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Small Signal Voltage Gain with respect to Input Resistance Formula

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GoVoltage Gain for Small Signal Formula

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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). Check FAQs

A v = (\frac{R in}{R in + R si}) \cdot \frac{\frac{R s \cdot R out}{R s + R out}}{\frac{1}{g m} + (\frac{R s \cdot R out}{R s + R out})}

A_v - Voltage Gain?R_in - Input Amplifier Resistance?R_si - Self Induced Resistance?R_s - Source Resistance?R_out - Output Resistance?g_m - Transconductance?

Small Signal Voltage Gain with respect to Input Resistance Example

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Here is how the Small Signal Voltage Gain with respect to Input Resistance equation looks like with Values.

Here is how the Small Signal Voltage Gain with respect to Input Resistance equation looks like with Units.

Here is how the Small Signal Voltage Gain with respect to Input Resistance equation looks like.

0.0006 = (\frac{1.4}{1.4 + 14.3}) \cdot \frac{\frac{12.6 \cdot 4.5}{12.6 + 4.5}}{\frac{1}{0.5} + (\frac{12.6 \cdot 4.5}{12.6 + 4.5})}

0.0006 = (\frac{1.4kΩ}{1.4kΩ + 14.3kΩ}) \cdot \frac{\frac{12.6 \cdot 4.5kΩ}{12.6 + 4.5kΩ}}{\frac{1}{0.5mS} + (\frac{12.6 \cdot 4.5kΩ}{12.6 + 4.5kΩ})}

0.0006 = (\frac{1.4}{1.4 + 14.3}) \cdot \frac{\frac{12.6 \cdot 4.5}{12.6 + 4.5}}{\frac{1}{0.5} + (\frac{12.6 \cdot 4.5}{12.6 + 4.5})}

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Small Signal Voltage Gain with respect to Input Resistance Solution

Follow our step by step solution on how to calculate Small Signal Voltage Gain with respect to Input Resistance?

FIRST Step Consider the formula

A v = (\frac{R in}{R in + R si}) \cdot \frac{\frac{R s \cdot R out}{R s + R out}}{\frac{1}{g m} + (\frac{R s \cdot R out}{R s + R out})}

Next Step Substitute values of Variables

∴

A v = (\frac{1.4kΩ}{1.4kΩ + 14.3kΩ}) \cdot \frac{\frac{12.6 \cdot 4.5kΩ}{12.6 + 4.5kΩ}}{\frac{1}{0.5mS} + (\frac{12.6 \cdot 4.5kΩ}{12.6 + 4.5kΩ})}

Next Step Convert Units

∴

A v = (\frac{1400Ω}{1400Ω + 14300Ω}) \cdot \frac{\frac{12.6 \cdot 4500Ω}{12.6 + 4500Ω}}{\frac{1}{0.0005S} + (\frac{12.6 \cdot 4500Ω}{12.6 + 4500Ω})}

Next Step Prepare to Evaluate

∴

A v = (\frac{1400}{1400 + 14300}) \cdot \frac{\frac{12.6 \cdot 4500}{12.6 + 4500}}{\frac{1}{0.0005} + (\frac{12.6 \cdot 4500}{12.6 + 4500})}

Next Step Evaluate

∴

A v = 0.000556717311951685

LAST Step Rounding Answer

∴

A v = 0.0006

Small Signal Voltage Gain with respect to Input Resistance Formula Elements

Variables

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).

Symbol: A_v

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Voltage Gain

Input Amplifier Resistance

The Input Amplifier Resistance is the resistance that opposes the flow of current as it enters the transistor.

Symbol: R_in

Measurement: Electric ResistanceUnit: kΩ

Note: Value should be greater than 0.

Formulas to find Input Amplifier Resistance

Self Induced Resistance

Self Induced Resistance is the internal resistance that occurs due to the presence of the FET's own charge carriers (electrons or holes).

Symbol: R_si

Measurement: Electric ResistanceUnit: kΩ

Note: Value should be greater than 0.

Formulas to find Self Induced Resistance

Source Resistance

Source Resistance is the amount of resistance applied at the source terminal of the transistor.

Symbol: R_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Source Resistance

Output Resistance

Output resistance refers to the resistance of an electronic circuit to the flow of current when a load is connected to its output.

Symbol: R_out

Measurement: Electric ResistanceUnit: kΩ

Note: Value should be greater than 0.

Formulas to find Output Resistance

Transconductance

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.

Symbol: g_m

Measurement: Electric ConductanceUnit: mS

Note: Value can be positive or negative.

Formulas to find Transconductance

Other Formulas to find Voltage Gain

Go Small-Signal Voltage Gain with respect to Drain Resistance

A v = (g m \cdot (\frac{R out \cdot R d}{R out + R d}))

Go Voltage Gain for Small Signal

A v = \frac{g m \cdot (\frac{1}{(\frac{1}{R L}) + (\frac{1}{R d})})}{1 + (g m \cdot R si)}

Go Voltage Gain using Small Signal

A v = g m \cdot \frac{1}{\frac{1}{R L} + \frac{1}{R fi}}

Other formulas in Small Signal Analysis category

Go Transconductance Given Small Signal Parameters

g m = 2 \cdot K n \cdot (V gsq - V t)

Go Output Voltage of Small Signal P-Channel

V out = g m \cdot V sg \cdot (\frac{R out \cdot R d}{R d + R out})

Go Small Signal Output Voltage

V out = g m \cdot V sg \cdot R L

Go Common Drain Output Voltage in Small Signal

V out = g m \cdot V c \cdot (\frac{R s \cdot r o}{R s + r o})

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

Small Signal Voltage Gain with respect to Input Resistance evaluator 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 evaluate 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 evaluate Small Signal Voltage Gain with respect to Input Resistance using this online evaluator? To use this online evaluator 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.

FAQs on Small Signal Voltage Gain with respect to Input Resistance

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

The formula of Small Signal Voltage Gain with respect to Input Resistance is expressed as 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))). Here is an example- 0.000557 = (1.4/(1.4+14.3))*((12.6*4500)/(12.6+4500))/(1/0.0005+((12.6*4500)/(12.6+4500))).

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

With Input Amplifier Resistance (R_in), Self Induced Resistance (R_si), Source Resistance (R_s), Output Resistance (R_out) & Transconductance (g_m) we can find Small Signal Voltage Gain with respect to Input Resistance using the 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))).

What are the other ways to Calculate Voltage Gain?

Here are the different ways to Calculate Voltage Gain-

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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Small Signal Voltage Gain with respect to Input Resistance Formula

​GoSmall-Signal Voltage Gain with respect to Drain Resistance Formula

​GoVoltage Gain for Small Signal Formula

Small Signal Voltage Gain with respect to Input Resistance Example

Small Signal Voltage Gain with respect to Input Resistance Solution

Small Signal Voltage Gain with respect to Input Resistance Formula Elements

Other Formulas to find Voltage Gain

Other formulas in Small Signal Analysis category

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

FAQs on Small Signal Voltage Gain with respect to Input Resistance

Variable Name

GoSmall-Signal Voltage Gain with respect to Drain Resistance Formula

GoVoltage Gain for Small Signal Formula