Introduction

Until now, we have discussed the design of the amplifier’s signal-path, thereby assuming that the desired operating conditions of the active devices were fixed with ideal current and voltage sources, as described in Chapter Amplification Mechanism. In this chapter, we will discuss methods to minimize the number of bias sources, as well as the way in which the remaining bias sources can be derived from the power supplies. We will not yet discuss the design of the bias sources themselves.

A structured approach to biasing

A definition of biasing has been given in Chapter Introduction to amplifier biasing.

Definition

Biasing is the process of fixing the electrical operating conditions of electronic devices, and deriving the required bias voltage and current sources from the power supply voltage(s).

The biasing design problem can thus be formulated as follows:

Derive the input and output bias quantities of the amplifier stages from the power supply voltages in such a way that:

1. The amplifier stage is accurately biased in the desired operating point over the whole temperature and power supply range.

2. The amplifier stage is sufficiently isolated from the power supply.

3. The degradation of the amplifiers’s performance caused by the biasing, is acceptable.

The biasing of amplifier stages and amplifiers is known to be difficult. First of all, this is because the design and the implementation of a feasible biasing concept, show a strong interaction with the design of all kinds of performance aspects of the amplifier. In particular, the number of feasible circuit topologies shows a strong interaction with the supply voltage. Secondly, biasing is a complex process because the bias elements themselves are passive elements each of which needs to be biased in a proper operating point as well.

A network element is called passive if it dissipates power. This is the case if the real part of the sum of the products of all its branch currents and branch voltages is positive. A network element is called active if it delivers power to its external circuit. This is the case if the real part of the sum of products of all its branch currents and branch voltages is negative.

For these reasons, biasing circuits are often designed concurrently with the signal path. Possible design conflicts that result from interactions between the bias circuits and the signal path are usually resolved in design loops. Such a design approach may be suited to experienced designers, but it may be very confusing for novice designers and it does not lend itself to automation.

In this book, we will introduce a structured approach to biasing that clearly shows the interaction between the design of the signal path, the design of the biasing scheme and the implementation of bias sources. We will use a step-by-step approach in which we will explicitly motivate and describe the subsequent design steps. By doing so, this approach is believed to be suited to non-experienced designers and may also be used as a basis for algorithm-based design automation.

We will introduce techniques that can be used to minimize interactions between the design of the biasing circuits and the signal path, as well as techniques for optimization of the design of the signal path with respect to biasing.

Basic passive biasing elements

Since the power supply is the only active element in a circuit, biasing elements have to be realized with passive network elements that behave as voltage or current sources. Within the context of biasing, we will use the following definitions for elements that behave as voltage or current sources:

1. A two-terminal network element has a voltage source character if, at frequencies of interest, the magnitude of its small-signal impedance is smaller than the ratio of the DC voltage across the element and the DC current through it.

2. A two-terminal network element has a current source character if, at frequencies of interest, the magnitude of its small-signal impedance is larger than the ratio of the DC voltage across the element and the DC current through it.

With the above definitions, it will be clear that at nonzero frequencies, inductors have a current source character and capacitors a voltage source character. Hence, for biasing purposes capacitors can be inserted in series with the signal path and inductors can be placed in parallel with the signal path. This is called AC coupling.

Nonlinear resistors

Biasing elements that exhibit a voltage or current source character at all frequencies, can be realized with nonlinear resistive elements, or shortly: nonlinear resistors. However, since the \(V-I\) characteristic of a passive nonlinear resistive element passes through the origin, such an element can only exhibit a voltage or a current source character over a limited operating range. In the vicinity of \((V,I)=(0,0)\) any passive nonlinear resistor behaves as a linear resistor:

Assume no discontinuity in the \(V-I\) characteristic and its derivative at \((V,I)=(0,0)\).

\[\frac{V}{I}=\frac{dV}{dI},\]

where \(V\) and \(I\) are the voltage across the device and the current through the device, respectively.

Fig. 489A shows a \(V-I\) characteristic of a nonlinear resistor with a current source character over a wide operating range. The lower limit of the voltage across a nonlinear resistor, at which it exhibits a current source character, is called the saturation voltage. The upper limit of this voltage is called the breakdown voltage.

Fig. 489B shows a \(V-I\) characteristic of a nonlinear resistor with a voltage source character over a wide operating range. The lower limit of the current through a nonlinear resistor, at which it exhibits a voltage source character, is called the cut-off current. The upper limit of this current is called the saturation current.

