Lecture 13
•Review:
•Operational Amplifiers
•Operational amplifier examples
•Dependent Sources
•Related educational modules:
–Sections 1.8.0, 1.8.1, 1.8.2
Operational Amplifiers
• Circuit Symbol:
ip
+
vin
-
in
• Assume: ip = 0, in = 0; vin = 0; V - < vout < V +
Lecture 12, example 1
VOUT
 Rf 
Vin
 
 Rin 
Op-amp circuit applications
• Operational-amplifier based circuits are often used
to implement mathematical operations
• Example:
• The circuit of Lecture 12, example 1 performs
multiplication by a negative constant
VOUT
 Rf 
Vin   KVin
 
 Rin 
• Inverting voltage amplifier
Saturation
• The op-amp output is limited by V+ and V• The operational amplifier output is not purely linear
• If the output reaches the supply “rails”, the output “saturates”
• Lecture 12, Example 1:
VOUT   KVin
Þ
Op-amp circuit – Example 1
• Find Vout
R
R
R
V1 +-
+
V2 +
-
+
VOUT
-
Op-amp circuit – example 2
• Find Vout
Op-amp circuit applications
• Operational-amplifier can be used to isolate
sections of a circuit from one another
• The operational amplifier has a very high input
resistance
• Example:
• The circuit example 2 draws no power from Vin
Example 2 – revisited
• We have a 3k load which requires 6V, but we only have
access to a 12V supply.
Dependent Sources
• Operational amplifier based circuits are often
modeled as dependent sources
• Review: Four types of dependent sources:
•
•
•
•
Voltage controlled voltage source (VCVS)
Current controlled voltage source (CCVS)
Voltage controlled current source (VCCS)
Current controlled current source (CCCS)
Dependent Sources – circuit symbols
• VCVS:
• CCVS:
• VCCS:
• CCCS:
Op-amp circuit as dependent source -- example
• Inverting voltage amplifier:
VOUT
 Rf 
Vin
 
 Rin 
Analysis of circuits with dependent sources
• Can still use:
–
–
–
–
–
KVL
KCL
Ohm’s Law
Nodal analysis
Mesh analysis
Dependent source analysis – example 1
• Find the current, i
Dependent source analysis – example 2
• Find the voltage, v