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⚡electrical circuits and systems i review

Vout = vin(1 + rf/r1)

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

The equation vout = vin(1 + rf/r1) represents the output voltage of a non-inverting amplifier in an electronic circuit, where vout is the output voltage, vin is the input voltage, rf is the feedback resistor, and r1 is the resistor connected to the ground. This formula highlights how the amplifier can increase the amplitude of the input signal based on the ratio of the feedback resistor to the input resistor. Understanding this relationship is crucial for designing amplifiers that meet specific gain requirements in various applications.

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5 Must Know Facts For Your Next Test

  1. In a non-inverting amplifier configuration, the input signal is applied to the non-inverting terminal of the operational amplifier, allowing for direct amplification without phase inversion.
  2. The gain of a non-inverting amplifier can be adjusted by changing the values of rf and r1, giving designers flexibility in achieving desired amplification levels.
  3. This equation indicates that as the ratio of rf to r1 increases, the output voltage significantly increases, demonstrating the importance of feedback resistance in controlling gain.
  4. The formula assumes ideal conditions where the operational amplifier has infinite input impedance and zero output impedance, leading to accurate gain calculations.
  5. Real-world applications for this configuration include audio amplifiers, signal conditioning circuits, and active filters, highlighting its relevance in practical electronic design.

Review Questions

  • How does changing the values of rf and r1 affect the output voltage in a non-inverting amplifier?
    • Changing the values of rf and r1 directly impacts the gain of the non-inverting amplifier. Increasing rf relative to r1 increases the gain, resulting in a higher output voltage for a given input voltage. Conversely, decreasing rf or increasing r1 will lower the gain and reduce the output voltage. This relationship allows engineers to fine-tune amplifier performance based on specific circuit requirements.
  • Discuss how feedback plays a role in stabilizing the performance of a non-inverting amplifier as described by vout = vin(1 + rf/r1).
    • Feedback in a non-inverting amplifier is essential for controlling and stabilizing its performance. The formula vout = vin(1 + rf/r1) illustrates how feedback resistors determine gain. Properly designed feedback ensures that variations in input voltage or other external factors do not lead to distortion or instability. By adjusting rf and r1, designers can achieve consistent gain across different operating conditions, enhancing overall circuit reliability.
  • Evaluate how understanding vout = vin(1 + rf/r1) contributes to designing effective audio amplification systems.
    • Understanding vout = vin(1 + rf/r1) is vital for designing effective audio amplification systems because it allows engineers to calculate and predict how much an audio signal will be amplified before reaching speakers or further processing stages. By carefully selecting values for rf and r1, designers can optimize gain without introducing unwanted noise or distortion. This understanding also aids in integrating amplifiers into larger audio systems where consistent signal strength is critical for maintaining sound quality across various components.