Video summary

Electrical Engineering: Ch 5: Operational Amp (18 of 28) Design a Circuit: Example 2

Main summary

Key takeaways

Educational

Main ideas / concepts

  • The video designs a difference amplifier using an operational amplifier to produce a specific weighted output:
    • Goal: (V_{out} = 3V_2 - 5V_1)
  • The standard difference-amplifier formula only works under a specific resistor ratio condition; otherwise, a more general equation must be used.
  • The design process is therefore:
    1. Use the general difference-amplifier equation
    2. Match the coefficients of (V_2) and (V_1) by choosing resistor values
    3. Verify the math and then assign convenient resistor magnitudes

Method / design steps (detailed)

1) Use the correct (general) difference amplifier equation

  • The general form used in the video is: [ V_{out} = \frac{RF}{R1}\left(\frac{1}{1 + \frac{R3}{R4}}\right) V_2 \;-\; \frac{RF}{R1}V_1 ]

  • The video emphasizes this is needed because the coefficient in front of (V_2) is not automatically the same as the coefficient in front of (V_1).

2) Match the coefficient of (V_1)

  • Target coefficient for (V_1) is (-5): [ \frac{RF}{R1} = 5 ]

  • Choose resistor values to satisfy (\frac{RF}{R1} = 5):

    • (RF = 50\,k\Omega)
    • (R1 = 10\,k\Omega)

This gives (\frac{RF}{R1} = 5), ensuring the (-5V_1) term.

3) Match the coefficient of (V_2)

  • After substituting (\frac{RF}{R1}=5), the coefficient on (V_2) becomes: [ 5\cdot \frac{1 + \frac{RF}{R1}}{1 + \frac{R3}{R4}} ]

  • The instructor simplifies it to an intermediate expression leading to: [ \frac{30}{1 + \frac{R3}{R4}} = 3 ]

  • Solve for (\frac{R3}{R4}):

    • Divide both sides by 3: [ \frac{10}{1 + \frac{R3}{R4}} = 1 ]

    • Cross-multiply: [ 10 = 1 + \frac{R3}{R4} ]

    • Subtract 1: [ \frac{R3}{R4} = 9 ]

  • Choose resistor values to satisfy (\frac{R3}{R4} = 9):

    • (R3 = 90\,k\Omega)
    • (R4 = 10\,k\Omega)

4) Verification (substitute the ratios back)

  • With (\frac{RF}{R1}=5) and (\frac{R3}{R4}=9), the coefficients resolve to: [ V_{out} = 3V_2 - 5V_1 ]

5) Final resistor selection (example circuit values)

  • The circuit values provided are:
    • (RF = 50\,k\Omega)
    • (R1 = 10\,k\Omega) (so (RF/R1 = 5))
    • (R3 = 90\,k\Omega)
    • (R4 = 10\,k\Omega) (so (R3/R4 = 9))
  • Conclusion: this resistor set produces exactly the desired output relationship.

Speakers / sources

  • No specific speaker name or external source is identified in the provided subtitles (only “welcome to elect…” / “Elector online” is mentioned as the channel context).

Original video