Introduction

In Chapter Basic amplification: CS stage, we have seen that a CS stage operating in the saturation region can provide a large available power gain. We have also seen that the source-to-load transfer of a CS stage suffers from noise addition, nonlinearity and bandwidth limitation. In addition, we learned that a single CS stage shares one terminal of the input port with one terminal of the output port. Hence, such an amplifier stage cannot provide port isolation without using transformers. In this chapter, we will discuss the use of balancing techniques. These techniques can be applied for improvement of the port isolation and for reduction of reproducible errors due to offset and nonlinearity.

Additive compensation

Balancing is a form of additive compensation. We will speak of additive compensation if an undesired effect is compensated by adding an opposite effect. Additive compensation can be used to compensate for reproducible errors.

Fig. 169 Principle of additive compensation.

The principle of additive compensation is elucidated in Fig. 169. A known error signal \(\epsilon(t)\) which equals the error caused by the nonideal behavior of an amplifier with small-signal gain \(A\), is subtracted from the output signal of the amplifier. The resulting output signal is the amplified signal: \(y(t)=Ax(t)\).

Balancing

Balancing is a technique in which anti-series, complementary series, anti parallel and complementary-parallel connections of amplifier stages are used to obtain such compensating effects. Parallel connections are used to add or subtract currents, while series connections are used to add or subtract voltages.

Fig. 170 Balancing technique using amplifiers or amplifier stages with complementary characteristics.

Fig. 170 illustrates this principle using complementary amplifiers or amplifier stages. The input signal is supplied to both amplifiers. If both amplifiers have complementary characteristics, their errors have opposite signs. After addition, the error is eliminated and the output signal is doubled.

Alternatively, one could use a setup as shown in Fig. 171. There, both amplifiers are equal but they carry either the non-inverted or the inverted signal at their input. Their output signals are subtracted which results in elimination of the error and doubling of the desired signal.

Fig. 171 Balancing technique using identical amplifiers with inverted signals.

Multiplicative or cascaded compensation

Aside from additive compensation, there exists multiplicative or cascaded compensation. This type of compensation uses cascade connections of compensating systems. It can be used for linearization and for correction of the small-signal dynamic transfer of a system.

Fig. 172 Multiplicative or cascaded compensation uses cascaded systems that together constitute a linear and instantaneous relation between the input and the output signal.

Fig. 172 shows an arrangement in which two cascaded systems together constitute a linear and instantaneous relation between the input and the output signal.

Odd function synthesis

The \(v-i\) characteristics of the input and the output port, as well as the transfer characteristics of an ideal amplifier, are first order odd characteristics. These functions are of the form

\[y(x)=a_{1}x,\]

where \(y\) is the response signal and \(x\) is the excitation.

The instantaneous source-to-load transfer characteristics, as well as the \(v-i\) characteristics of the input port and of the output port of amplifier stages such as the CS stage have both even and odd terms.

The series expansion of instantaneous nonlinear functions with odd and even nonlinearity can be written in the form

(79)\[y(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+...\ . \label{eq-non-lin-series}\]

Odd and even functions can be synthesized from these functions. This can be seen if we write ((79)) as the sum of an odd function \(y_{odd}(x)\) and an even function \(y_{even}(x)\):

\[y(x)=y_{odd}(x)+y_{even}(x),\]

where:

\[y_{odd}(x)=a_{1}x+a_{3}x^{3}+...\ ,\]

and

\[y_{even}(x)=a_{0}+a_{2}x^{2}+...\ .\]

The functions \(y_{odd}(x)\) and \(y_{even}(x)\) can be obtained from \(y(x)\) as

\[\begin{split}y_{odd}(x) & =\frac{1}{2}\left( y(x)-y(-x)\right) ,\\ y_{even}(x) & =\frac{1}{2}\left( y(x)+y(-x)\right) .\end{split}\]

In order to obtain odd characteristics for amplifiers, even order terms can be compensated for by adding \(-y(-x)\) to \(y(x)\). This can be done with the aid of a complementary amplifier as shown in Fig. 170, or by passing the \(x(t)\) and \(-x(t)\) through two equal amplifiers and subtracting their output signals as shown in Fig. 171.

This chapter

In this chapter, we will discuss the application of balancing techniques with two-terminal elements and for two-ports. Balancing of two-terminal elements will be discussed in section Balancing of two-terminal devices. We will start with an introduction of the basic balancing techniques:

1. Anti-series connection of equal devices

2. Anti-parallel connection of equal devices

3. Series connection of complementary devices

4. Parallel connection of complementary devices.

We will see that balancing converts the biasing quantities into common-mode quantities and the signal quantities into differential-mode quantities. This makes balanced amplifiers less sensitive to changes in the operating conditions due to temperature variations. This mechanism is often referred to as offset compensation and compensation of the offset drift.

In section Balancing of two-ports we will discuss the balancing of two-ports. Practical implementations of balancing techniques with the basic amplifier stages will be discussed in section Balanced CE and CS stages.