Op Amp Gain Bandwidth Calculator
Free Op amp gain bandwidth Calculator for electronics & circuits. Enter variables to compute results with formulas and detailed steps.
Calculator
Adjust values & calculateFrequency Response
Formula
Where GBW is the gain-bandwidth product of the op amp (a fixed specification), and the closed-loop gain determines how much bandwidth is available. For non-inverting circuits, the noise gain equals the signal gain. For inverting circuits, the noise gain is 1 + |signal gain|.
Last reviewed: December 2025
Worked Examples
Example 1: Inverting Amplifier Bandwidth
Example 2: High-Speed Non-Inverting Amplifier
Background & Theory
The Op Amp Gain Bandwidth Calculator applies the following established principles and formulas. Computers represent all information using binary, a base-2 number system consisting solely of the digits 0 and 1, each called a bit. Because long binary strings are unwieldy, programmers routinely use octal (base 8) and hexadecimal (base 16) as compact shorthand. Converting between bases follows a consistent algorithm: divide the source number repeatedly by the target base, collecting remainders in reverse order. Hexadecimal digits A through F represent the values 10 through 15, allowing a single character to encode four binary bits, making it the preferred notation for memory addresses, color codes, and bytecode. Bitwise operations manipulate individual bits within integers. AND produces a 1 only when both input bits are 1, making it useful for masking. OR produces a 1 when either bit is 1 and is used for combining flags. XOR flips bits that differ, enabling simple toggle logic and efficient swap algorithms. NOT inverts every bit (one's complement), while left and right shifts multiply or divide by powers of two in constant time. Data storage units ascend in binary multiples of 1024: 8 bits form one byte, 1024 bytes form one kibibyte (KiB), 1024 KiB form one mebibyte (MiB), and so forth. Hard-drive manufacturers historically use decimal prefixes (1 KB = 1000 bytes), creating the persistent confusion between binary and decimal interpretations of the same label. The IEC standardized the binary prefixes KiB, MiB, GiB, and TiB in 1998 to resolve this ambiguity. Network bandwidth is measured in bits per second (bps), most commonly megabits per second (Mbps) or gigabits per second (Gbps). A 100 Mbps connection transfers 100 million bits every second, equating to roughly 12.5 megabytes per second. IP subnet masks define network boundaries; CIDR notation appends a prefix length (e.g., /24) to an address, indicating how many leading bits are fixed. A /24 subnet contains 256 addresses with 254 usable hosts. Algorithm efficiency is described using Big-O notation, which characterises the worst-case growth of time or space relative to input size. O(1) is constant, O(log n) is logarithmic (binary search), O(n) is linear, and O(n²) is quadratic. Cryptographic hash functions like SHA-256 produce a fixed 256-bit (32-byte) digest regardless of input length. File compression algorithms exploit statistical redundancy to reduce storage footprint, and compression ratio equals the original file size divided by the compressed size.
History
The history behind the Op Amp Gain Bandwidth Calculator traces back through the following developments. The conceptual foundation of modern computing traces back to Charles Babbage, whose Analytical Engine design of 1837 introduced the idea of a general-purpose mechanical computer with separate storage and processing units, including what he called the Store and the Mill. Ada Lovelace wrote what many consider the first algorithm intended for machine execution while annotating a translation of Luigi Menabrea's account of Babbage's work, also recognising the machine's potential to manipulate symbols beyond mere numbers. George Boole published "The Laws of Thought" in 1854, formalising a two-valued algebra of logic that would later map perfectly to electrical circuits. It remained largely a mathematical curiosity until Claude Shannon's landmark 1937 master's thesis demonstrated that Boolean algebra could describe switching circuits, laying the theoretical groundwork for all digital electronics. Shannon's 1948 paper "A Mathematical Theory of Communication" defined the bit as the fundamental unit of information and established information theory as a rigorous discipline. The same year, the transistor was invented at Bell Labs by Bardeen, Brattain, and Shockley, eventually replacing vacuum tubes and enabling miniaturisation at scale. ENIAC, completed in 1945, was one of the first general-purpose electronic computers, occupying 1800 square feet and consuming 150 kilowatts of power while performing roughly 5000 additions per second. The ASCII standard was ratified in 1963, assigning 7-bit codes to 128 characters and enabling interoperability between computers from different manufacturers. Through the 1970s, the microprocessor consolidated an entire CPU onto a single chip; Intel's 4004 in 1971 marked the beginning of this trend. The Apple II launched in 1977 and the IBM PC in 1981 brought computing to homes and offices, triggering a mass-market software industry. Tim Berners-Lee proposed the World Wide Web in 1989 and launched the first website in 1991 at CERN, transforming the internet from an academic and military network into a global information infrastructure. Mobile computing accelerated through the 2000s with smartphones integrating powerful processors, wireless networking, and GPS into pocket-sized devices, extending computation into every facet of daily life and cementing TCP/IP as the universal communications fabric.
