BJT Differential Amplifier Experiment with Solved Problem

The Basic BJT Differential Amplifier is a fundamental building block in analog electronics, widely used in applications such as operational amplifiers, audio equipment, and communication systems. Its ability to amplify the difference between two input signals while rejecting common-mode signals makes it indispensable in modern electronics. In this blog post, we’ll explore the theory, experiment, and a solved problem on the BJT Differential Amplifier, along with practical insights and resources to deepen your understanding.

What is a BJT Differential Amplifier?

A BJT Differential Amplifier consists of two matched transistors (Bipolar Junction Transistors) configured symmetrically to amplify the difference between two input signals. It is characterized by its high Common-Mode Rejection Ratio (CMRR), which ensures that any noise or interference common to both inputs is rejected, while the differential signal is amplified.

Key Features of a BJT Differential Amplifier

• Differential Gain: Amplifies the difference between two input signals.

• Common-Mode Rejection: Rejects signals that are common to both inputs.

• High Input Impedance: Minimizes loading effects on the input sources.

• Balanced Output: Provides two outputs that are 180° out of phase.

  For more details see How Does a Differential Amplifier Work? and BJT Differential Amplifier with Active Load.

Solved Problem on BJT Differential Amplifier

Let’s solve a practical problem to understand how a BJT Differential Amplifier works.

Problem Statement

A BJT Differential Amplifier has the following parameters:

• Supply Voltage ($V_{CC}$): 12 V

• Tail Current ($I_{EE}$): 2 mA

• Collector Resistors ($R_C$): 5 kΩ

• Input Signals: $V_{in1}=1\text{V}$, $V_{in2}=0.9\text{V}$

• Transistor Parameters: $\beta =100$, $V_{BE}=0.7\text{V}$

Calculate:

1. The differential gain ($A_d$).

2. The common-mode gain ($A_{cm}$).

3. The Common-Mode Rejection Ratio (CMRR).

Solution

1. Differential Gain ($A_d$):

   $$A_d=\frac{R_C}{2\cdot r_e}$$

   Where $r_e$ is the emitter resistance:

   $$r_e=\frac{V_T}{I_E}\approx \frac{26\text{mV}}{1\text{mA}}=26\mathrm{\Omega }$$

   Thus:

   $$A_d=\frac{5\text{k}\mathrm{\Omega }}{2\cdot 26\mathrm{\Omega }}\approx 96.15$$

2. Common-Mode Gain ($A_{cm}$):

   $$A_{cm}=\frac{R_C}{2\cdot R_{EE}}$$

   Assuming $R_{EE}=10\text{k}\mathrm{\Omega }$:

   $$A_{cm}=\frac{5\text{k}\mathrm{\Omega }}{2\cdot 10\text{k}\mathrm{\Omega }}=0.25$$

3. Common-Mode Rejection Ratio (CMRR):

   $$\text{CMRR}=\frac{A_d}{A_{cm}}=\frac{96.15}{0.25}=384.6$$

   In decibels:

   $$\text{CMRR (dB)}=20{\log }_{10}(384.6)\approx 51.7\text{dB}$$

BJT Differential Amplifier Experiment

To further understand the BJT Differential Amplifier, you can perform a simple experiment using the following steps:

1. Set Up the Circuit:

   • Use two matched BJTs (e.g., 2N3904) and configure them in a differential pair.

   • Add a tail current source using a resistor or a current mirror.

   • Connect collector resistors ($R_C$) and measure the output voltages.

2. Measure Differential Gain:

   • Apply a small differential input signal and measure the output voltage.

   • Calculate the differential gain using the formula:

     $$A_d=\frac{V_{out}}{V_{in1}-V_{in2}}$$

3. Measure Common-Mode Gain:

   • Apply a common-mode input signal and measure the output voltage.

   • Calculate the common-mode gain using the formula:

     $$A_{cm}=\frac{V_{out}}{V_{in}}$$

4. Calculate CMRR:

   • Use the measured values of $A_d$ and $A_{cm}$ to calculate the CMRR.

Improving CMRR in BJT Differential Amplifiers

The Common-Mode Rejection Ratio (CMRR) is a critical parameter for differential amplifiers. To improve CMRR:

• Use a current mirror for the tail current source.

• Ensure matched transistors and resistors.

• Increase the tail resistance ($R_{EE}$).

For a detailed guide on improving CMRR, check out this resource:
How to Improve CMRR of BJT Differential Amplifier

Types of BJT Differential Amplifiers

BJT Differential Amplifiers can be configured in different ways depending on the application:

1. Dual Input, Unbalanced Output:
   Learn more about this configuration here:
   Dual Input Unbalanced Output BJT Differential Amplifier

2. Single Input, Balanced Output:
   Explore this configuration in detail:
   Single Input Balanced Output BJT Differential Amplifier

Conclusion

The BJT Differential Amplifier is a versatile and essential circuit in analog electronics. By understanding its theory, solving practical problems, and performing experiments, you can master its design and application. Whether you’re working on audio amplifiers, instrumentation, or communication systems, the BJT Differential Amplifier is a key tool in your arsenal. For more insights and detailed guides, explore the resources linked above and enhance your knowledge of this critical circuit.