Operational Amplifiers - Differential Amplifiers

Summary

In this educational video, David Williams, an instructor at Okanogan College, explains the workings of a differential amplifier, distinguishing it from a differentiator. He assumes an ideal operational amplifier and uses the superposition principle to demonstrate how the output voltage is proportional to the difference between the two input voltages, V1 and V2. Williams simplifies the concept by showing how the output is affected by each input separately and then combines these effects to reveal the overall operation. He also discusses special cases, such as when all resistors are equal or when specific pairs of resistors are equal, and their impact on the output.

Takeaways

• 🎓 David Williams, an instructor at Okanogan College, introduces the concept of differential amplifiers, emphasizing their distinction from differentiators.
• 🔍 Differential amplifiers are designed to amplify the difference between two input signals, V1 and V2, with the output (V_out) being proportional to this difference.
• 🧠 The explanation assumes an ideal operational amplifier (opamp), characterized by no current flowing into its input terminals and equal voltages at the non-inverting and inverting terminals.
• 🔬 The superposition principle is used to analyze the circuit's behavior by considering one input at a time while grounding the other.
• 🔗 When V2 is grounded (shorted), the circuit behaves as an inverting amplifier, and the output voltage (V_out1) is calculated based on the input V1 and the resistor values.
• 🔄 Reintroducing V2 but grounding V1 allows the calculation of V_out2, which is the output voltage solely due to V2, considering the voltage division across resistors R2 and RG.
• 🔢 The overall output voltage (V_out) is the sum of the individual effects of V1 and V2 on the output, as derived from the resistor ratios and input voltages.
• 💡 In a special case where all resistors are equal, the output voltage is exactly the difference between V2 and V1, simplifying the amplifier's behavior.
• 🔧 Another special configuration is when R1 equals R2 and RF equals RG, but they are not necessarily the same, which results in a gain factor being applied to the difference between the input voltages.
• 📚 The tutorial concludes by reinforcing the understanding of differential amplifiers and hints at further learning in subsequent videos.

Q & A

What is the main difference between a differential amplifier and a differentiator?

A differential amplifier takes the difference between two input signals, whereas a differentiator, also built with op-amps, takes the derivative of an incoming signal.

What assumptions does David Williams make about the op-amp in his explanation?

David Williams assumes that the op-amp is ideal, meaning that the voltage at the non-inverting terminal is equal to the voltage at the inverting terminal, and that no current flows into either terminal.

How does the superposition principle relate to the explanation of the differential amplifier?

The superposition principle is used to analyze the output of the differential amplifier in relation to one input at a time, assuming the other input is grounded, and then combining the effects to understand the overall behavior.

What is the significance of the voltage at the non-inverting terminal being equal to the voltage at the inverting terminal in an ideal op-amp?

In an ideal op-amp, this equality implies that the input impedance is infinite, and thus no current flows into the inputs, which simplifies the analysis of the circuit.

How does the current through R1 relate to the current through RF in the ideal op-amp model?

In the ideal op-amp model, the current through R1 is equal to the current through RF because the inverting terminal is at a virtual ground, and the currents through the feedback network must be conserved.

What is the expression for V_out1 when only V1 is considered in the differential amplifier circuit?

V_out1 is equal to -(RF/R1) * V1, which represents the output voltage due to V1 when V2 is shorted to ground.

How is V_out2 determined when only V2 is considered in the differential amplifier circuit?

V_out2 is determined by the voltage at the non-inverting terminal, which is V2 * RG/(R2 + RG), and is then used to find the output voltage using the relationship between the currents through R1 and RF.

What is the overall expression for V_out in terms of V1 and V2 when both inputs are considered?

The overall V_out is the sum of the individual effects of V1 and V2 on the output, which is V_out = V2 * (RG/(R2 + RG) * (R1 + RF)/R1) - V1 * (RF/R1).

In what special case would the output voltage V_out be exactly the difference between V2 and V1?

The output voltage V_out would be exactly the difference between V2 and V1 if all resistors (R1, R2, RF, RG) are equal in value.

What is the significance of the resistor values in determining the gain of the differential amplifier?

The resistor values determine the gain of the differential amplifier by setting the ratio of the feedback resistor to the input resistor, which can amplify or attenuate the difference between the input voltages.