Introduction#
In this chapter, we will discuss the design of multi-stage negative feedback amplifiers. We will formulate considerations for the design of the various performance aspects of such an amplifier, and present a step-by-step approach for the design of high-performance negative feedback amplifiers.
Summary of previous chapters#
The design approach presented in this chapter is based upon the theory discussed in the preceding chapters. We will briefly summarize the conclusions of these chapters below.
Modeling and characterization of amplifiers#
In Chapter Modeling and specification of amplifiers, we started with an introduction to amplifiers. We have seen that an amplifier has to provide its load with an amplified copy of the source signal. The word ‘amplified’ in this context means that the available signal power at the amplifier’s output exceeds that of the source.
We continued with the classification and characterization of amplifiers. We have seen that amplifiers can be classified according to their source and load characteristics. The appropriate amplifier type for a specific source and load can be found by answering the following questions:
What would be the ideal value of the amplifier’s input impedance, or alternatively, which electrical quantity of the source (current or voltage) should be taken as input quantity for the amplifier?
What would be the ideal value of the amplifier’s output impedance, or, alternatively, which electrical quantity should be used to drive the load?
What is the desired source-to-load transfer that needs to be established?
Which ports (input, output and power port) should be isolated with respect to each other?
Is unilateral behavior required?
The answers to these questions together define the functional behavior of the amplifier. They give us the ideal values of the required port impedances
and of the transfer characteristics. We have seen that the functional behavior of an amplifier can be described with the aid of two-ports. The Transmission-1 matrix parameters \(A,B,C\) and \(D\), in conjunction with the source and load impedances, provide high-level descriptions for the source-to-load transfer and the port impedances of the idealized amplifier.
Practical amplifiers suffer from non-idealities. Like all information processing systems, imperfections in their behavior arise as a result of the physical limitation of speed and power, the addition of noise and imperfections in the physical operating principle used for their implementation. These imperfections limit the amount of information that can be processed by the amplifier. We have seen that application-specific error description methods should be used to reflect the effects of the information processing errors, as they will be observed in the application.
Another error source in amplifiers is the imperfect port isolation. It introduces susceptibility to power supply noise and common-mode noise. We have seen that the regularly used description methods with the (voltage) CMRR, the (voltage) common-mode rejection factor and the (voltage) PSRR are far from complete. Application-specific test benches are required to complete such specifications.
Amplification mechanism#
In Chapter Amplification Mechanism, we studied the amplification mechanism. We have seen that the application of specific passive devices together with (active) bias sources, provide the means for building electronic amplifiers. Because of their amplifying capabilities, such passive devices are usually called active devices.
Device modeling#
In order to understand the amplification mechanism and its physical limitations, we briefly discussed the construction, the operation and the modeling of active devices in Chapter Active Devices. We have seen that properly biased bipolar junction transistors (BJTs), junction field-effect transistors (JFET) and MOSFETs can provide a large available power gain.
In that chapter, we also presented simplified device models for symbolic analysis. Such models can be used for finding methods to affect specific behavioral aspects of interest by design and setting up design equations.
CS stage#
The common-source (CS) stage can be considered as the basic MOS amplifier stage; its performance is discussed in Chapter Basic amplification: CS stage. When properly biased, this stage provides a large available power gain. The name of this stage refers to the fact that the source is the common terminal for the input port and the output port. Hence, port isolation with this stage is not possible.
The drain-gate capacitance causes non-unilateral behavior and may seriously limit the bandwidth of the stage or the stage’s contribution to the loop gain-poles product in a negative feedback amplifier. Such effects can be kept small by shorting the stage, while taking the short circuit output current as information carrying quantity.
The noise addition by a CS stage can be minimized by optimizing both its device geometry and its drain current. In high-frequency applications, the device should operate in strong inversion and at a high cut-off frequency. At low frequencies, the influence of flicker-noise may become dominant and a longer channel and a lower operating current may be optimal.
The nonlinearity of the CS stage strongly depends on the frequency, the drive and termination conditions and the operating conditions.
The accuracy of the source-to-load transfer is limited due to fabrication tolerances. All performance aspects of the CS stage depend on temperature.
CE stage#
The common-emitter or CE stage can be considered as the basic three-terminal BJT amplifier stage. The name of this stage refers to the fact that the emitter is the common terminal for the input port and the output port. Hence, port isolation with this stage is not possible.
The collector-base capacitance causes non-unilateral behavior and may seriously limit the bandwidth of the stage or the stage’s contribution to the loop gain-poles product in a negative feedback amplifier. Such effects can be kept small by shorting the stage, while taking the short circuit output current as information carrying quantity.
