30. Inductance.. 1-2. Self & Mutual Inductance Inductance: unit : H (henry)
Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.
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Transcript of Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.
![Page 1: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/1.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Inductance and Capacitance
![Page 2: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/2.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Objectives1. Find the current (voltage) for a capacitance
or inductance given the voltage (current) as a function of time.
2. Compute the capacitance of a parallel-plate capacitor.
3. Compute the stored energy in a capacitance or inductance.
4. Describe typical physical construction of capacitors and inductors
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitors and Capacitance
• Capacitance – the ability of a component to store energy in the form of an electrostatic charge
• Capacitor – is a component designed to provide a specific measure of capacitance
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitors and Capacitance• Capacitor Construction
– Plates
– Dielectric
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitor Charge• Electrostatic Charge Develops• Electrostatic Field Stores energy
Insert Figure 12.2
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitor Discharge
Insert Figure 12.3
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitors and Capacitance
• Capacity – amount of charge that a capacitor can store per unit volt applied
where C = the capacity (or capacitance) of the component, in
coulombs per volt Q = the total charge stored by the component V = the voltage across the capacitor corresponding to the
value of Q
CVQV
QC or
![Page 9: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/9.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
![Page 10: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/10.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitance
Insert Figure 12.4
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitance
• Unit of Measure – farad (F) = 1 coulomb per volt (C/V)
• Capacitor Ratings– Most capacitors rated in the picofarad (pF) to
microfarad (F) range– Capacitors in the millifarad range are commonly rated
in thousands of microfarads: 68 mF = 68,000 F– Tolerance
• Usually fairly poor• Variable capacitors used where exact values required
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitors and Capacitance• Physical Characteristics of Capacitors
where C = the capacity of the component, in farads
(8.85 X 10-12) = the permittivity of a vacuum, in farads per meter (F/m) or expressed as o
r = the relative permittivity of the dielectric A = the area of either plate d = the distance between the plates (i.e., the thickness
of the dielectric)
d
AxC r)1085,8( 12
![Page 13: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/13.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitance of the Parallel-Plate Capacitor
WLAd
AεC
mF 1085.8 120
ε
0 r
![Page 14: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/14.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitance
CvQ
dt
dvCi
0)(0)(
ti
t
tvFor DC
It acts as a voltage source
t
vC
t
Cv
t
Q
![Page 15: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/15.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Voltage in terms of Current
C
tqdtti
Ctv
t
t
0
0
1
0
0
tqdttitqt
t
, q(to) is the initial charge
C
qvCvq ,
0
0
1tvdtti
Ctv
t
t
C
tqtv 00
![Page 16: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/16.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Stored Energy
)()()( titvtp t
tvCti
)(
)(
t
vCvtp
)(
t
t
tv
tv
t
t o oo
Cvdvtwdtdt
dvCvtwdttptw
)(
)()(,)(,)()(
)(2
1)(
2
1)( 22
otCvtCvtw
![Page 17: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/17.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Series Capacitors
• Series Capacitors
Where CT = the total series capacitance Cn = the highest-numbered capacitor in the string
n
T
CCC
C1
.....11
1
21
![Page 18: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/18.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Parallel Capacitors
• Connecting Capacitors in Parallel
where Cn = the highest-numbered capacitor in the parallel
circuit
nT CCCC .....21
![Page 19: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/19.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
![Page 20: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/20.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
![Page 21: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/21.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
![Page 22: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/22.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Inductance
• Unit of Measure – Henry (H)– Inductance is measured in volts per rate of change in
current– When a change of 1A/s induces 1V across an inductor,
the amount of inductance is said to be 1 H
Insert Figure 10.5dt
diLvL
![Page 23: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/23.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Inductance• Induced Voltage
where vL = the instantaneous value of induced voltage L = the inductance of the coil, measured in henries (H)
= the instantaneous rate of change in inductor current (in amperes per second)
dt
diLvL
dt
di
![Page 24: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/24.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
![Page 25: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/25.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Inductance
dt
diLtv
0)(0)(
tvdt
tdiFor DC
It acts as a short circuit
![Page 26: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/26.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Current in terms of Voltage
dttvL
dit
t
ti
ti oo )(
1)(
)(
vdtL
didt
diLv
1,
t
to
o
dttvL
titi )(1
)()(
)()(1
)( o
t
ttidttv
Lti
o
![Page 27: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/27.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Stored Energy
)()()( titvtp dt
tdiLtv
)()(
dt
tditLi
dt
tdiLtitvtitp
)()(
)()()()()(
t
t
ti
ti
t
t o oo
Liditwdtdt
diLitwdttptw
)(
)()(,)(,)()(
)(2
1)(
2
1)( 22
otLitLitw
![Page 28: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/28.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Inductance
Insert Figure 10.8
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Connecting Inductors in Series
