Lecture 13 Review: Operational amplifier examples Dependent Sources Operational Amplifiers Operational amplifier examples Dependent Sources Related educational materials: Chapter 5.1 - 5.4

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

Lecture 12, example 1

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

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:

Op-amp circuit – Example 1 Find 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: VCCS: CCVS: CCCS:

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

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