Input Resistance of Common Emitter Amplifier Given Small-Signal Input Resistance Calculator

Formula Used:

\[ R_{in} = \left( \frac{1}{R_b} + \frac{1}{R_{b2}} + \frac{1}{R_{sm} + (\beta + 1) \cdot R_e} \right)^{-1} \]

Base Resistance (Rb):

Base Resistance 2 (Rb2):

Small Signal Input Resistance (Rsm):

Collector Base Current Gain (β):

Emitter Resistance (Re):

Input Resistance (Rin):

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1. What is Input Resistance of Common Emitter Amplifier?

The input resistance of a common emitter amplifier is the opposition that the amplifier presents to the input signal. It's a crucial parameter that affects how the amplifier interacts with the signal source and determines the amount of signal voltage that appears at the amplifier input.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R_{in} = \left( \frac{1}{R_b} + \frac{1}{R_{b2}} + \frac{1}{R_{sm} + (\beta + 1) \cdot R_e} \right)^{-1} \]

Where:

\( R_b \) — Base resistance (Ω)
\( R_{b2} \) — Base resistance 2 (Ω)
\( R_{sm} \) — Small signal input resistance between base and emitter (Ω)
\( \beta \) — Collector base current gain
\( R_e \) — Emitter resistance (Ω)

Explanation: The formula calculates the parallel combination of base biasing resistances and the input resistance looking into the base terminal, which includes the effect of emitter resistance multiplied by (β+1).

3. Importance of Input Resistance Calculation

Details: Accurate input resistance calculation is essential for proper impedance matching, maximizing power transfer from source to amplifier, and preventing signal attenuation at the input stage.

4. Using the Calculator

Tips: Enter all resistance values in ohms (Ω). The collector base current gain (β) is a dimensionless quantity. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is input resistance important in amplifier design?
A: Input resistance determines how much the amplifier loads the signal source. Higher input resistance means less loading and better signal transfer from source to amplifier.

Q2: How does emitter resistance affect input resistance?
A: Emitter resistance increases the input resistance significantly because it's multiplied by (β+1) in the input resistance calculation.

Q3: What are typical values for input resistance in common emitter amplifiers?
A: Typical values range from a few hundred ohms to several kilohms, depending on the biasing arrangement and transistor parameters.

Q4: How does β affect the input resistance?
A: Higher β values result in higher input resistance because the term (β+1)*Re becomes larger, reducing the loading effect on the input.

Q5: Can this calculator be used for AC analysis?
A: Yes, this calculator provides the small-signal input resistance which is used in AC analysis of common emitter amplifiers.