Operational Amplifiers

Used to amplify signals. Active devices that need their own power sources

Inside

Ideal

• $A=\infty$
• $R_i=\infty$
• $R_o=0$
• $i_p=i_n=0$
• $v_p=v_n$ ($v_{+}=v_{-}$)

Realistic

• Output voltage $v_o$ cannot exceed the supply voltages (rails), it will saturate
• With finite gain $A$, $v_p-v_n$ has a narrow range of linear operation

$$v_o=\{\begin{array}{ll}-V_{CC}& \text{if }A(v_p-v_n)<-V_{CC}\\ A(v_p-v_n)& \text{if }-V_{CC}\le A(v_p-v_n)\le +V_{CC}\\ +V_{CC}& \text{if }A(v_p-v_n)>+V_{CC}\end{array}$$

Feedback Path

Wire from output to input. Since internal amplification, $A$ is bypassed with the rule that $v_p=v_n$, the feedback path provides a way to control the output voltage

Analyzing Ideal

1. Check for a negative feedback path. If it exists, assume the op amp operations in its linear region
2. Write a KCL equation at the inverting input terminal
3. Solve the KCL equation and use the solution to find the op amp’s output voltage.
4. Compare the op amp’s output voltage to the power supply voltages to determine if the op amp is operation in its linear region or if it is saturated

Thevenin Equivalent of Ideal

• $V_{Th}=V_o$, $R_{Th}=R_o=0$
• So the output of an op-amp acts like an ideal voltage source

Operational Amplifier Applications