Gain Bandwidth Product Calculator

✖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.ⓘ Transconductance [g_m]			+10% -10%
✖Load resistance is the cumulative resistance of a circuit, as seen by the voltage, current, or power source driving that circuit.ⓘ Load Resistance [R_L]			+10% -10%
✖Capacitance is the ratio of the amount of electric charge stored on a conductor to a difference in electric potential.ⓘ Capacitance [C_t]			+10% -10%
✖Gate to Drain Capacitance is defined as the capacitance that is observed between the gate and drain of the Junction of MOSFET.ⓘ Gate to Drain Capacitance [C_gd]			+10% -10%

✖The gain bandwidth product for an amplifier is the product of the amplifier's bandwidth and the gain at which the bandwidth is measured.ⓘ Gain Bandwidth Product [GB]

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Formula

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Gain Bandwidth Product

Formula

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

Example

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

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Gain Bandwidth Product Solution

STEP 0: Pre-Calculation Summary

Formula Used

Gain Bandwidth Product = (Transconductance*Load Resistance)/(2*pi*Load Resistance*(Capacitance+Gate to Drain Capacitance))
GB = (g_m*R_L)/(2*pi*R_L*(C_t+C_gd))
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Gain Bandwidth Product - (Measured in Hertz) - The gain bandwidth product for an amplifier is the product of the amplifier's bandwidth and the gain at which the bandwidth is measured.
Transconductance - (Measured in Siemens) - 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.
Load Resistance - (Measured in Ohm) - Load resistance is the cumulative resistance of a circuit, as seen by the voltage, current, or power source driving that circuit.
Capacitance - (Measured in Farad) - Capacitance is the ratio of the amount of electric charge stored on a conductor to a difference in electric potential.
Gate to Drain Capacitance - (Measured in Farad) - Gate to Drain Capacitance is defined as the capacitance that is observed between the gate and drain of the Junction of MOSFET.

STEP 1: Convert Input(s) to Base Unit

Transconductance: 4.8 Millisiemens --> 0.0048 Siemens (Check conversion here)
Load Resistance: 1.49 Kilohm --> 1490 Ohm (Check conversion here)
Capacitance: 2.889 Microfarad --> 2.889E-06 Farad (Check conversion here)
Gate to Drain Capacitance: 1.345 Microfarad --> 1.345E-06 Farad (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

GB = (g_m*R_L)/(2*pi*R_L*(C_t+C_gd)) --> (0.0048*1490)/(2*pi*1490*(2.889E-06+1.345E-06))

Evaluating ... ...

GB = 180.430733783915

STEP 3: Convert Result to Output's Unit

180.430733783915 Hertz --> No Conversion Required

FINAL ANSWER

180.430733783915 ≈ 180.4307 Hertz <-- Gain Bandwidth Product

(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri

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< Response of Cascode Amplifier Calculators

Gain Bandwidth Product

Go Gain Bandwidth Product = (Transconductance*Load Resistance)/(2*pi*Load Resistance*(Capacitance+Gate to Drain Capacitance))

3-DB Frequency in Design Insight and Trade-Off

Go 3 dB Frequency = 1/(2*pi*(Capacitance+Gate to Drain Capacitance)*(1/(1/Load Resistance+1/Output Resistance)))

Drain Resistance in Cascode Amplifier

Go Drain Resistance = 1/(1/Finite Input Resistance+1/Resistance)

Gain Factor

Go Gain Factor = Amplifier Gain in Mid Band/Mid Band Gain

< Multi Stage Amplifiers Calculators

Gain Bandwidth Product

Go Gain Bandwidth Product = (Transconductance*Load Resistance)/(2*pi*Load Resistance*(Capacitance+Gate to Drain Capacitance))

3-DB Frequency in Design Insight and Trade-Off

Go 3 dB Frequency = 1/(2*pi*(Capacitance+Gate to Drain Capacitance)*(1/(1/Load Resistance+1/Output Resistance)))

Drain Resistance in Cascode Amplifier

Go Drain Resistance = 1/(1/Finite Input Resistance+1/Resistance)

Amplifier Gain given Function of Complex Frequency Variable

Go Amplifier Gain in Mid Band = Mid Band Gain*Gain Factor

Gain Bandwidth Product Formula

Gain Bandwidth Product = (Transconductance*Load Resistance)/(2*pi*Load Resistance*(Capacitance+Gate to Drain Capacitance))
GB = (g_m*R_L)/(2*pi*R_L*(C_t+C_gd))

What is CS amplifier?

In electronics, a common-source amplifier is one of three basic single-stage field-effect transistor (FET) amplifier topologies, typically used as a voltage or transconductance amplifier. The easiest way to tell if a FET is a common source, common drain, or common gate is to examine where the signal enters and leaves.

How to Calculate Gain Bandwidth Product?

Gain Bandwidth Product calculator uses Gain Bandwidth Product = (Transconductance*Load Resistance)/(2*pi*Load Resistance*(Capacitance+Gate to Drain Capacitance)) to calculate 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 calculate Gain Bandwidth Product using this online calculator? To use this online calculator 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. Here is how the Gain Bandwidth Product calculation can be explained with given input values -> 180.4307 = (0.0048*1490)/(2*pi*1490*(2.889E-06+1.345E-06)).

FAQ

What is 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 and is represented as GB = (g_m*R_L)/(2*pi*R_L*(C_t+C_gd)) or Gain Bandwidth Product = (Transconductance*Load Resistance)/(2*pi*Load Resistance*(Capacitance+Gate to Drain Capacitance)). 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, Load resistance is the cumulative resistance of a circuit, as seen by the voltage, current, or power source driving that circuit, Capacitance is the ratio of the amount of electric charge stored on a conductor to a difference in electric potential & Gate to Drain Capacitance is defined as the capacitance that is observed between the gate and drain of the Junction of MOSFET.

How to calculate 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 is calculated using Gain Bandwidth Product = (Transconductance*Load Resistance)/(2*pi*Load Resistance*(Capacitance+Gate to Drain Capacitance)). To calculate Gain Bandwidth Product, you need Transconductance (g_m), Load Resistance (R_L), Capacitance (C_t) & Gate to Drain Capacitance (C_gd). With our tool, you need to enter the respective value for Transconductance, Load Resistance, Capacitance & Gate to Drain Capacitance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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