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The aim of nodal analysis is to determine the voltage at each node relative ... simultaneous equations to solve. ... Current sources cause no problems.
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Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
Aim of Nodal Analysis
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
The aim of nodal analysis is to determine the voltage at each node relativeto the reference node (or ground). Once you have done this you can easilywork out anything else you need.
Aim of Nodal Analysis
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
The aim of nodal analysis is to determine the voltage at each node relativeto the reference node (or ground). Once you have done this you can easilywork out anything else you need.There are two ways to do this:(1)
Nodal Analysis
(2)
Circuit Manipulation
Reminders: A node is all the points in a circuitthat are directly interconnected.We assume the interconnectionshave zero resistance so all pointswithin a node have the samevoltage. Five nodes:
A,
· · ·
, E
.
Aim of Nodal Analysis
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
The aim of nodal analysis is to determine the voltage at each node relativeto the reference node (or ground). Once you have done this you can easilywork out anything else you need.There are two ways to do this:(1)
Nodal Analysis
(2)
Circuit Manipulation
Reminders: A node is all the points in a circuitthat are directly interconnected.We assume the interconnectionshave zero resistance so all pointswithin a node have the samevoltage. Five nodes:
A,
· · ·
, E
.
Ohm’s Law:
V
BD
=
IR
5
Aim of Nodal Analysis
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
The aim of nodal analysis is to determine the voltage at each node relativeto the reference node (or ground). Once you have done this you can easilywork out anything else you need.There are two ways to do this:(1)
Nodal Analysis
(2)
Circuit Manipulation
Reminders: A node is all the points in a circuitthat are directly interconnected.We assume the interconnectionshave zero resistance so all pointswithin a node have the samevoltage. Five nodes:
A,
· · ·
, E
.
Ohm’s Law:
V
BD
=
IR
5
KVL:
V
BD
=
V
B
−
V
D
KCL:
Total current exiting any closed region is zero.
Nodal Analysis Stage 1: Label Nodes
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
To find the voltage at each node, the firststep is to label each node with its voltageas follows (1) Pick any node as the voltage reference. Label its voltage as
0 V
.
(2) If any fixed voltage sources are connected to a labelled node, label theirother ends by adding the value of the source onto the voltage of thelabelled end.(3) Pick an unlabelled node and label it with
X, Y,...
, then go back to
step (2) until all nodes are labelled.
Nodal Analysis Stage 1: Label Nodes
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
To find the voltage at each node, the firststep is to label each node with its voltageas follows (1) Pick any node as the voltage reference. Label its voltage as
0 V
.
(2) If any fixed voltage sources are connected to a labelled node, label theirother ends by adding the value of the source onto the voltage of thelabelled end.(3) Pick an unlabelled node and label it with
X, Y,...
, then go back to
step (2) until all nodes are labelled.
Nodal Analysis Stage 1: Label Nodes
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
To find the voltage at each node, the firststep is to label each node with its voltageas follows (1) Pick any node as the voltage reference. Label its voltage as
0 V
.
(2) If any fixed voltage sources are connected to a labelled node, label theirother ends by adding the value of the source onto the voltage of thelabelled end. (3) Pick an unlabelled node and label it with
X, Y,...
, then go back to
step (2) until all nodes are labelled.
Nodal Analysis Stage 1: Label Nodes
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
To find the voltage at each node, the firststep is to label each node with its voltageas follows (1) Pick any node as the voltage reference. Label its voltage as
0 V
.
(2) If any fixed voltage sources are connected to a labelled node, label theirother ends by adding the value of the source onto the voltage of thelabelled end. (3) Pick an unlabelled node and label it with
X, Y,...
, then go back to
step (2) until all nodes are labelled.
Nodal Analysis Stage 1: Label Nodes
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
To find the voltage at each node, the firststep is to label each node with its voltageas follows (1) Pick any node as the voltage reference. Label its voltage as
0 V
.
(2) If any fixed voltage sources are connected to a labelled node, label theirother ends by adding the value of the source onto the voltage of thelabelled end. (3) Pick an unlabelled node and label it with
X, Y,...
, then go back to
step (2) until all nodes are labelled.
Nodal Analysis Stage 2: KCL Equations
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
The second step is to write down a KCL equation for each node labelledwith a variable by setting the total current flowing out of the node to zero.For a circuit with
N
nodes and
S
voltage sources you will have
N
−
S
−
1
simultaneous equations to solve. We only have one variable:^ X
−
8
1 k
X
−
0
2 k
X
−
(
−
3 k
= 0
Nodal Analysis Stage 2: KCL Equations
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
The second step is to write down a KCL equation for each node labelledwith a variable by setting the total current flowing out of the node to zero.For a circuit with
N
nodes and
S
voltage sources you will have
N
−
S
−
1
simultaneous equations to solve. We only have one variable:^ X
−
8
1 k
X
−
0
2 k
X
−
(
−
3 k
= 0
Numerator for a resistor is always of the form
X
−
V
N
where
V
N
is the
voltage on the other side of the resistor.
Nodal Analysis Stage 2: KCL Equations
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
The second step is to write down a KCL equation for each node labelledwith a variable by setting the total current flowing out of the node to zero.For a circuit with
N
nodes and
S
voltage sources you will have
N
−
S
−
1
simultaneous equations to solve. We only have one variable:^ X
−
8
1 k
X
−
0
2 k
X
−
(
−
3 k
= 0
⇒
(
X
−
X
X
11
X
= 44
⇒
X
= 4
Numerator for a resistor is always of the form
X
−
V
N
where
V
N
is the
voltage on the other side of the resistor.
Current Sources
Aim of Nodal Analysis Nodal Analysis Stage 1: Nodal Analysis Stage 2: Current Sources Floating Voltage Sources Weighted Average Circuit Digital-to-Analog Dependent Sources Dependent Voltage Universal Nodal Analysis Summary
Current sources cause no problems.