The noise addition by a CE stage can be minimized by optimizing its device geometry and its collector current. Low-noise amplification with a CE stage requires a transistor with a large DC current gain factor, a high cut-off frequency and a small base resistance.
The nonlinearity of the CE stage strongly depends on the frequency and the drive and termination conditions of the stage. At low frequencies, the parameters \(A\) and \(D\) can have a relatively low differential-gain, while the parameter \(B\) is inversely proportional to the collector current and the parameter \(C\) is proportional to the collector current. At high frequencies, the nonlinearity is strongly dominated by the nonlinear \(Q-V\) relations of the junctions and the voltage and current dependency of the transit time.
Even when accurately biased, the accuracy of the small-signal source-to-load transfer of a CE stage is limited due to fabrication tolerances. Since most device parameters depend on temperature, all performance aspects of the CE stage will be temperature dependent. Hence, accurate amplification with a single CE stage is then only possible with properly selected devices over a small temperature range.
Single-stage amplifiers#
In many RF applications, the accuracy and the temperature stability of the gain are not the dominant requirements. In such applications, automatic gain control is often used to stabilize the gain. Usually, low-noise and low-distortion operation over a limited frequency range, is then of primary interest. In such applications, and at low signal levels, a single CE stage or CS stage amplifier may perform well enough.
Straightforward design of the different performance aspects of the CE stage or the CS stage is only possible if design parameters can be found that more or less independently fix the different performance aspects.
Usually, we only have a limited number of design parameters at our disposal to fix all kinds of different performance aspects. The most important design parameters are:
The device type and geometry
The operating current
The operating voltage
With these three parameters we are not able to design all the performance aspects independently. An extra degree of freedom can be obtained through application of impedance transformation techniques at the source and/or at the load. Impedance transformation can be implemented with wide-band transformers, resonant networks or transmission lines.
In many situations the demand for high-quality information processing requires improvement of performance of the CE or CS stage. Such improvements can be obtained through application of error reduction techniques.
Balanced amplifier stages#
In Chapter Balancing techniques, we discussed the application of balancing techniques and introduced the anti-series stage or differential pair and the complementary-parallel stage or push-pull stage.
Balancing is a compensation technique will limited error reduction capabilities. With balancing techniques, we can improve the following performance aspects:
Linearity
Ideally, the anti-series and the complementary-parallel connection of CE or CS stages have odd transfer characteristics. Even terms such as the offset and its associated temperature drift are compensated. Differential-mode bias sources are replaced with common-mode bias sources.
Port isolation
With the aid of anti-series connection of CE or CS stages, we obtain so-called differential pairs that can be considered as basic four-terminal amplifier stages. They have improved isolation between the input port and the output port.
Power efficiency
With the aid of complementary-parallel connected CE or CS stages, we obtain push-pull stages. These stages can source and sink currents that exceed the quiescent operating current of its constituting CE or CS stages.
The odd order nonlinearity, the dynamic behavior, the noise behavior, as well as the accuracy and the temperature dependency of the transfer, however, cannot be improved with balancing.
Negative feedback amplifiers#
A significant improvement of the quality of the amplifier’s signal transfer can be obtained through application of negative feedback. Negative feedback is a powerful error reduction technique in which available gain of amplifying devices is used for quality improvement of the source-to-load transfer. Each transmission parameter of a negative feedback amplifier can be given an accurate value with the aid of a feedback loop around a high-gain controller. The task of this controller is to nullify the error between the actual source-to-load transfer and the one determined by the feedback networks.
Negative feedback has stronger error-reduction capabilities than balancing. The noise performance and the influence of input offset and bias sources, and the load drive capability cannot be improved by negative feedback, they at best equal those of the controller. The accuracy, the linearity and the bandwidth are at best determined by the feedback networks. Such networks can be realized with accurate passive components.
The synthesis of negative feedback amplifier configurations is discussed in Chapter Design of feedback amplifier configurations. All unilateral and non-unilateral, isolated and non-isolated amplifier types that have been defined in Chapter Modeling and specification of amplifiers, can be realized with the aid of negative feedback. The basic synthesis techniques for negative feedback amplifiers are:
Sensing of the load quantity
Design of a feedback network that converts the sensing result into an accurate copy of the source quantity
Comparison of this copy with the source quantity
Nullification of the comparison result with the aid of a high-gain controller.
If nonenergic feedback elements are used, the noise performance and the power efficiency of the negative feedback amplifier equal those of its controller. Practical use of nonenergic feedback is often limited to unity-gain feedback. Amplifiers with a gain that differs from unity are often realized with passive feedback.
