Inverting Amplifier Gain Calculator With Frequency

Inverting Amplifier Gain:

\[ Gain = -\frac{R_f}{R_{in}} \]

At DC (frequency = 0 Hz)

\[ Gain(f) = -\frac{R_f}{R_{in}} \times \frac{1}{\sqrt{1 + (2\pi f R_f C_f)^2}} \]

With frequency effects (if capacitor present)

Feedback Resistor (Rf):

ohms

Input Resistor (Rin):

ohms

Frequency:

Feedback Capacitor (Cf - optional):

Farads

DC Gain (without frequency effects):

Calculated Gain:

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1. What is an Inverting Amplifier?

An inverting amplifier is a basic operational amplifier (op-amp) configuration that produces an output that is 180° out of phase with the input. The gain is determined by the ratio of feedback resistor (Rf) to input resistor (Rin).

2. How Does the Calculator Work?

The calculator uses the inverting amplifier gain equation:

\[ Gain = -\frac{R_f}{R_{in}} \]

With frequency effects (if capacitor Cf is present):

\[ Gain(f) = -\frac{R_f}{R_{in}} \times \frac{1}{\sqrt{1 + (2\pi f R_f C_f)^2}} \]

Where:

\( R_f \) — Feedback resistor (ohms)
\( R_{in} \) — Input resistor (ohms)
\( f \) — Frequency (Hz)
\( C_f \) — Feedback capacitor (Farads)

Explanation: The basic gain is determined by the resistor ratio. At higher frequencies, a feedback capacitor will cause the gain to roll off.

3. Importance of Gain Calculation

Details: Accurate gain calculation is crucial for designing amplifier circuits, predicting circuit behavior, and understanding frequency response.

4. Using the Calculator

Tips: Enter resistor values in ohms, frequency in Hz (optional), and capacitor value in Farads (optional). All resistor values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the gain negative?
A: The negative sign indicates phase inversion - the output signal is inverted relative to the input.

Q2: What happens at very high frequencies?
A: With a feedback capacitor, the gain will decrease (roll off) at higher frequencies, typically at 20dB per decade.

Q3: What if I don't enter a capacitor value?
A: The calculator will only compute the DC gain (frequency-independent gain).

Q4: What are typical values for Rf and Rin?
A: Common values range from 1kΩ to 1MΩ, but depend on application. The ratio determines the gain.

Q5: How does this differ from non-inverting amplifier?
A: Non-inverting configuration has positive gain (no phase inversion) and different input impedance characteristics.