High CMRR and High Voltage Gain Differential Amplifier Design

In differential amplifier design, achieving high Common-Mode Rejection Ratio (CMRR) and maximizing voltage gain are essential goals for optimal performance. The CMRR is a key factor in rejecting unwanted common-mode signals and improving the amplifier’s ability to distinguish between differential signals. Understanding how to manipulate the voltage gain and CMRR is crucial for designing high-quality amplifiers. This article explores the relationship between these parameters and the techniques used to enhance both through current mirrors, active loads, and tail current control.

Voltage Gain in Differential Amplifiers

A basic BJT differential amplifier with a single-ended output typically exhibits a voltage gain represented by the equation:

$$\text{Voltage Gain (A)} = \frac{R_C}{2r_e}$$

Where:

• $R_C$ is the collector resistance.
• $r_e$ is the emitter resistance.

This voltage gain is crucial in determining the output signal strength for differential amplifiers. The gain is inversely proportional to the emitter resistance, and increasing the resistance value improves the overall gain.

Common-Mode Rejection Ratio (CMRR)

The common-mode voltage gain in a differential amplifier is given by:

$$\text{Common-Mode Voltage Gain} = \frac{R_C}{2R_E}$$

Where $R_E$ is the external emitter resistance. The ratio of the differential voltage gain to the common-mode voltage gain defines the CMRR, as shown by the following equation:

$$\text{CMRR} = \frac{R_E}{r_e$$here:

• $R_E$ is the emitter resistance.
• $r_e$ is the intrinsic emitter resistance or emitter ac resistance of the transistor.

A larger value of $R_E$ results in a higher CMRR, meaning the amplifier is better at rejecting common-mode signals while amplifying differential signals. Therefore, increasing $R_E$ is a key factor in improving differential amplifier CMRR.

Using Current Mirrors to Improve CMRR

To achieve a high equivalent $R_E$, a common technique is the use of a current mirror. A current mirror generates a stable tail current in a differential amplifier, which is essential for maintaining consistent operation. The circuit diagram illustrates the configuration of a current mirror used in a differential amplifier design.

The current through the compensating diode(Transistor Q4) is calculated as:

$$I_R = \frac{V_{CC} + V_{EE} - V_{BE}}{R$$Where:

• $V_{CC}$ is the positive supply voltage.
• $V_{EE}$ is the negative supply voltage.
• $V_{BE}$ is the base-emitter voltage of the transistor.
• $R$ is the resistance in the current mirror circuit.

The use of a current mirror ensures that the tail current remains constant across the amplifier, and since the Q3 transistor behaves like a constant current bias source, it has a very high output impedance. This high impedance contributes to an equivalent $R_E$ in the range of hundreds of megohms, which significantly improves the CMRR.

In the circuit, transistor Q4 is shown as a diode because its base and collector leads are shorted, causing it to act as a diode. This is a standard practice inside integrated circuits (ICs) for biasing purposes.

Active Load for Improved Voltage Gain

The voltage gain in a differential amplifier can be further improved by using an active load. An active load replaces a traditional resistor($R_C$) with a current mirror, which provides a high equivalent load resistance. The voltage gain is given by:

$$\text{Voltage Gain (A)} = \frac{R_C}{2r_e'}$$

Where $r_e'$ is the effective resistance when using an active load. In the circuit diagram above, a PNP current mirror is used as the active load in a differential amplifier. This configuration ensures that Q2 sees an equivalent collector resistance ($R_C$) in the hundreds of megohms range, providing a much higher voltage gain compared to a resistor-based load. A worked out example calculation can be found in Discrete Vs Op-Amp Differential Amplifier.

Active loading is a technique commonly used in operational amplifiers (op-amps). The higher effective resistance provided by the current mirror results in increased voltage gain, making this method extremely effective in high-precision applications.

Watch the following video which shows how the above differential amplifier works with input signals and the output signal.

Conclusion

In summary, achieving high voltage gain and CMRR in differential amplifiers is crucial for many high-performance applications. The use of a current mirror to generate a stable tail current significantly improves both parameters by increasing the equivalent emitter resistance and ensuring consistent current flow. Furthermore, utilizing an active load in the form of a current mirror greatly enhances the voltage gain by providing a high equivalent load resistance. These techniques are commonly employed in modern operational amplifier designs and are key to achieving high-performance amplification in many electronic circuits.

If you want to build differential amplifier then you can use our online free differential amplifier design calculator.