OpenSpecEngineering

Works out the closed-loop gain of the two basic op-amp amplifiers, inverting and non-inverting, and the output voltage for a given input. It can also run the other way: give a target gain and the input resistor, and it finds the feedback resistor and the nearest standard value. Use it when scaling a sensor signal, setting up a preamp or checking a schematic.

Equations

Inverting: A_v = −R_f/R_in

Non-inverting: A_v = 1 + R_f/R_in

V_out = A_v·V_in

R_f is the feedback resistor, from the output to the inverting (−) input. R_in is the input resistor: in the inverting amplifier it runs from the signal to the − input, and in the non-inverting one from the − input to ground. A_v is the voltage gain and V_in the input voltage. The minus sign means the inverting amplifier flips the signal. Solving for R_f gives R_f = |A_v|·R_in for the inverting amplifier and R_f = (A_v − 1)·R_in for the non-inverting one, which can’t go below a gain of 1. These hold for an ideal op-amp with very high open-loop gain [1]. The nearest standard R_f comes from the chosen IEC 60063 series [2].

Limits and common mistakes

• The output can’t swing past the supply rails. If V_out comes out larger than the supply allows, the real amplifier clips.
• Gain falls with frequency. An op-amp with a gain-bandwidth product of 1 MHz set to a gain of 100 has only about 10 kHz of bandwidth.
• The gain shown when solving for R_f is the target. Fitting the nearest standard R_f changes it slightly; enter the standard value in the first mode to see the real gain.
• The inverting amplifier’s input resistance is only R_in, which loads a weak source. Keep resistors roughly between 1 kΩ and 1 MΩ.

Worked example

A sensor gives up to 75 mV and must be scaled to about 2.5 V for an ADC, a gain of 33 without inversion. R_in is 4.7 kΩ. What feedback resistor is needed?

1. Choose Configuration Non-inverting and Solve for Feedback Resistor (Rf) (given target Gain & Rin).
2. Enter Input resistor (R_in) 4.7 kΩ, Target Gain Magnitude |Av| 33 and Input voltage (V_in) 0.075 V.
3. Choose Also show the nearest standard Rf from (IEC 60063) E24 (±5 %) and press Solve. The Solution shows: Required Rf: 150,400 Ω
   Nearest E24 value (±5 %): 150 kΩ (0.27 % below)
   Gain (A_v): 33
   Output voltage (V_out): 2.475 V
4. To see the gain with the standard part, choose Solve for Gain & Output Voltage (given Rf & Rin), enter Feedback resistor (R_f) 150 kΩ and press Solve: Gain (A_v): 32.9149
   Output voltage (V_out): 2.46862 V

Check by hand: (33 − 1) × 4.7 kΩ = 150.4 kΩ. With 150 kΩ, 1 + 150/4.7 = 32.91, and 32.91 × 75 mV = 2.469 V. That 0.26 % loss of gain is far smaller than the ±5 % tolerance of the resistors themselves.