Small Signal Voltage Gain With Respect To Input Resistance Calculator

Formula Used:

\[ Av = \frac{Rin}{Rin + Rsi} \times \frac{\frac{Rs \times Rout}{Rs + Rout}}{\frac{1}{gm} + \frac{Rs \times Rout}{Rs + Rout}} \]

Input Amplifier Resistance (Rin):

Self Induced Resistance (Rsi):

Source Resistance (Rs):

Output Resistance (Rout):

Transconductance (gm):

Voltage Gain (Av):

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1. What Is Small Signal Voltage Gain?

Small Signal 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 as a dimensionless quantity or in decibels (dB).

2. How Does The Calculator Work?

The calculator uses the following formula:

\[ Av = \frac{Rin}{Rin + Rsi} \times \frac{\frac{Rs \times Rout}{Rs + Rout}}{\frac{1}{gm} + \frac{Rs \times Rout}{Rs + Rout}} \]

Where:

\( Rin \) — Input Amplifier Resistance (Ω)
\( Rsi \) — Self Induced Resistance (Ω)
\( Rs \) — Source Resistance (Ω)
\( Rout \) — Output Resistance (Ω)
\( gm \) — Transconductance (S)

Explanation: This formula calculates the voltage gain by considering the input resistance division, the parallel combination of source and output resistances, and the transconductance of the amplifier.

3. Importance Of Voltage Gain Calculation

Details: Accurate voltage gain calculation is crucial for designing and analyzing amplifier circuits, ensuring proper signal amplification, and maintaining signal integrity in electronic systems.

4. Using The Calculator

Tips: Enter all resistance values in ohms (Ω) and transconductance in siemens (S). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is transconductance (gm)?
A: Transconductance is defined as the ratio of the change in output current to the change in input voltage, with the gate-source voltage held constant.

Q2: How does input resistance affect voltage gain?
A: Higher input resistance generally leads to higher voltage gain as it allows more signal voltage to appear at the input of the amplifier.

Q3: What is the significance of source resistance?
A: Source resistance affects how the signal is coupled into the amplifier and can influence both the input impedance and the overall gain.

Q4: When should this formula be used?
A: This formula is particularly useful for analyzing FET amplifier circuits where the input resistance, source resistance, and transconductance play significant roles.

Q5: Are there limitations to this calculation?
A: This calculation assumes small signal conditions and may not be accurate for large signal amplitudes or in circuits with significant non-linearities.