
The gain–bandwidth product (designated as GBWP, GBW, GBP, or GB) for an
amplifier
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It is a two-port electronic circuit that uses electric power from a power su ...
is a
figure of merit
A figure of merit (FOM) is a performance metric that characterizes the performance of a device, system, or method, relative to its alternatives. Examples
*Absolute alcohol content per currency unit in an alcoholic beverage
*accurizing, Accuracy o ...
calculated by
multiplying
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a '' product''. Multiplication is often de ...
the amplifier's
bandwidth
Bandwidth commonly refers to:
* Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range
* Bandwidth (computing), the rate of data transfer, bit rate or thr ...
and the
gain at which the bandwidth is measured.
For devices such as
operational amplifier
An operational amplifier (often op amp or opamp) is a direct coupling, DC-coupled Electronic component, electronic voltage amplifier with a differential input, a (usually) Single-ended signaling, single-ended output, and an extremely high gain ( ...
s that are designed to have a simple one-pole
frequency
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
response, the gain–bandwidth product is nearly independent of the gain at which it is measured; in such devices the gain–bandwidth product will also be equal to the unity-gain bandwidth of the amplifier (the bandwidth within which the amplifier gain is at least 1).
For an amplifier in which negative feedback reduces the gain to below the
open-loop gain The open-loop gain of an electronic amplifier is the gain obtained when no overall feedback is used in the circuit.
The open-loop gain of many electronic amplifiers is exceedingly high (by design) – an ''ideal'' operational amplifier (op-amp) h ...
, the gain–bandwidth product of the closed-loop amplifier will be approximately equal to that of the open-loop amplifier.
"The parameter characterizing the frequency dependence of the operational amplifier gain is the finite gain–bandwidth product (GB)."
Relevance to design
This quantity is commonly specified for
operational amplifier
An operational amplifier (often op amp or opamp) is a direct coupling, DC-coupled Electronic component, electronic voltage amplifier with a differential input, a (usually) Single-ended signaling, single-ended output, and an extremely high gain ( ...
s, and allows
circuit design
In electrical engineering, the process of circuit design can cover systems ranging from complex electronic systems down to the individual transistors within an integrated circuit. One person can often do the design process without needing a pl ...
ers to determine the maximum gain that can be extracted from the device for a given frequency (or bandwidth) and vice versa.
When adding
LC circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can act ...
s to the input and output of an amplifier the gain rises and the bandwidth decreases, but the product is generally bounded by the gain–bandwidth product.
Examples
If the GBWP of an operational amplifier is 1 MHz, it means that the gain of the device falls to unity at 1 MHz. Hence, when the device is wired for unity gain, it will work up to 1 MHz (GBWP = gain × bandwidth, therefore if BW = 1 MHz, then gain = 1) without excessively distorting the signal. The same device when wired for a gain of 10 will work only up to 100 kHz, in accordance with the GBW product formula. Further, if the maximum frequency of operation is 1 Hz, then the maximum gain that can be extracted from the device is 1.
We can also analytically show that for
frequencies
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
GBWP is constant.
Let
be a first-order transfer function given by:
We will show that:
Proof: We will expand
using
Taylor series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor ser ...
and retain the constant and first term, to obtain:
Example for
Note that the error in this case is only about 2%, for the constant term, and using the second term,
, the error drops to .06%.
Transistors
For
transistor
A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...
s, the current-gain–bandwidth product is known as the or ''transition frequency''.
It is calculated from the low-frequency (a few
kilohertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base ...
) current gain under specified test conditions, and the ''cutoff frequency'' at which the current gain drops by 3 decibels (70% amplitude); the product of these two values can be thought of as the frequency at which the current gain would drop to 1, and the transistor current gain between the cutoff and transition frequency can be estimated by dividing by the frequency. Usually, transistors must be used at frequencies well below to be useful as amplifiers and oscillators.
[Martin Hartley Jones ''A practical introduction to electronic circuits'', Cambridge University Press, 1995 page 148] In a bipolar junction transistor, frequency response declines owing to the internal capacitance of the junctions. The transition frequency varies with collector current, reaching a maximum for some value and declining for greater or lesser collector current.
References
External links
"Op-amp gain-bandwidth-product"masteringelectronicsdesign.com
{{DEFAULTSORT:Gain-bandwidth product
Electronic amplifiers