Key Features
- Calculate data transfer time for any file size across connection speeds ranging from dial-up to 10Gbps fiber, accounting for protocol overhead and real-world throughput.
- Convert between all storage units (bits, bytes, KB, MB, GB, TB, PB) using both decimal (SI) and binary (IEC) standards to resolve the common confusion between manufacturers and operating systems.
- Compute pixel density (PPI) from screen resolution and physical dimensions, helping users evaluate display sharpness for monitors, phones, and tablets.
- Estimate server rack capacity and RAID configuration outcomes (RAID 0, 1, 5, 6, 10) including usable storage, fault tolerance, and rebuild time.
- Calculate battery life from mAh capacity and device power consumption in milliwatts, with adjustments for screen-on time, background drain, and charge cycle degradation.
- Generate subnet masks, network addresses, broadcast addresses, and host ranges from CIDR notation, supporting both IPv4 and IPv6 planning.
- Quantify the effect of network latency and jitter on real-time applications such as VoIP, gaming, and video conferencing using round-trip time thresholds.
- Estimate monthly cloud infrastructure costs for compute instances, object storage, data egress, and managed databases across major providers.
Frequently Asked Questions
Formula
Bandwidth = GBW / Closed-Loop Gain
Where GBW is the gain-bandwidth product of the op amp (a fixed specification), and the closed-loop gain determines how much bandwidth is available. For non-inverting circuits, the noise gain equals the signal gain. For inverting circuits, the noise gain is 1 + |signal gain|.
Worked Examples
Example 1: Inverting Amplifier Bandwidth
Problem: An LM741 op amp (GBW = 1 MHz) is configured as an inverting amplifier with gain = -10 (Rf=10k, Ri=1k). What is the bandwidth?
Solution: Signal gain = -Rf/Ri = -10k/1k = -10 (magnitude 10)\nNoise gain = 1 + Rf/Ri = 1 + 10 = 11\nBandwidth = GBW / noise gain = 1 MHz / 11 = 90.9 kHz\nGain in dB = 20 log10(10) = 20 dB\nRise time = 0.35 / 90.9e3 = 3.85 microseconds\nPhase at 50 kHz = -arctan(50k/90.9k) = -28.8 degrees
Result: Bandwidth: 90.9 kHz | Rise Time: 3.85 us | Phase at 50kHz: -28.8 deg
Example 2: High-Speed Non-Inverting Amplifier
Problem: An OPA637 (GBW = 80 MHz) is set to non-inverting gain of 5. Find bandwidth and gain at 5 MHz.
Solution: Bandwidth = GBW / gain = 80 MHz / 5 = 16 MHz\nGain at DC = 5 (14 dB)\nAt 5 MHz: gain = 5 / sqrt(1 + (5/16)^2)\n= 5 / sqrt(1 + 0.0977) = 5 / sqrt(1.0977)\n= 5 / 1.0477 = 4.772 (13.57 dB)\nGain reduction = 14 - 13.57 = 0.43 dB\nPhase = -arctan(5/16) = -17.4 degrees
Result: Bandwidth: 16 MHz | Gain at 5MHz: 4.772 (13.57 dB) | Only 0.43 dB rolloff
Frequently Asked Questions
What is gain-bandwidth product (GBW) and why is it constant for op amps?
