# BJT Differential Amplifier with Constant Current Bias

The basic BJT differential amplifier has a fixed emitter resistance which is the source of problem in improving the common mode rejection ration(CMRR) of a differential amplifier. The problem with the emitter resistance to improve CMRR was explained in previous tutorial How to improve CMRR of BJT differential amplifier. CMMR stands for Common Mode Rejection Ratio, and it is a measure of how well a differential amplifier rejects common-mode signals. Methods of improve the CMRR of a differential amplifier includes using constant current bias or current mirror or active load. Here it is explained how the BJT differential amplifier circuit with constant current bias operates and the constant current bias improves the CMRR value.

The BJT differential amplifier with constant current bias is an amplifier that uses two BJTs to amplify the difference between two input signals. The constant current bias provides a stable bias current to the BJTs, which helps improve the linearity and stability of the amplifier. The BJT differential amplifier with constant current bias is modification of the basic BJT differential amplifier circuit which has an emitter resistor $$R_E$$. The emitter resistance in the basic BJT differential amplifier is replaced with constant current bias in order to improve the CMRR(Common  Mode Rejection Ratio).

Following shows the circuit diagram of BJT differential amplifier with constant current bias.

As shown in the above diagram, the constant current source consist of third BJT transistor Q3 with biasing resistors R1, R2 and R3 such that the base is grounded via the resistor R1. This constant current bias circuit provides, as we will soon see, a stabilized current that does not disturb the operating point of the differential amplifier.

Working operation of  constant current source

The resistors R1 and R2 are used to bias the transistor Q3 properly. The dc collector current $$I_{C3}$$ of the transistor Q3 is setup by the resistors R1, R2 and R3.

The voltage at the Q3 base is,

$$V_{B3} = \frac{-R_1 V_{EE}}{R_1+R_2}$$        ------->(1)

The voltage at the Q3 emitter is,

$$V_{E3}=V_{B3}-V_{BE3}$$

using (1) we have,

$$V_{E3}=-\frac{R_1 V_{EE}}{R_1+R_2}-V_{BE3}$$   ------->(2)

The emitter current of Q3 is,

$$I_{E3} = \frac{V_{E3}-(-V_{EE})}{R_3}$$

or,  $$I_{E3} = \frac{V_{E3}+V_{EE}}{R_3}$$

Substituting $$V_{E3}$$ from(2) we get,

$$I_{E3} = \frac{-\frac{R_1 V_{EE}}{R_1+R_2}-V_{BE3}+V_{EE}}{R_3}$$

or, $$I_{E3} = \frac{V_{EE}-[\frac{R_1 V_{EE}}{R_1+R_2}]-V_{BE3}}{R_3}$$   ------->(3)

Since for identical transistors and in general the collector current is nearly equal to emitter current we have,

$$I_{C3} \approx \frac{V_{EE}-[\frac{R_1 V_{EE}}{R_1+R_2}]-V_{BE3}}{R_3}$$   ------->(4)

In equation(13) we see that the right hand side contains only constant terms. Thus equation(13) shows that the constant current source provides constant current $$I_{C3}$$ that is independent on any current or voltage variable.

Furthermore, since this Q3 collector current is sourced equally to the emitters of Q1 and Q2, we have,

$$I_{E1}= I_{E2}= \frac{I_{C3}}{2}$$   ------->(5)

That is,

$$I_{E1}= I_{E2}= \frac{V_{EE}-[\frac{R_1 V_{EE}}{R_1+R_2}]-V_{BE3}}{2R_3}$$   ------->(6)

Thus the constant current source circuit provides constant emitter current to both the differential amplifier bipolar transistors Q1 and Q2.

In addition to providing stabilized current to the BJT differential amplifier, the constant current source also provides high impedance to the differential amplifier. This is because in ac operation, the dc current source is effectively open circuit. Since it is open circuit in ac operation, the impedance is high and so the common mode gain is ideally zero and the CMRR is ideally infinity, since CMRR is the ratio of differential mode gain to common mode gain.

Applications of BJT Differential Amplifier with Constant Current Bias

The BJT differential amplifier with constant current bias has a wide range of applications in electronic circuits. Some of its common applications include:

• Instrumentation Amplifiers: The BJT differential amplifier is used in instrumentation amplifiers to amplify small differential signals from sensors and transducers. It is used in applications such as temperature sensing, pressure sensing, and strain gauges.
• Audio Amplifiers: The BJT differential amplifier is used in audio amplifiers to amplify the difference between left and right audio channels. It is used in high-fidelity audio systems, home theater systems, and automotive audio systems.
• Analog Signal Processing: The BJT differential amplifier is used in analog signal processing circuits to amplify, filter, and process analog signals. It is used in instrumentation systems, medical equipment, and control systems.
• Communication Systems: The BJT differential amplifier is used in communication systems to amplify differential signals and reject common mode signals. It is used in applications such as radio transmitters, receivers, and modems.

Conclusion

The BJT differential amplifier with constant current bias is a versatile circuit that is widely used in electronic circuits. Its ability to amplify differential signals while rejecting common mode signals makes it an important component in many applications, such as instrumentation amplifiers, audio amplifiers, and communication systems. With its stable bias current and high linearity, the BJT differential amplifier with constant current bias continues to be a popular choice among engineers and hobbyists alike.

References:

[4] Differential Amplifier Differential and Common Mode Operation