Operational Amplifiers (Op-Amps)
Operational Amplifier (Op-Amp) Not a discrete device (resistor, cap, ind, diode, transistor etc.) IC ! 2-input terminals Inverting and non-inverting Output terminal Two supply terminals Inexpensive – yet very useful in instrumentation applications We will only consider ideal op-amps !
Operational Amplifiers (Op-Amps)
Ideal Op-Amps 5 characteristics Infinite open-loop voltage gain Infinite input impedance Zero output impedance Infinite bandwidth Zero input voltage offset
A Simple Model for the Op-Amp Very High Gain amplifier with a high input and low output resistance ! AOL: “Open-Loop” Gain (105- 107) RIN: input resistance (Mohms) ROUT: Output Resistance (10s of ohms)
Input Current (IN) is zero ! Ideal Op-Amps “Golden Rules” Input currents = 0 Difference in input voltages = 0 Input Current (IN) is zero ! V+=V-
Ideal Op-Amps Analysis Procedure Calculate the input voltage Write node equation at op-amp input to find the output voltage
Inverting Amplifier Since Ia = 0, I1 = If Vb = 0 Va = 0 Find the voltage gain Vo/Vi. Calculate the input voltage Write node equation at op-amp input to find the output voltage
Non-Inverting Amplifier Since Ia = 0, I1 = If Vb = Vi Va = Vi Find the voltage gain Vo/Vi. Calculate the input voltage Write node equation at op-amp input to find the output voltage
Integrator By KVL, Vout = –VC
Differentiator
Two-Stage Amplifier Gain = Vo1/Vi Gain = Vo2/Vo1 Total Gain = (Vo1/Vi) (Vo2/Vo1) = Vo2/Vi
Example
Example
Work this Example!_________