Lecture 13 Review Operational Amplifiers Operational amplifier examples

Lecture 13 • Review: • 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 3 k load which requires 6 V, but we only have access to a 12 V 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:

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