# Gain-bandwidth product

The

**gain bandwidth product (GBW or GB)**for an amplifier is the product of the open loop gain (constant for a givenamplifier ) and its 3 dB bandwidth.**Relevance to design**This quantity is commonly specified for

operational amplifier s, and allowscircuit design 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 s to the input and output of an amplifier the gain raises and the bandwidth decreases, but the product remains constant.**Theory**The gain-bandwidth product may be understood from a conservation-of-power viewpoint. The difference between the output signal power and the input signal power can never be greater than the DC power supplied to the amplifier through its bias circuitry. Stated mathematically, if "P"

_{out}is the total output signal power from the amplifier, "P"_{in}is the total signal power input to the amplifier, and "P"_{DC}is the total DC power supplied to the amplifier, then$P\_\{out\}\; -\; P\_\{in\}\; le\; P\_\{DC\}$.

In practice, equality in the above expression is never achieved since the DC bias circuitry supplies DC current as well as DC voltage, and the DC current flows through resistors which convert some of the available electrical energy into heat energy. So, this expression represents a theoretical upper limit on how much amplification ("i"."e"., gain) can be obtained from the device. We may now express the total input and output signal power as an integral over their respective power spectral density functions. If "s"("t") is the input signal as a function of time, and "S"(ω) is the signal as a function of frequency ("i"."e"., the

Fourier transform of "s"("t"), or the powerspectral density of the input signal), then if "G"(ω) is the gain of the amplifier as a function of frequency, the equation above can be rewritten as:$int\; G(omega\; )\; S(omega)\; ,domega\; -\; int\; S(omega)\; ,domega\; le\; P\_\{DC\}$

or,

$int\; [G(omega\; )-1]\; S(omega)\; ,domega\; le\; P\_\{DC\}$

If the amplifier gain is much greater than unity over its operational bandwidth, this expression can be approximated as:

$int\; G(omega\; )\; S(omega)\; ,domega\; le\; P\_\{DC\}$

If we denote the amplifier bandwidth as BW, then if both the gain and the signal spectra are constant over the bandwidth BW (at "G" and S respectively), then the equation above becomes:

$G\; imes\; BW\; le\; P\_\{DC\}/S$

and we see the origin of the gain-bandwidth product limit for amplifiers. The available DC power to the amplifier can either be put to use as high signal gain over a limited bandwidth or limited gain over a wide bandwidth. We also note that for fixed DC input power, the greatest signal gains are achieved with weak input signals. To get high gains in already amplified signals (as in output stages), increased amounts of DC power must be used.

**Examples**If the GBWP of an op-amp 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 (GBW product = gain x bandwidth, therefore if BW = 1 MHz, 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 x 10

^{6}.

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Operational amplifier**— A Signetics μa741 operational amplifier, one of the most successful op amps. An operational amplifier ( op amp ) is a DC coupled high gain electronic voltage amplifier with a differential input and, usually, a single ended output.[1] An op amp… … Wikipedia**Fully differential amplifier**— A fully differential amplifier, usually referred to as an FDA for brevity, is a DC coupled high gain electronic voltage amplifier with differential inputs and differential outputs. In its ordinary usage, the output of the FDA is controlled by two … Wikipedia**Logarithmic video amplifier**— A logarithmic video amplifier or LVA is typically part of radar and electronic countermeasures microwave systems and sonar navigation systems, used to convert a very large dynamic range input power to an output voltage that increases… … Wikipedia**Current-feedback operational amplifier**— Representative schematic of a current feedback op amp or amplifier. The current feedback operational amplifier otherwise known as CfoA or CfA is a type of electronic amplifier whose inverting input is sensitive to current, rather than to voltage… … Wikipedia**Distributed amplifier**— Distributed amplifiers are circuit designs that incorporate transmission line theory into traditional amplifier design to obtain a larger gain bandwidth product than is realizable by conventional circuits. N stage traveling wave amplifier … Wikipedia**Adel Sedra**— is an Egyptian electrical engineer whose research specialization is microelectronics, with particular emphasis on applications in communication and instrumentation systems. He received his bachelor of science in electrical engineering from Cairo… … Wikipedia**GB**— may stand for:In geography* Gabon (FIPS 10 4 and NATO (obsolete) country code: GB), a country in Central Africa. * Gambia (ICAO airport designator prefix and WMO country code: GB), a country in West Africa. * Great Britain, an island in Europe.… … Wikipedia**GBW (disambiguation)**— GBW is a three letter acronym that could refer to:* Green Bay and Western Railroad reporting mark|GBW * Glowing Brightwood Staff * Gain bandwidth product (GB or GBW), product of amplifier midband gain and bandwidth (e.g., unity gain frequency of… … Wikipedia**Лавинный фотодиод**— Структура лавинного фотодиода на основе кремния: 1 омические контакты, 2 антиотражающее покрытие Лавинные фотодиоды (ЛФД; англ. avalanche photodiode APD) высокочувствительные полупроводниковые приборы, преобразующие… … Википедия**Ampli-op**— Amplificateur opérationnel Pour les articles homonymes, voir Amplificateur. Des amplificateurs opérationnels … Wikipédia en Français