Inverting OP AMP Gain Calculator | Gain, Rf, Rin & Vout

How to use the inverting OP AMP calculator

To use the OP AMP calculator enter three values. The blank field will automatically be calculated. If you fill in all four fields, the last calculated value will be recalculated. You can modify the units using the selectors.

How an inverting OP AMP works

An inverting OP AMP stage produces an output with opposite polarity to the input signal around the reference node. If 'Rf' is larger than 'Ri', the magnitude of the gain is larger; if 'Rf' is smaller, the stage attenuates. In the classic ideal equation, a positive input produces a negative output. In real circuits, the output still remains limited by the supply rails, output swing, input range, and load current. With dual supplies, that negative swing is straightforward. With a single supply, the circuit usually needs a bias or virtual-reference voltage so the signal can swing inside the available output range. The equation of the inverting OP AMP is the following:

A practical note: many common OP AMPs can only source or sink around 20 mA, sometimes less depending on the part. That is enough for signal work, but not for delivering useful power to a load. If what you really need is a stable supply rail or a current-hungry output, the voltage regulator calculator is a much better fit.

If you are still deciding between topologies, compare this stage with the non-inverting OP AMP calculator. When frequency response starts to matter, the loop compensator calculator is usually the next place to look.

$$V_{out} = -V_{in}\cdot\left(\dfrac{R_f}{R_i}\right)$$

Concept of Gain in OP AMPs

The gain of an OP AMP indicates how much the OP AMP amplifies the input signal. In the inverting configuration, the gain depends directly on the ratio between Rf and Ri. This gain can be greater or smaller than one in magnitude. Inverting OP AMPs produce a 180° phase shift and are commonly used in active filters, summing stages, audio mixers, and signal-processing circuits.

Example #1

You have an OP AMP in inverting configuration with 5[V] at the input. 'Rin' is 2k[Ω] and 'Rf' has a value of 4k[Ω]. What will be the value of 'Vout'?

• To calculate the output voltage we use the previous equation and substitute values: $$V_{out} = -V_{in}\cdot\left(\dfrac{R_f}{R_i}\right) = $$
  $$= -5\cdot\left(\dfrac{4000}{2000}\right) = -10[V]$$

Example #2

You want to record audio from a microphone on PC. Your sound card accepts voltages between +5[V] and -5[V], but the output signal of your microphone moves between +15[V] and -15[V], so you have to modify the signal or you could damage the sound card. Thus, you decide to use an OP AMP in inverting configuration. You need to scale the microphone signal by a third. What resistor configuration do you use?

• We can fix one of the two resistances to a value that is convenient for us and calculate the other. For example, we will set 'Rin' to 6k[Ω]. Later we isolate Rf from the equation and substitute: $$R_f = R_i\cdot\left(\dfrac{-V_{out}}{V_{in}}\right)= $$ $$= 6000\cdot\left(\dfrac{-(-5)}{15}\right)= 2K[Ω]$$
• Note that 'Vout' is inverted due to the inverting setting of the OP AMP. Along with the '-' in the equation, we end up with a positive value resistor.

Frequently Asked Questions

• Why is the output voltage negative?
  An inverting amplifier inverts the polarity of the input signal by 180 degrees. If the input is positive, the output is negative, and vice versa. Important: The supply voltages must be sufficient (sufficiently negative) to allow the output to reach the desired negative voltage.
• Can the gain be less than 1?
  Yes, if the feedback resistor (Rf) is smaller than the input resistor (Rin), the gain will be less than 1 (attenuation).
• What determines the input impedance?
  The input impedance is determined primarily by the input resistor (Rin), as the inverting terminal is a virtual ground. This is true as long as the OP AMP is operating within its linear range (not saturated).
• What are common applications of inverting OP AMPs?
  Inverting OP AMPs are commonly used in signal processing applications such as active filters, audio mixers, and instrumentation amplifiers due to their ability to provide precise gain control. With inverting OP AMPs, designers can easily implement functions like summing amplifiers and integrators, making them versatile components in analog circuit design.