Fig. 489 Nonlinear resistors that exhibit a current source or a voltage source character over a limited operating range: A: Symbol and characteristic of a nonlinear resistor with a current source character when \(V_{\text{sat}}<V<V_{\text{br}}\). B: Symbol and characteristic of a nonlinear resistor with a voltaget source character when \(I_{\text{cut-off}}<I<I_{\text{sat}}.\)

One of the difficult aspects of biasing is that the biasing elements themselves need to be biased in an operating point at which they deliver the proper value of the bias quantity, while they maintain their current or voltage source character for all signal values and power supply variations.

Outline of the biasing approach

The outline of the structured approach to the biasing of amplifier stages and amplifiers is sketched below:

1. The signal path design with four bias sources per transistor, as discussed in Chapter Amplification Mechanism, is the starting point for the design of the biasing. Theoretically, all of these bias sources are capable of delivering power.

   In practice, only the power supply sources deliver power to the circuit, all other elements are passive elements that either dissipate power or store electrical energy. The latter ones are capable of delivering power over a limited time interval, but the time average of the power, delivered by those elements, equals zero.

2. The power supply voltage sources will be added to the signal path diagram. One of the terminals of each power supply will be connected to the reference node (the ground) of the signal path.

3. \label{step-generation-bias}The bias currents need to be delivered by the power supply voltage(s). This is achieved by redirecting the bias current sources via the power supplies and the ground. In order to minimize the number of biasing elements, parallel connections of bias current sources will be replaced with a single current source and series connections of voltage sources will be replaced with a single voltage source.

4. Since the power supply source is the only active device in the circuit, all remaining bias sources need to be replaced with passive nonlinear resistors that exhibit a voltage or current source character. This requires that the branch current of each biasing element flows from the terminal with the most positive voltage to the one with the most negative voltage.

   The power dissipation in the biasing element is positive.

   In this design step, bias sources will be added to ensure such behavior.

5. At a later stage, we will see that floating voltage sources are difficult to realize. For this reason, their number needs to be minimized. We will show that this can be done either by changing the operating voltages of the active devices, by replacing them with grounded voltage sources, or by generating alternative amplifier topologies that have similar signal performance, but different biasing requirements.

6. Before judging the feasibility of biasing elements, we need to define their requirements.

7. If one or more feasible bias solutions can be found, we will select the most promising solution and continue with step step-design-bias, else we will evaluate the application of error reduction techniques and go back to step step-generation-bias.

   Error reduction techniques that can be applied are:

• Compensation (temperature compensation, model-based biasing)

• Error feed forward

• Negative feedback (application of local, over-all, differential-mode and common-mode feedback techniques)

• Sampling/switching (auto-zero biasing)

• Modulation/demodulation (chopper stabilized biasing)

8. \label{step-design-bias}Start the detailed design of the biasing elements.

Drawing conventions

In order to illustrate the process of biasing in a comprehensible way, we will use some circuit drawing conventions. Fig. 490 shows the drawing conventions for some devices, as they will be used in this chapter:

• The positive direction of the current flow in a schematic is from top to bottom. Hence, p-type devices are drawn with their emitter or source up, while n-type devices are drawn with their collector or drain down. Devices that operate at a higher voltage level are drawn at a higher position in the circuit diagram than devices that operate at a lower voltage level.

  

  Fig. 490 Drawing conventions.

• Information flow in a schematic is from left to right. In feedback networks it may be from right to left.

• For the sake of simplicity, the substrate connection of bipolar devices is not drawn. When properly biased, the substrate voltage has only a minor influence on the performance aspects of the device.

• In IC technology the common bulk of equal NMOS devices is connected to the supply with their largest negative voltage in the circuit. The common bulk of equal PMOS devices is connected to the one with their largest positive voltage.

This chapter

The motivation for separating the design of the signal path and the biasing has already been given in section Signal path and biasing. In this chapter, we will introduce a step-by-step approach to the biasing of amplifier stages and amplifiers.

In section Setting up the initial biasing scheme, we will discuss the way in which the bias quantities of amplifier stages can be derived from one or more power supply voltage sources, thereby using only passive nonlinear resistors (step 1 through 4 of the list in section Outline of the biasing approach). We will demonstrate this technique for CE or CS stages, local feedback stages and balanced stages.

Other sections, such as the minimization of floating voltage sources, setting up the requirements for biasing elements and improvement of the biasing using error-reduction techniques still need to be added.