1. Lecture 13 Review: Operational amplifier examples Dependent Sources
Operational Amplifiers
Operational amplifier examples
Dependent Sources
Related educational materials:
Chapter

2. Operational Amplifiers
Circuit Symbol:
Assume: ip = 0, in = 0; vin = 0; V - < vout < V +

3. Lecture 12, example 1

4. 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
Inverting voltage amplifier

5. 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:

6. Op-amp circuit – Example 1
Find Vout

7. Op-amp circuit – example 2
Find Vout

8. 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

9. Example 2 – revisited
We have a 3k load which requires 6V, but we only have access to a 12V supply.

10. 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)

11. Dependent Sources – circuit symbols
VCVS:
VCCS:
CCVS:
CCCS:

12. Op-amp circuit as dependent source -- example
Inverting voltage amplifier:

13. Analysis of circuits with dependent sources
Can still use:
KVL
KCL
Ohm’s Law
Nodal analysis
Mesh analysis

14. Dependent source analysis – example 1
Find the current, i

15. Dependent source analysis – example 2
Find the voltage, v