Passive feedback networks increase the contribution of the equivalent input noise sources of the controller to the total noise. If those networks comprise resistive elements, they also contribute noise themselves.
Passive feedback networks may also contribute to the energy storage or dissipation of the amplifier. As a result, the power efficiency of the amplifier will be less than that of its controller.
Not all amplifier configurations can be realized with the aid of passive feedback around a single controller. This is because feedback elements that behave as natural two-ports cannot be constructed using exclusively passive elements. Configurations that cannot be realized with passive feedback around a single controller, can be realized with balanced feedback, active feedback or indirect feedback techniques.
The design of the feedback configuration is the first step in the design of negative feedback amplifiers. In this step the controller is assumed to have nullor properties, which means that it has an infinite available power gain and that it behaves as a natural two-port. The gain of a negative feedback amplifier with a nullor as controller is called the ideal gain.
Feedback modeling#
The second step in the design of negative feedback amplifiers, is the design of the controller. This step requires knowledge about the relation between the performance aspects of the controller and those of the negative feedback amplifier which it is part of. The asymptotic gain model provides this information; it is presented in Chapter Modeling of negative feedback circuits. If the loop gain reference variable is chosen such that an infinite loop gain turns the controller into a nullor, the design of negative feedback amplifiers can be performed in two steps:
Design of the feedback network with a nullor as controller
Design of the controller
Controller design#
In Chapter Amplifier performance and controller requirements, we related the performance aspects of the controller to those of the negative feedback amplifier. We obtained the following design conclusions:
If the loop gain reference variable has been selected properly, the servo function is a measure for the deviation of the source-to-load transfer from the ideal gain. The servo function is completely defined by the loop gain, which comprises contributions of the controller, the source impedance, the load impedance and the feedback networks. The ideal value of the servo function is unity.
The relative inaccuracy of the servo function at midband frequencies is determined by the mid-band loop gain.
The low-pass cut-off frequency of the servo function is determined by the product of the dominant poles of the loop gain and the midband value of the loop gain.
The differential gain of the servo function at midband frequencies, equals the ratio of the differential gain of the loop gain and the value of the loop gain at mid-band frequencies.
Frequency compensation#
With a sufficiently large loop gain-poles product, the negative feedback amplifier can obtain its required bandwidth. However, this does not mean that the error with respect to the ideal behavior of the amplifier is small. For this to be the case, the servo function should have an all-pole transfer with its poles in, or close to MFM positions. In most cases we will have to apply frequency compensation techniques to manipulate the poles into these positions. These techniques have been discussed in Chapter Frequency compensation. We have seen that compensation with phantom zeros minimally affects other performance aspects, such as noise and over drive recovery, while maintaining the bandwidth of the servo function close to its designed value.
Local feedback amplifier stages#
The application of negative feedback around a single CE or CS stage results in local feedback stages. These stages have been studied in Chapter Local feedback stages. Commonly used nonenergic local feedback stages are the emitter follower, the source follower, the CB stage and the CG stage. Single-loop, single-transistor, passive feedback stages are the series stage and the shunt stage. Dual-loop, single transistor feedback stages, as well as stages that exploit indirect feedback, such as the voltage mirror and the current mirror, have also been introduced in Chapter Local feedback stages. Balanced, local feedback stages are obtained after applying balancing techniques to the basic feedback stages.
The properties of feedback stages can easily be predicted by considering the behavioral modifications that are a result of negative feedback:
Each feedback loop fixes one transmission parameter.
Parallel feedback at a port reduces the port impedance (ideally to zero).
Series feedback at a port increases the port impedance (ideally to infinity).
Both series and shunt feedback at a port establishes a finite non-zero port impedance primarily defined by the feedback networks.
The properties of balanced feedback stages can easily be predicted by considering the behavioral modifications that are the result of balancing:
Balancing provides odd characteristics.
Differential-mode bias sources convert into common-mode bias sources.
Anti-series connection provides a four-terminal stage with a current limiting charachter.
Complementary-parallel connection provides push-pull stages with a voltage limiting character. Those stages can source and sink currents that exceed the stage’s quiescent operating current.
This chapter#
In this chapter, we will put all the knowledge obtained from the previous chapters together, and define an approach for the design of multi-stage negative feedback amplifiers.
In section Controller design considerations, we will formulate basic considerations for the design of the controller. The following topics that be discussed:
Design of the input stage
Design of the output stage
Design of the number of stages
Interconnection of stages
Interconnection of the feedback network and the controller
The use of cascode stages
Application of local feedback stages
Chapter Amplifier Biasing is devoted to biasing of the stages in the controller.