## 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)))
Av = (Rin/(Rin+Rsi))*((Rs*Rout)/(Rs+Rout))/(1/gm+((Rs*Rout)/(Rs+Rout)))
This formula uses 6 Variables
Variables Used
Voltage Gain - The Voltage Gain is the ratio of the output voltage to the input voltage.
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) - The Output Resistance is the resistance detected at the end output of the transistor.
Transconductance - (Measured in Siemens) - Transconductance in small signal amplifiers refers to the change in current output for a small change in input voltage. It is a measure of the amplifier's ability to follow small signal variations.
STEP 1: Convert Input(s) to Base Unit
Input Amplifier Resistance: 1.4 Ohm --> 1.4 Ohm No Conversion Required
Self Induced Resistance: 14.3 Ohm --> 14.3 Ohm No Conversion Required
Source Resistance: 12.6 --> No Conversion Required
Output Resistance: 24 Ohm --> 24 Ohm No Conversion Required
Transconductance: 1.57 Siemens --> 1.57 Siemens No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Av = (Rin/(Rin+Rsi))*((Rs*Rout)/(Rs+Rout))/(1/gm+((Rs*Rout)/(Rs+Rout))) --> (1.4/(1.4+14.3))*((12.6*24)/(12.6+24))/(1/1.57+((12.6*24)/(12.6+24)))
Evaluating ... ...
Av = 0.0827896935279485
STEP 3: Convert Result to Output's Unit
0.0827896935279485 --> No Conversion Required
0.0827896935279485 0.08279 <-- Voltage Gain
(Calculation completed in 00.004 seconds)
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## Credits

Created by Ritwik Tripathi
Vellore Institute of Technology (VIT Vellore), Vellore
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## < 15 Small Signal Analysis Calculators

Small Signal Voltage Gain with respect to Input Resistance
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
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
Output Voltage = Transconductance*Critical Voltage*((Source Resistance*Small Signal Resistance)/(Source Resistance+Small Signal Resistance))
Output Voltage of Small Signal P-Channel
Output Voltage = Transconductance*Source to Gate Voltage*((Output Resistance*Drain Resistance)/(Drain Resistance+Output Resistance))
Voltage Gain for Small Signal
Voltage Gain = (Transconductance*(1/((1/Load Resistance)+(1/Drain Resistance))))/(1+(Transconductance*Self Induced Resistance))
Small-Signal Voltage Gain with respect to Drain Resistance
Voltage Gain = -(Transconductance*((Output Resistance *Drain Resistance)/(Output Resistance+Drain Resistance)))
Output Current of Small Signal
Output Current = (-Transconductance*Critical Voltage)*(Drain Resistance/(Load Resistance+Drain Resistance))
Input Current of Small Signal
Input Current Of Small Signal = -(Critical Voltage*((1+Transconductance*Self Induced Resistance)/Self Induced Resistance))
Amplification Factor for Small Signal MOSFET Model
Amplification Factor = 1/Electron Mean Free Path*sqrt((2*Process Transconductance Parameter)/Drain Current)
Transconductance Given Small Signal Parameters
Transconductance = 2*Transconductance Parameter*(DC Component of Gate to Source Voltage-Total Voltage)
Gate to Source Voltage in Small Signal
Critical Voltage = -Input Voltage/(1+Self Induced Resistance*Transconductance)
Voltage Gain using Small Signal
Voltage Gain = Transconductance*1/(1/Load Resistance+1/Finite Resistance)
Small Signal Output Voltage
Output Voltage = Transconductance*Source to Gate Voltage*Load Resistance
Drain Current of MOSFET Small Signal
Drain Current = 1/(Electron Mean Free Path*Output Resistance)
Amplification Factor in Small Signal MOSFET Model
Amplification Factor = Transconductance*Output Resistance

## Small Signal Voltage Gain with respect to Input Resistance Formula

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)))
Av = (Rin/(Rin+Rsi))*((Rs*Rout)/(Rs+Rout))/(1/gm+((Rs*Rout)/(Rs+Rout)))

## 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 Av 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 (Rin), Self Induced Resistance (Rsi), Source Resistance (Rs), Output Resistance (Rout) & Transconductance (gm) 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 -> 0.088458 = (1.4/(1.4+14.3))*((12.6*24)/(12.6+24))/(1/1.57+((12.6*24)/(12.6+24))).

### 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 Av = (Rin/(Rin+Rsi))*((Rs*Rout)/(Rs+Rout))/(1/gm+((Rs*Rout)/(Rs+Rout))) 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, The Output Resistance is the resistance detected at the end output of the transistor & Transconductance in small signal amplifiers refers to the change in current output for a small change in input voltage. It is a measure of the amplifier's ability to follow small signal variations.
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 (Rin), Self Induced Resistance (Rsi), Source Resistance (Rs), Output Resistance (Rout) & Transconductance (gm). 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 2 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)) Let Others Know