Gain-Bandwidth Product
GBW = Gain × f
Quick answer
This calculator solves GBW = Gain × f for Gain-Bandwidth Product. With Voltage Gain 0.5, Frequency 100 kHz, the result is 50 kHz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The gain-bandwidth product is a constant for a given op-amp, meaning that as closed-loop gain increases, the usable bandwidth decreases proportionally. An op-amp with a GBW of 10 MHz can provide a gain of 10 up to 1 MHz, a gain of 100 up to 100 kHz, or unity gain up to 10 MHz. This fundamental tradeoff arises from the dominant-pole compensation used to ensure stability in feedback configurations. Selecting an op-amp with sufficient GBW for the required gain at the signal frequency is a critical design step.
Variables
- GBW — Gain-bandwidth product (Hz)
- Gain — Closed-loop voltage gain (V/V, dimensionless)
- f — Maximum usable frequency at that gain (Hz)
Practical Notes
GBW applies to voltage-feedback op-amps with a single dominant pole. Current-feedback op-amps do not follow this rule and can maintain high gain at high frequencies. Common GBW values: LM358 1 MHz, TL072 3 MHz, OPA2134 8 MHz, AD8065 145 MHz. For stability, ensure the loop gain crosses 0 dB at a rate of 20 dB/decade.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| GBW | Gain-Bandwidth Product | MHz | Hz, kHz, MHz, GHz |
| Gain | Voltage Gain | — | — |
| f | Frequency | kHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Voltage Gain 0.5, Frequency 100 kHz
- 2. The relation: GBW = Gain × f
- 3. Substitute: Gain = 0.5, f = 100 kHz
- 4. Result: Gain-Bandwidth Product = 50 kHz
Worked examples
Minimum range
Given: Voltage Gain 0.025, Frequency 100 Hz
Result: Gain-Bandwidth Product = 2.5 Hz
Low range
Given: Voltage Gain 0.25, Frequency 1 kHz
Result: Gain-Bandwidth Product = 0.25 kHz
Typical
Given: Voltage Gain 0.5, Frequency 100 kHz
Result: Gain-Bandwidth Product = 50 kHz
High range
Given: Voltage Gain 0.8, Frequency 0.5 MHz
Result: Gain-Bandwidth Product = 0.4 MHz
Maximum range
Given: Voltage Gain 8, Frequency 5 MHz
Result: Gain-Bandwidth Product = 40 MHz
Solving for each variable
Solve for Gain-Bandwidth Product
Voltage Gain 0.025, Frequency 100 Hz → 2.5 Hz
Solve for Voltage Gain
Gain-Bandwidth Product 100 kHz, Frequency 100 Hz → 1000
Solve for Frequency
Gain-Bandwidth Product 100 kHz, Voltage Gain 0.025 → 4 MHz
How Gain-Bandwidth Product changes with Voltage Gain
| Voltage Gain (input) | Gain-Bandwidth Product (result) |
|---|---|
| 0.05 | 5 kHz |
| 0.125 | 12.5 kHz |
| 0.25 | 25 kHz |
| 0.375 | 37.5 kHz |
| 0.5 | 50 kHz |
| 0.75 | 75 kHz |
| 1 | 100 kHz |
| 2 | 0.2 MHz |
| 3.5 | 0.35 MHz |
| 5 | 0.5 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 50000 |
| kHz | 50 |
| MHz | 0.05 |
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<p><a href="https://vbatpower.com/formulas/opamp-gbw/">Gain-Bandwidth Product</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Gain-Bandwidth Product?
Use GBW = Gain × f. With Voltage Gain 0.5, Frequency 100 kHz, Gain-Bandwidth Product works out to 50 kHz.
What is the formula for Gain-Bandwidth Product?
The formula is GBW = Gain × f. The gain-bandwidth product is a constant for a given op-amp, meaning that as closed-loop gain increases, the usable bandwidth decreases proportionally.
How do you find Voltage Gain when you know the other values?
Rearrange for Voltage Gain: with Gain-Bandwidth Product 100 kHz, Frequency 100 Hz, Voltage Gain is 1000.
How do you find Frequency when you know the other values?
Rearrange for Frequency: with Gain-Bandwidth Product 100 kHz, Voltage Gain 0.025, Frequency is 4 MHz.
What units does Gain-Bandwidth Product use?
Gain-Bandwidth Product is shown in Hz, kHz, MHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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