Calculating Input Resistance of A Emitter Follower

What is an Emitter Follower?

An emitter follower is a basic transistor amplifier circuit where the transistor's emitter is connected to the output, and the base is connected to the input. This configuration provides voltage gain while maintaining a low output impedance, making it useful for buffering signals.

The key characteristics of an emitter follower include:

• Voltage gain close to 1 (typically 0.9 to 0.99)
• Low output impedance
• High input impedance
• Phase inversion (180° phase shift)

These properties make emitter followers useful in many applications, including signal buffering, impedance matching, and as the first stage in more complex amplifier circuits.

Input Resistance Formula

The input resistance of an emitter follower can be calculated using the following formula:

The small-signal input resistance r_π is calculated as:

For practical calculations, you can use the simplified formula:

How to Calculate Input Resistance

To calculate the input resistance of an emitter follower, follow these steps:

1. Determine the current gain (β) of the transistor from its datasheet
2. Calculate the collector current (I_C) based on your circuit design
3. Use the thermal voltage V_T (approximately 26 mV at room temperature)
4. Calculate r_π using V_T / I_C
5. Multiply β by r_π to get the input resistance R_in

For most practical purposes, you can use the simplified formula R_in ≈ β × (V_T / I_C).

Example Calculation

Let's calculate the input resistance for a 2N3904 transistor with β = 100 and I_C = 1 mA (0.001 A).

1. V_T = 26 mV = 0.026 V
2. r_π = V_T / I_C = 0.026 / 0.001 = 26 Ω
3. R_in = β × r_π = 100 × 26 = 2600 Ω

Using the simplified formula: R_in ≈ 100 × (0.026 / 0.001) = 2600 Ω.

The calculated input resistance is 2600 Ω.

Practical Applications

The input resistance of an emitter follower is important in several practical applications:

• Signal buffering: Maintaining high input impedance while providing low output impedance
• Impedance matching: Connecting circuits with different impedance levels
• Voltage follower: Creating a buffer that maintains the same voltage as the input
• First stage of amplifiers: Providing voltage gain while maintaining stability

Understanding the input resistance helps in designing circuits that meet specific performance requirements.

Limitations

While emitter followers are useful, they have some limitations:

• Phase inversion: The output is 180° out of phase with the input
• Voltage drop: There is a small voltage drop across the base-emitter junction
• Current gain variation: The current gain β can vary with temperature and transistor type
• Frequency response: The input resistance may change at higher frequencies

These limitations should be considered when designing circuits using emitter followers.