff eqn.
approach
Super
sneaky…
no DEs
![Page 20: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/20.jpg)
20
Back to
21
L
Rj
LC
L
Rj
V
V
i
r
+ –
L
rI
C +
– rV
iV RLet’s study this transfer function
Review complex algebra in Appendix C of textbook
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21
Graphically
2221 RCLC
RC
V
V
i
r
:Low
:High
:1
LC
Find limit
+ –
L
rI
C +
– rV
iV R
![Page 22: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/22.jpg)
22
Graphically
2221 RCLC
RC
V
V
i
r
:Low
:High
:1
LC
Observe
+ –
L
rI
C +
– rV
iV R
![Page 23: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/23.jpg)
1
Is there an even simpler way to get Vp ?
RCj
VV i
p
1
t
agony
sneaky
approach
Eff
ort
easy
Usual
diff eqn.
approach
? Is there
any even
simpler
way
without
DEs?
RCj
VV i
p
1
![Page 24: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/24.jpg)
1
The Impedance Model
Is there an even simpler way to get Vp ?
Consider resistor:
R
Ri+
– RvResistor
![Page 25: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/25.jpg)
2
The Impedance Model -- Capacitor Consider capacitor:
C
Ci+
– CvCapacitor
![Page 26: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/26.jpg)
3
The Impedance Model -- Inductor Consider Inductor:
L
Li+
– LvInductor
![Page 27: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/27.jpg)
1
The Impedance Model -- Inductor Consider Inductor:
L
Li+
– Lv
ts
lL eIi
ts
lL eVv
dt
diLv L
L
Inductor
![Page 28: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/28.jpg)
2
inductor resistor capacitor
The Impedance Model -- Summary
![Page 29: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/29.jpg)
1
Back to RC example…
+
– Cv
Iv + –
R
C
capacitor
sCZC
1
cCc IZV
impedance
cI
+
– cV CZ
Is there an even simpler way to get Vp ?
![Page 30: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/30.jpg)
1
Impedance model:
Back to RC example…
+
– Cv
Iv + –
R
C
+
– cViV +
–
RZR
sCZC
1
cI
capacitor
sCZC
1
cCc IZV
impedance
cI
+
– cV CZ
Is there an even simpler way to get Vp ?
![Page 31: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/31.jpg)
2
t
sneaky
approach
Eff
ort
agony
easy
Usual
diff eqn.
approach
There you have it
super
sneaky… no DEs!
Impedance method Today
![Page 32: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/32.jpg)
1
Signal Notation
![Page 33: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/33.jpg)
2
Impedance Method Summary
![Page 34: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/34.jpg)
1
Another example, recall series RLC Remember, we want only the steady-state response to sinusoid (SSS)
![Page 35: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/35.jpg)
1
Another example, recall series RLC Remember, we want only the steady-state response to sinusoid (SSS)
![Page 36: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/36.jpg)
1
The Big Picture… Vi coswt Vp cos wt +ÐVpéë ùû
set up DE
usual circuit model
nightmare trig.
Vi e st
drive complex algebra
take real part
complex algebra
impedance-based circuit model
No D.E.s, No trig!
t
agony
sneaky
approach
Eff
ort
easy
Usual
diff eqn.
approach
Super
sneaky…
no DEs
![Page 37: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/37.jpg)
1
Back to
21
L
Rj
LC
L
Rj
V
V
i
r
+ –
L
rI
C +
– rV
iV RLet’s study this transfer function
Review complex algebra in Appendix C of textbook
![Page 38: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/38.jpg)
2
Graphically
2221 RCLC
RC
V
V
i
r
:Low
:High
:1
LC
Find limit
+ –
L
rI
C +
– rV
iV R
![Page 39: 6.002x CIRCUITS AND ELECTRONICS€¦ · 2 n Sinusoidal Steady State (SSS) Reading 13.1, 13.2 + – v v I V i sZt R C Review n Focus on sinusoids. n Focus on steady state, only care](https://reader034.vdocuments.us/reader034/viewer/2022050111/5f48870e77253049e1348696/html5/thumbnails/39.jpg)
1
Graphically
2221 RCLC
RC
V
V
i
r
:Low
:High
:1
LC
Observe
+ –
L
rI
C +
– rV
iV R