The gain-bandwidth product is a fundamental specification of operational amplifiers that states the product of closed-loop gain and bandwidth remains approximately constant. If an op amp has a GBW of 1 MHz, it can provide a gain of 10 with a bandwidth of 100 kHz, or a gain of 100 with a bandwidth of 10 kHz. This relationship arises from the single dominant pole in the op amp frequency response, which causes the open-loop gain to roll off at 20 dB per decade (6 dB per octave). The GBW is determined during the IC design process by the internal compensation capacitor. Faster op amps have higher GBW products, with modern high-speed op amps reaching into the GHz range for demanding applications.
How does closed-loop gain affect the available bandwidth of an op amp circuit?
As you increase the closed-loop gain of an op amp circuit, the available bandwidth decreases proportionally according to the GBW relationship: bandwidth = GBW / gain. A unity-gain buffer (gain = 1) has the maximum bandwidth equal to the full GBW. At gain of 10, bandwidth is GBW/10. At gain of 100, bandwidth is GBW/100. This tradeoff is one of the most important considerations in analog circuit design. If you need both high gain and wide bandwidth, you can cascade multiple lower-gain stages. Two stages of gain 10 each (total gain 100) give 10 times more bandwidth than a single stage of gain 100, though at the cost of added noise and complexity.
What is the difference between non-inverting and inverting gain configurations?
In a non-inverting configuration, the closed-loop gain equals 1 + Rf/Ri, where Rf is the feedback resistor and Ri is the input resistor. The output is in phase with the input and the minimum gain is 1 (unity gain follower). In an inverting configuration, the gain equals -Rf/Ri, with the negative sign indicating a 180-degree phase inversion. The noise gain (which determines bandwidth) in the inverting case is (1 + Rf/Ri), which is always one more than the magnitude of the signal gain. This means an inverting amplifier with gain of -1 actually has a noise gain of 2 and therefore half the bandwidth of a non-inverting unity-gain buffer. This distinction between signal gain and noise gain is crucial for correctly predicting bandwidth and stability.
How does the rise time of an op amp circuit relate to its bandwidth?
Rise time (10% to 90% of final value for a step input) and bandwidth are inversely related by the approximation: rise time = 0.35 / bandwidth. This relationship comes from the single-pole response characteristic of feedback amplifiers. A circuit with 100 kHz bandwidth has a rise time of 3.5 microseconds. A 10 MHz bandwidth circuit has a rise time of 35 nanoseconds. This approximation assumes a single-pole rolloff, which is valid for most properly compensated op amp circuits operating within their GBW. For cascaded stages, the overall rise time is approximately the square root of the sum of squares of individual stage rise times. This rise time calculation is essential for digital interface circuits, pulse amplifiers, and data acquisition systems.
What factors should I consider when selecting an op amp for a specific application?
Op amp selection involves balancing multiple specifications against application requirements. For signal bandwidth, ensure the GBW provides adequate bandwidth at your required gain with at least 5-10 times margin. For output swing, verify the slew rate supports your signal amplitude and frequency. For precision applications, consider input offset voltage, bias current, and their temperature drifts. Noise performance matters for low-level signal amplification and is specified as voltage noise density (nV per root Hz) and current noise density. Supply voltage and current consumption determine compatibility with your power supply. Input impedance type (JFET vs bipolar) affects source loading. Output drive capability must match your load impedance. Finally, package, cost, and availability influence the practical selection.
What is noise gain and why does it differ from signal gain in inverting configurations?
Noise gain is the gain that the op amp feedback loop applies to input-referred noise sources and also determines the loop gain and bandwidth. For non-inverting configurations, noise gain equals signal gain (1 + Rf/Ri). For inverting configurations, noise gain equals (1 + Rf/Ri), which is always one more than the magnitude of the signal gain (Rf/Ri). This difference exists because the feedback network attenuates the op amp output differently for signals applied at the non-inverting input (including noise) versus the inverting input. The bandwidth of any op amp circuit is always GBW divided by the noise gain, not the signal gain. This means an inverting amplifier with signal gain of -1 has the same bandwidth as a non-inverting amplifier with gain of +2.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy