Small Signal Voltage Gain with respect to Input Resistance Calculator

✖The Input Amplifier Resistance is the resistance that opposes the flow of current as it enters the transistor.ⓘ Input Amplifier Resistance [R_in]			+10% -10%
✖Self Induced Resistance is the internal resistance that occurs due to the presence of the FET's own charge carriers (electrons or holes).ⓘ Self Induced Resistance [R_si]			+10% -10%
✖Source Resistance is the amount of resistance applied at the source terminal of the transistor.ⓘ Source Resistance [R_s]			+10% -10%
✖Output resistance refers to the resistance of an electronic circuit to the flow of current when a load is connected to its output.ⓘ Output Resistance [R_out]			+10% -10%
✖Transconductance is defined as the ratio of the change in the output current to the change in the input voltage, with the gate-source voltage held constant.ⓘ Transconductance [g_m]			+10% -10%

✖Voltage gain is a measure of the amplification of an electrical signal by an amplifier . It is the ratio of the output voltage to the input voltage of the circuit, expressed in decibels (dB).ⓘ Small Signal Voltage Gain with respect to Input Resistance [A_v]

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Formula

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Small Signal Voltage Gain with respect to Input Resistance

Formula

`"A"_{"v"} = ("R"_{"in"}/("R"_{"in"}+"R"_{"si"}))*(("R"_{"s"}*"R"_{"out"})/("R"_{"s"}+"R"_{"out"}))/(1/"g"_{"m"}+(("R"_{"s"}*"R"_{"out"})/("R"_{"s"}+"R"_{"out"})))`

Example

`"0.000557"=("1.4kΩ"/("1.4kΩ"+"14.3kΩ"))*(("12.6"*"4.5kΩ")/("12.6"+"4.5kΩ"))/(1/"0.5mS"+(("12.6"*"4.5kΩ")/("12.6"+"4.5kΩ")))`

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Small Signal Voltage Gain with respect to Input Resistance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Voltage Gain = (Input Amplifier Resistance/(Input Amplifier Resistance+Self Induced Resistance))*((Source Resistance*Output Resistance)/(Source Resistance+Output Resistance))/(1/Transconductance+((Source Resistance*Output Resistance)/(Source Resistance+Output Resistance)))
A_v = (R_in/(R_in+R_si))*((R_s*R_out)/(R_s+R_out))/(1/g_m+((R_s*R_out)/(R_s+R_out)))
This formula uses 6 Variables

Variables Used

Voltage Gain - Voltage gain is a measure of the amplification of an electrical signal by an amplifier . It is the ratio of the output voltage to the input voltage of the circuit, expressed in decibels (dB).
Input Amplifier Resistance - (Measured in Ohm) - The Input Amplifier Resistance is the resistance that opposes the flow of current as it enters the transistor.
Self Induced Resistance - (Measured in Ohm) - Self Induced Resistance is the internal resistance that occurs due to the presence of the FET's own charge carriers (electrons or holes).
Source Resistance - Source Resistance is the amount of resistance applied at the source terminal of the transistor.
Output Resistance - (Measured in Ohm) - Output resistance refers to the resistance of an electronic circuit to the flow of current when a load is connected to its output.
Transconductance - (Measured in Siemens) - Transconductance is defined as the ratio of the change in the output current to the change in the input voltage, with the gate-source voltage held constant.

STEP 1: Convert Input(s) to Base Unit

Input Amplifier Resistance: 1.4 Kilohm --> 1400 Ohm (Check conversion here)
Self Induced Resistance: 14.3 Kilohm --> 14300 Ohm (Check conversion here)
Source Resistance: 12.6 --> No Conversion Required
Output Resistance: 4.5 Kilohm --> 4500 Ohm (Check conversion here)
Transconductance: 0.5 Millisiemens --> 0.0005 Siemens (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_v = (R_in/(R_in+R_si))*((R_s*R_out)/(R_s+R_out))/(1/g_m+((R_s*R_out)/(R_s+R_out))) --> (1400/(1400+14300))*((12.6*4500)/(12.6+4500))/(1/0.0005+((12.6*4500)/(12.6+4500)))

Evaluating ... ...

A_v = 0.000556717311951685

STEP 3: Convert Result to Output's Unit

0.000556717311951685 --> No Conversion Required

FINAL ANSWER

0.000556717311951685 ≈ 0.000557 <-- Voltage Gain

(Calculation completed in 00.004 seconds)

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< 15 Small Signal Analysis Calculators

Small Signal Voltage Gain with respect to Input Resistance

Go Voltage Gain = (Input Amplifier Resistance/(Input Amplifier Resistance+Self Induced Resistance))*((Source Resistance*Output Resistance)/(Source Resistance+Output Resistance))/(1/Transconductance+((Source Resistance*Output Resistance)/(Source Resistance+Output Resistance)))

Gate to Source Voltage with respect to Small Signal Resistance

Go Critical Voltage = Input Voltage*((1/Transconductance)/((1/Transconductance)*((Source Resistance*Small Signal Resistance)/(Source Resistance+Small Signal Resistance))))

Common Drain Output Voltage in Small Signal

Go Output Voltage = Transconductance*Critical Voltage*((Source Resistance*Small Signal Resistance)/(Source Resistance+Small Signal Resistance))

Output Voltage of Small Signal P-Channel

Go Output Voltage = Transconductance*Source to Gate Voltage*((Output Resistance*Drain Resistance)/(Drain Resistance+Output Resistance))

Voltage Gain for Small Signal

Go Voltage Gain = (Transconductance*(1/((1/Load Resistance)+(1/Drain Resistance))))/(1+(Transconductance*Self Induced Resistance))

Small-Signal Voltage Gain with respect to Drain Resistance

Go Voltage Gain = (Transconductance*((Output Resistance*Drain Resistance)/(Output Resistance+Drain Resistance)))

Output Current of Small Signal

Go Output Current = (Transconductance*Critical Voltage)*(Drain Resistance/(Load Resistance+Drain Resistance))

Input Current of Small Signal

Go Input Current Of Small Signal = (Critical Voltage*((1+Transconductance*Self Induced Resistance)/Self Induced Resistance))

Amplification Factor for Small Signal MOSFET Model

Go Amplification Factor = 1/Electron Mean Free Path*sqrt((2*Process Transconductance Parameter)/Drain Current)

Transconductance Given Small Signal Parameters

Go Transconductance = 2*Transconductance Parameter*(DC Component of Gate to Source Voltage-Total Voltage)

Gate to Source Voltage in Small Signal

Go Critical Voltage = Input Voltage/(1+Self Induced Resistance*Transconductance)

Voltage Gain using Small Signal

Go Voltage Gain = Transconductance*1/(1/Load Resistance+1/Finite Resistance)

Small Signal Output Voltage

Go Output Voltage = Transconductance*Source to Gate Voltage*Load Resistance

Drain Current of MOSFET Small Signal

Go Drain Current = 1/(Electron Mean Free Path*Output Resistance)

Amplification Factor in Small Signal MOSFET Model

Go Amplification Factor = Transconductance*Output Resistance

Small Signal Voltage Gain with respect to Input Resistance Formula

What is the importance of Small Signal Voltage Gain ?

Small signal voltage gain is important in amplifier design as it determines the amplifier's ability to accurately reproduce small signals without significant distortion. A high small signal voltage gain allows for better signal-to-noise ratio and improved linearity, which are essential for applications such as audio and radio communication.

How to Calculate Small Signal Voltage Gain with respect to Input Resistance?

