Transcript Lecture 1 - Digilent Inc.

Lecture 2
•Review Passive Sign Convention
•Power Generation, Absorption
•Power Sources
•Resistance
•Related educational modules:
–Sections 1.1, 1.2, 1.3
Passive sign convention – review
• Passive sign convention:
• For passive circuit elements, we assume that the current
enters the node with the higher voltage potential
• Your analyses will not be reliable unless you do this correctly
• Examples:
Subscript notation can denote voltage polarity
• Voltage polarity is sometimes indicated by subscript
notation
• The order of the subscripts indicates the polarity
• The first subscript indicates assumed higher-voltage node
• The second subscript is the assumed lower-voltage node
Note:
vBA = -vAB
“Ground”
• Voltages are often represented as relative to “ground”:
• Ground (symbol:
) is a reference voltage; often 0V
• Voltages relative to ground generally not called a voltage
difference; they are a difference relative to zero volts
• Voltages relative to ground often represented with a single
subscript
Power Generation and Dissipation
• Circuit elements can either dissipate or generate
power
• Power is dissipated (or absorbed) if current enters the
positive voltage node
–
• Power is generated (or supplied) if current enters the
negative voltage node
Power Generation and Dissipation
• Power = voltagecurrent (p= vi)
• Power is absorbed if the power is positive (voltage and
current are consistent with the passive sign convention)
• Power is generated if the power is negative (voltage and
current not consistent with the passive sign convention)
6W absorbed
6W generated
Examples
• Determine the power
absorbed by the circuit
element below.
• The circuit element absorbs
10W. Determine the
current in the element.
Power Supplies
• Power supplies provide a source of electrical power
• Conceptual types of power supplies (models of
physical supplies):
• Voltage, current sources
• Independent, dependent sources
• Ideal and non-ideal sources
Independent voltage sources
• Common symbols:
• Independent voltage sources maintain specified
voltage, regardless of the current
Independent voltage sources – continued
• Voltage-current characteristic for constant voltage
source:
VS
i
Power generated
when current is
negative
Power absorbed
when current is
positive
Independent current sources
• Common symbol:
• Independent current sources maintain specified
current, regardless of the voltage
Independent current sources – continued
• Voltage-current characteristic for constant current
source:
v
Power generated
when voltage is
positive
Power absorbed
when voltage is
negative
IS
i
Ideal power sources – limitations
• Ideal sources can provide infinite power
• Voltage sources provide specified voltage, regardless of
the current  current can be infinite  power can be
infinite
• Current sources provide specified current, regardless of
the voltage  voltage can be infinite  power can be
infinite
• These models can be unrealistic
• We will examine more realistic power source models
later
Dependent Power Supplies
• Some active circuit elements can be modeled as
dependent power sources
• The current or voltage delivered by the source is
controlled by a current or voltage somewhere else in the
circuit
• Four possible combinations
•
•
•
•
Voltage controlled voltage source (VCVS)
Current controlled voltage source (CCVS)
Voltage controlled current source (VCCS)
Current controlled current source (CCCS)
Dependent Power Supplies – continued
• Examples:
Resistors
• Circuit symbol:
• Voltage-current
relation (Ohm’s Law):
v( t )  R  i( t )
• R is the resistance
• Units are ohms ()
Resistors – continued
• Notes:
• Resistors can only dissipate energy
• The voltage-current relation is algebraic
Resistor Power Dissipation
• Ohm’s Law:
v( t )  R  i( t )

• Power:
v( t )
i( t ) 
R
p( t )  v( t )  i( t )
• Combining:
v( t )
p( t )  v( t ) 
R
p( t )  i( t )  Ri( t )


v2( t )
p( t ) 
R
p( t )  Ri 2 ( t )
Example
• Determine the power (generated or absorbed) by
the resistor below:
Conservation of energy
• In an electrical circuit, the power generated is the
same as the power absorbed
• Slightly more mathematically,
p 0
All elements
• Recall that power absorbed is positive and power
generated is negative
Conservation of power – example
• Determine the power (absorbed or generated) by the
voltage source VS