T-Parameter Model

A small-signal equivalent model of a BJT used for amplifier circuit analysis. A tiny resistance r_e, which represents the forward dynamic resistance of the emitter diode, represents the base–emitter junction in this model.

The emitter resistance is given by:

r_e = \frac{V_T}{I_E}

where:

• V_T: Thermal voltage
• I_E: Emitter current at the operating (Q) point

The collector current is controlled by the base current and is expressed as:

I_c = \beta I_b

In the T-model, a dependent current source represents the collector current, while an additional resistance r_o may appear between collector and emitter due to the Early effect.

r_o = \frac{V_A}{I_C}

where V_A is the Early voltage.

This model is widely used for analyzing common emitter and common base amplifier circuits.

Analysis of Common Emitter Transistor Using T-Model

For AC analysis of a common emitter amplifier, the transistor is replaced by its T-equivalent circuit and DC sources are short-circuited.

Input Impedance

The input impedance is:

Z_{in} = R_1 \parallel R_2 \parallel (1 + \beta)r_e

Since \beta \gg 1,

Z_{in} \approx R_1 \parallel R_2 \parallel \beta r_e

Output Impedance

The output impedance is given by:

Z_o = r_o \parallel R_C

Voltage Gain

The voltage gain of the amplifier is:

A_v = \frac{V_0}{V_{in}}

Using the T-model,

A_v = -\frac{R_C \parallel r_o}{r_e}

The negative sign indicates that the output signal is inverted with respect to the input.

Voltage Gain Considering Source Resistance

When the source resistance R_s is included, the voltage gain becomes:

A_{VS} = A_v \frac{Z_{in}}{Z_{in} + R_s}

Analysis of Common Emitter Transistor with Unbypassed Resistor

If the bypass capacitor C_E is removed, the emitter resistor R_E remains in the AC circuit. This configuration is called a common emitter amplifier with an unbypassed emitter resistor.

The presence of R_E introduces negative feedback, which affects the amplifier characteristics.

Effects of Unbypassed Emitter Resistor

• Input resistance increases
• Voltage gain decreases
• Amplifier stability improves

Input Impedance

The input impedance becomes:

Z_{in} = R_1 \parallel R_2 \parallel \left[(1 + \beta)(r_e + R_E)\right]

Output Impedance

The output impedance remains approximately:

Z_o = r_o \parallel R_C

Voltage Gain

The voltage gain is reduced due to the emitter resistance:

A_v = -\frac{R_C}{r_e + R_E}

Voltage Gain Considering Source Resistance

When source resistance is included:

A_{VS} = A_v \frac{Z_{in}}{Z_{in} + R_s}