• Series-Connected Coils
where Ln = the highest-numbered inductor in the circuit
nT LLLLL ...321
![Page 30: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/30.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Characteristic of Capacitor and Inductor Under AC Excitation
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Connecting Inductors in Parallel• Parallel-Connected Coils
where Ln = the highest-numbered inductor in the circuit
n
T
LLL
L1
....11
1
21
![Page 32: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/32.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Alternating Voltage and Current Characteristics
• AC Coupling and DC Isolation: An Overview– DC Isolation – a capacitor prevents flow of charge once
it reaches its capacity
Insert Figure 12.6
![Page 33: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/33.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
AC Coupling and DC Isolation• AC Coupling – DC offset is blocked
Insert Figure 12.7
![Page 34: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/34.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitor Current
where iC = the instantaneous value of capacitor current C = the capacity of the component(s), in farads
= the instantaneous rate of change in capacitor voltage
dt
dvCiC
dt
dv
![Page 35: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/35.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Alternating Voltage and Current Characteristics
• Sine-Wave Values of
– reaches its maximum value when v = 0
Insert Figure 12.8
dt
dv
dt
dvCiC
dt
dv
![Page 36: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/36.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
The Phase Relationship Between Capacitor Current and Voltage
• Current leads voltage by 90°
• Voltage lags current by 90°
)90sin(
cos/
sin
otCV
tCVdtCdvi
tVv
![Page 37: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/37.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
![Page 38: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/38.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitive Reactance (XC)• Series and Parallel Values of XC
Insert Figure 12.18
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Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitive Reactance (XC)• Capacitor Resistance
– Dielectric Resistance – generally assumed to be infinite
– Effective Resistance – opposition to current, also called capacitive reactance (XC)
Insert Figure 12.15
![Page 40: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/40.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitive Reactance (XC)
• Calculating the Value of XC
CfX
I
VX C
rms
rmsC 2
1or
![Page 41: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/41.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitive Reactance (XC)• XC and Ohm’s Law
– Example: Calculate the total current below
Insert Figure 12.17
mAV
X
VI
FHzfX
c
scc 26.8
121
10,121
)22)(60(2
1
2
1
![Page 42: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/42.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
The Phase Relationship Between Inductor Current and Voltage
• Sine-Wave Values of
– reaches its maximum value when i = 0
Insert Figure 10.9
dt
di
dt
diLvL
![Page 43: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/43.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
The Phase Relationship Between Inductor Current and Voltage
• Voltage leads current by 90°
• Current lags voltage by 90°
)90sin(
cos/
sin
otLI
tLIdtiLdv
tIi
![Page 44: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/44.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Inductive Reactance (XL)• Inductor Opposes Current
Insert Figure 10.15
kmA
V
I
VOpposition
rms
rms 101
10
![Page 45: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/45.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Inductive Reactance (XL)
• Inductive Reactance (XL) – the opposition (in ohms) that an inductor presents to a changing current
• Calculating the Value of XL
LfXI
VX L
rms
rmsL 2or
![Page 46: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/46.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Inductive Reactance (XL)
• XL and Ohm’s Law– Example: Calculate the total current below
mAK
V
X
VI
L
s 121
12
![Page 47: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/47.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Capacitive Versus Inductive Phase Relationships
• Voltage (E) in inductive (L) circuits leads current (I) by 90° (ELI)
• Current (I) in capacitive (C ) circuits leads voltage (E) by 90° (ICE)
![Page 48: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/48.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Alternating Voltage and Current Characteristics
Insert Figure 12.10
![Page 49: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/49.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Figure 4.23
Euler’s identity
tfAtA
f
t
2coscos
2
In Euler expression,
A cos t = Real (Ae j t )
![Page 50: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/50.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
C
tjtj
tj
tj
ZCji
v
vCjiisthatAeCjithenAevif
dt
dvCiCapacitorFor
Aejdt
dy
Aey
1
,,,
,
( it is called the impedance of a capacitor)
L
tjtj
ZLji
vijLv
AeLjvthenAeiif
dt
diLvInductorFor
,
.,
,
( it is called the impedance of an inductor)
![Page 51: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/51.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Figure 4.29
The impedance element
![Page 52: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/52.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Figure 4.33
Impedances of R, L, and C in the complex plane
![Page 53: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/53.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Figure 4.37
![Page 54: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/54.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Figure 4.41
An AC circuit
![Page 55: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/55.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Figure 4.44
AC equivalent circuits
![Page 56: Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Inductance and Capacitance.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d225503460f949f8af8/html5/thumbnails/56.jpg)
Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING
Figure 4.45
Rules for impedance and admittance reduction