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Gain Bandwidth Product Formula

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The gain bandwidth product for an amplifier is the product of the amplifier's bandwidth and the gain at which the bandwidth is measured. Check FAQs

GB = \frac{g m \cdot R L}{2 \cdot π \cdot R L \cdot (C t + C gd)}

GB - Gain Bandwidth Product?g_m - Transconductance?R_L - Load Resistance?C_t - Capacitance?C_gd - Gate to Drain Capacitance?π - Archimedes' constant?

Gain Bandwidth Product Example

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Here is how the Gain Bandwidth Product equation looks like with Values.

Here is how the Gain Bandwidth Product equation looks like with Units.

Here is how the Gain Bandwidth Product equation looks like.

180.4307 = \frac{4.8 \cdot 1.49}{2 \cdot 3.1416 \cdot 1.49 \cdot (2.889 + 1.345)}

180.4307Hz = \frac{4.8mS \cdot 1.49kΩ}{2 \cdot 3.1416 \cdot 1.49kΩ \cdot (2.889μF + 1.345μF)}

180.4307 = \frac{4.8 \cdot 1.49}{2 \cdot 3.1416 \cdot 1.49 \cdot (2.889 + 1.345)}

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Gain Bandwidth Product Solution

Follow our step by step solution on how to calculate Gain Bandwidth Product?

FIRST Step Consider the formula

GB = \frac{g m \cdot R L}{2 \cdot π \cdot R L \cdot (C t + C gd)}

Next Step Substitute values of Variables

∴

GB = \frac{4.8mS \cdot 1.49kΩ}{2 \cdot π \cdot 1.49kΩ \cdot (2.889μF + 1.345μF)}

Next Step Substitute values of Constants

∴

GB = \frac{4.8mS \cdot 1.49kΩ}{2 \cdot 3.1416 \cdot 1.49kΩ \cdot (2.889μF + 1.345μF)}

Next Step Convert Units

∴

GB = \frac{0.0048S \cdot 1490Ω}{2 \cdot 3.1416 \cdot 1490Ω \cdot (2.9E-6F + 1.3E-6F)}

Next Step Prepare to Evaluate

∴

GB = \frac{0.0048 \cdot 1490}{2 \cdot 3.1416 \cdot 1490 \cdot (2.9E-6 + 1.3E-6)}

Next Step Evaluate

∴

GB = 180.430733783915Hz

LAST Step Rounding Answer

∴

GB = 180.4307Hz

Gain Bandwidth Product Formula Elements

Variables

Constants

Gain Bandwidth Product

The gain bandwidth product for an amplifier is the product of the amplifier's bandwidth and the gain at which the bandwidth is measured.

Symbol: GB

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Gain Bandwidth Product

Transconductance

Transconductance is the ratio of the change in current at the output terminal to the change in the voltage at the input terminal of an active device.

Symbol: g_m

Measurement: Electric ConductanceUnit: mS

Note: Value should be greater than 0.

Formulas to find Transconductance

Load Resistance

Load resistance is the cumulative resistance of a circuit, as seen by the voltage, current, or power source driving that circuit.

Symbol: R_L

Measurement: Electric ResistanceUnit: kΩ

Note: Value should be greater than 0.

Formulas to find Load Resistance

Capacitance

Capacitance is the ratio of the amount of electric charge stored on a conductor to a difference in electric potential.

Symbol: C_t

Measurement: CapacitanceUnit: μF

Note: Value should be greater than 0.

Formulas to find Capacitance

Gate to Drain Capacitance

Gate to Drain Capacitance is defined as the capacitance that is observed between the gate and drain of the Junction of MOSFET.

Symbol: C_gd

Measurement: CapacitanceUnit: μF

Note: Value should be greater than 0.

Formulas to find Gate to Drain Capacitance

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Response of Cascode Amplifier category

Go 3-DB Frequency in Design Insight and Trade-Off

f 3dB = \frac{1}{2 \cdot π \cdot (C t + C gd) \cdot (\frac{1}{\frac{1}{R L} + \frac{1}{R out}})}

Go Amplifier Gain given Function of Complex Frequency Variable

A m = A mid \cdot K

Go Drain Resistance in Cascode Amplifier

R d = \frac{1}{\frac{1}{R in} + \frac{1}{R t}}

Go Gain Factor

K = \frac{A m}{A mid}

How to Evaluate Gain Bandwidth Product?

Gain Bandwidth Product evaluator uses Gain Bandwidth Product = (Transconductance*Load Resistance)/(2*pi*Load Resistance*(Capacitance+Gate to Drain Capacitance)) to evaluate the Gain Bandwidth Product, The Gain bandwidth product formula is defined as the product of the open-loop voltage gain and the frequency at which it is measured. GBW is expressed in units of hertz. Gain Bandwidth Product is denoted by GB symbol.

How to evaluate Gain Bandwidth Product using this online evaluator? To use this online evaluator for Gain Bandwidth Product, enter Transconductance (g_m), Load Resistance (R_L), Capacitance (C_t) & Gate to Drain Capacitance (C_gd) and hit the calculate button.

FAQs on Gain Bandwidth Product

What is the formula to find Gain Bandwidth Product?

The formula of Gain Bandwidth Product is expressed as Gain Bandwidth Product = (Transconductance*Load Resistance)/(2*pi*Load Resistance*(Capacitance+Gate to Drain Capacitance)). Here is an example- 180.4307 = (0.0048*1490)/(2*pi*1490*(2.889E-06+1.345E-06)).

How to calculate Gain Bandwidth Product?

With Transconductance (g_m), Load Resistance (R_L), Capacitance (C_t) & Gate to Drain Capacitance (C_gd) we can find Gain Bandwidth Product using the formula - Gain Bandwidth Product = (Transconductance*Load Resistance)/(2*pi*Load Resistance*(Capacitance+Gate to Drain Capacitance)). This formula also uses Archimedes' constant .

Can the Gain Bandwidth Product be negative?

No, the Gain Bandwidth Product, measured in Frequency cannot be negative.

Which unit is used to measure Gain Bandwidth Product?

Gain Bandwidth Product is usually measured using the Hertz[Hz] for Frequency. Petahertz[Hz], Terahertz[Hz], Gigahertz[Hz] are the few other units in which Gain Bandwidth Product can be measured.

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Gain Bandwidth Product Formula

Gain Bandwidth Product Example

Gain Bandwidth Product Solution

Gain Bandwidth Product Formula Elements

Other formulas in Response of Cascode Amplifier category

How to Evaluate Gain Bandwidth Product?

FAQs on Gain Bandwidth Product

Variable Name