Small Signal Voltage Gain with respect to Input Resistance calculator uses Voltage Gain = (Input Amplifier Resistance/(Input Amplifier Resistance+Self Induced Resistance))*((Source Resistance*Output Resistance)/(Source Resistance+Output Resistance))/(1/Transconductance+((Source Resistance*Output Resistance)/(Source Resistance+Output Resistance))) to calculate the Voltage Gain, The Small Signal Voltage Gain with respect to Input Resistance formula is defined as the measure of the amplifier's ability to amplify small signals while rejecting large signals. It is defined as the ratio of the output voltage to the input voltage for a small signal input. Voltage Gain is denoted by A_v symbol.

How to calculate Small Signal Voltage Gain with respect to Input Resistance using this online calculator? To use this online calculator for Small Signal Voltage Gain with respect to Input Resistance, enter Input Amplifier Resistance (R_in), Self Induced Resistance (R_si), Source Resistance (R_s), Output Resistance (R_out) & Transconductance (g_m) and hit the calculate button. Here is how the Small Signal Voltage Gain with respect to Input Resistance calculation can be explained with given input values -> 0.000557 = (1.4/(1.4+14.3))*((12.6*4500)/(12.6+4500))/(1/0.0005+((12.6*4500)/(12.6+4500))).

FAQ

What is Small Signal Voltage Gain with respect to Input Resistance?

The Small Signal Voltage Gain with respect to Input Resistance formula is defined as the measure of the amplifier's ability to amplify small signals while rejecting large signals. It is defined as the ratio of the output voltage to the input voltage for a small signal input and is represented as A_v = (R_in/(R_in+R_si))*((R_s*R_out)/(R_s+R_out))/(1/g_m+((R_s*R_out)/(R_s+R_out))) or Voltage Gain = (Input Amplifier Resistance/(Input Amplifier Resistance+Self Induced Resistance))*((Source Resistance*Output Resistance)/(Source Resistance+Output Resistance))/(1/Transconductance+((Source Resistance*Output Resistance)/(Source Resistance+Output Resistance))). The Input Amplifier Resistance is the resistance that opposes the flow of current as it enters the transistor, Self Induced Resistance is the internal resistance that occurs due to the presence of the FET's own charge carriers (electrons or holes), Source Resistance is the amount of resistance applied at the source terminal of the transistor, Output resistance refers to the resistance of an electronic circuit to the flow of current when a load is connected to its output & Transconductance is defined as the ratio of the change in the output current to the change in the input voltage, with the gate-source voltage held constant.

How to calculate Small Signal Voltage Gain with respect to Input Resistance?

The Small Signal Voltage Gain with respect to Input Resistance formula is defined as the measure of the amplifier's ability to amplify small signals while rejecting large signals. It is defined as the ratio of the output voltage to the input voltage for a small signal input is calculated using Voltage Gain = (Input Amplifier Resistance/(Input Amplifier Resistance+Self Induced Resistance))*((Source Resistance*Output Resistance)/(Source Resistance+Output Resistance))/(1/Transconductance+((Source Resistance*Output Resistance)/(Source Resistance+Output Resistance))). To calculate Small Signal Voltage Gain with respect to Input Resistance, you need Input Amplifier Resistance (R_in), Self Induced Resistance (R_si), Source Resistance (R_s), Output Resistance (R_out) & Transconductance (g_m). With our tool, you need to enter the respective value for Input Amplifier Resistance, Self Induced Resistance, Source Resistance, Output Resistance & Transconductance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Voltage Gain?

In this formula, Voltage Gain uses Input Amplifier Resistance, Self Induced Resistance, Source Resistance, Output Resistance & Transconductance. We can use 3 other way(s) to calculate the same, which is/are as follows -

Voltage Gain = (Transconductance*((Output Resistance*Drain Resistance)/(Output Resistance+Drain Resistance)))
Voltage Gain = (Transconductance*(1/((1/Load Resistance)+(1/Drain Resistance))))/(1+(Transconductance*Self Induced Resistance))
Voltage Gain = Transconductance*1/(1/Load Resistance+1/Finite Resistance)

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