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General

Op-Amp Gain & Bandwidth Calculator

Calculate op-amp voltage gain, gain in dB, −3 dB bandwidth, and input impedance for inverting, non-inverting, and differential amplifier configurations.

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Formula

Avnon−inv=1+RfRin,Avinv=−RfRin,f−3dB=GBW∣Av∣A_v^{non-inv} = 1 + \frac{R_f}{R_{in}}, \quad A_v^{inv} = -\frac{R_f}{R_{in}}, \quad f_{-3dB} = \frac{GBW}{|A_v|}

Reference: Horowitz & Hill, The Art of Electronics, 3rd ed.

Av— Voltage gain (V/V)
Rf— Feedback resistor (R1) (kΩ)
Rin— Input resistor (R2) (kΩ)
GBW— Gain-bandwidth product (Hz)
f₋₃dB— −3 dB bandwidth (Hz)
Zin— Input impedance (Ω)

How It Works

Op-amp gain calculator computes closed-loop gain for inverting (G = -Rf/Rin) and non-inverting (G = 1 + Rf/Rin) configurations — essential for signal conditioning, instrumentation amplifiers, and active filter design. Analog circuit designers, sensor interface engineers, and audio designers use this to set precise gain stages while managing bandwidth and noise tradeoffs. Per Horowitz & Hill 'Art of Electronics' (3rd ed., Ch.4), the gain-bandwidth product (GBW) is constant for voltage-feedback op-amps: GBW = gain × bandwidth. A TL072 with GBW = 3MHz at gain = 100 has bandwidth of only 30kHz. For gains above 10, consider current-feedback amplifiers (AD8009: 1GHz bandwidth independent of gain) or instrumentation amplifiers (AD620: 0.1% gain accuracy).

Worked Example

Design a non-inverting amplifier with gain = 10 (20dB) using an OPA2134 (GBW = 8MHz) for audio preamp application. Calculate resistor values: Rf/Rin = G - 1 = 9. Choose Rin = 10kΩ (high enough to minimize loading, low enough for low noise). Then Rf = 90kΩ; use 91kΩ from E96 series. Bandwidth: BW = GBW/G = 8MHz/10 = 800kHz — adequate for 20Hz-20kHz audio with 40× margin. Verify noise: OPA2134 input noise = 8nV/√Hz; at gain = 10, output noise = 80nV/√Hz. Over 20kHz bandwidth: noise = 80nV × √20000 = 11.3μV RMS — equivalent to -98.9dBV, suitable for 16-bit audio (96dB dynamic range).

Practical Tips

  • ✓For gains of 1-10 at audio frequencies, TL07x series ($0.30) offers excellent performance; for gains above 100, use instrumentation amplifiers (INA128: 0.02% gain error)
  • ✓Add 100pF capacitor across Rf for gains > 10 to prevent oscillation — this limits bandwidth to 1/(2πRfCf) but ensures stability per TI application note AN-31
  • ✓For rail-to-rail output swing, use RRIO op-amps (OPA340, MCP6001) — standard op-amps clip 1-2V from supply rails under load

Common Mistakes

  • ✗Ignoring GBW limitations — setting gain = 1000 with GBW = 1MHz yields only 1kHz bandwidth; check GBW on datasheet before selecting gain
  • ✗Using 1% resistors for precision gain — resistor ratio error adds to gain error; use 0.1% resistors for ±0.1% gain accuracy or matched resistor networks
  • ✗Neglecting input bias current — a 1nA bias current through 1MΩ feedback resistor creates 1mV offset; use FET-input op-amps (10pA bias) for high-impedance sources

Frequently Asked Questions

Non-inverting: signal at V+ input, gain = 1 + Rf/Rin, input impedance = op-amp input impedance (10⁶-10¹² Ω). Inverting: signal at V- through Rin, gain = -Rf/Rin, input impedance = Rin. Non-inverting is preferred for high-impedance sources; inverting provides virtual ground for summing applications.
Negative feedback sets closed-loop gain independent of open-loop gain (typically 10⁵-10⁶). The feedback fraction β = Rin/(Rf+Rin) determines gain: G = 1/β for non-inverting. Loop gain Aβ > 1000 ensures <0.1% gain error from ideal. Positive feedback causes oscillation — avoid.
GBW product limits small-signal bandwidth: BW = GBW/gain. Slew rate limits large-signal bandwidth: SR_min = 2πfVpeak. For 10Vpeak at 100kHz: SR > 6.3V/μs. TL072 (SR = 13V/μs) handles this; LM358 (SR = 0.5V/μs) does not — output will be triangular instead of sinusoidal.
Yes — most op-amps are DC-coupled with bandwidth extending to 0Hz. However, input offset voltage (1-10mV typical) and offset drift (1-20μV/°C) cause DC errors. For precision DC: use chopper-stabilized op-amps (LTC2050: 3μV offset, 30nV/°C drift) or auto-zero types (OPA2188).
Match specs to requirements: GBW > gain × bandwidth; slew rate > 2πfVpeak; input noise < signal/SNR target; supply voltage compatible with system. For battery-powered: low quiescent current (MCP6001: 100μA). For high-speed: current-feedback (AD8009: 1GHz). For precision: low offset (OPA2188: 25μV).

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