BJT Small Signal Model

BJT SMALL SIGNAL MODEL

TRANSISTOR AS A TWO PORT DEVICE

A transistor can be treated as a two-port network. The voltage and current at port 1 are V₁ and i₁ and the voltage and current at port 2 are V₂ and i₂ as shown in Fig. 2.13. Any two parameters are considered to be independent variables and the other two parameters are expressed in terms of the independent variables.

Hybrid Parameters

The hybrid or h parameters are used for analysis of the transistor.

If the input current i₁ and the output voltage V₂are taken as independent variables, then the input voltage V₁ and output current i₂ are expressed in terms of i₁ and V₂.

Since the units of the four parameters are completely different from each other, these parameters are called hybrid parameters.

The four hybrid parameters h₁₁, h₁₂, h₂₁, h₂₂ are defined as

The units of the h-parameters h₁₁ and h₂₂ are Ω and m ho respectively. h₁₂ and h₂₁ are dimensionless.

As the units of h-parameters are different they are called hybrid parameters. The values of h-parameters depend upon

1. Transistor type

2. Transistor configuration

3. Operating point

4. Frequency

5. Temperature

Advantages of h-Parameters

i. Easy to measure from static characteristics of transistor

ii. Simple conversion from one configuration to other

iii. Used upto radio frequencies

iv. Convenient for circuit analysis and design

SMALL SIGNAL ANALYSIS

The operation of an amplifiers in the mid band region of its frequency response is analyzed. So it is also called midband analysis.

Assumptions

i. All the coupling and bypass capacitors are equivalent to short circuit.

ii. All the internal capacitances of the transistor are open circuited.

Steps

i. Draw the ac equivalent circuit of the amplifiers.

ii. Draw the hybrid equivalent circuit.

iii. Calculate input impedance, output impedance, current gain, voltage gain and power gain of the amplifier.

ANALYSIS OF CE AMPLIFIER

Let us analysis the Common Emitter (CE) amplifier as follows

Step 1: Draw ac equivalent circuit of the amplifier. Table 3.1 shows the ac equivalent circuit for different de elements.

To draw the ac equivalent circuit of the amplifier, the following steps should be followed.

i. Replace the dc voltage source by a short circuit.

ii. Replace coupling and bypass capacitor by the short circuit.

Step 2: Hybrid Equivalent Circuit

From the ac equivalent circuit, the hybrid equivalent circuit can be obtained as the ac shown in Fig. 2.15. The above Fig.2.15 can also be drawn as in Fig. 2.16 by connecting the common ground.

Input Impedance

From the Fig., the input impedance can be calculated as

If R_B >> h_ie, then

Output Impedance

It is defined as the impedance determined with input voltage V_i = 0

From Fig., if V_i = 0, then I_b = 0

⇒ h_fe I_b = 0

ie., the current source is open circuited

So 

Voltage Gain

Voltage gain is defined as the ratio of output voltage to input voltage.

The negative sign implies that there is 180° phase shift between input and output signals.

Current Gain

Curent gain is the ratio of output current to input current.