Demonstration: capacitively loaded CC stage.
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Capacitively loaded Common Collector Stage
The common collector stage (CC stage) is a nonenergic unity-gain negative feedback voltage amplifier that has a CE (common-emitter) stage as controller. Under ideal drive and load conditions, the loopgain in a CC stage is usually larger than the loop gain of its MOS equivalent: the CD stage. As a result, a capacitively loaded CC stage easily becomes instable.
A demonstration of the step response a capacitively loaded CC stage with a 2N3904 BJT shows this effect.
Presentation
The presentation “Capacitively loaded CC stage” discusses the analysis of the frequency response of the demonstrated stage with the aid of the asymptotic gain feedback model and elucidates frequency compensation with the aid of a phantom zero at the input and at the output of the stage.
Guidance with homework
Chapter 13
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Modeling of negative feedback circuits
Two-step design of negative-feedback amplifiers
The design of negative-feedback amplifiers can be performed in two steps:
This two-step design method requires that butgets for performance limitations of the amplifier are split into error budgets for the feedback networks and error budgets for the controller.
Presentation
The presentation “Two-step design of negative feedback amplifiers shows that a feedback model that supports the two-step design of negative feedback amplifiers will tell us in which way and to what extent performance limitations of the amplifier are affected by performance limitations of the controller(s).
Video
Two-step design of negative feedback amplifiers
Study
Chapter 10.1
Feedback model of Black
In 1927, Black built the first negative feedback amplifier. The feedback model of Black is commonly used to evaluate the dynamic performance of negative feedback systems. However, Black’s feedback model is not optimally suited for the analysis of dynamic behavior of electronic feedback amplifiers and providing meaningful design information from such analysis.
Presentation
The presentation “Feedback model of Black introduces the feedback model of Black and shows its limitations for the analysis of electronic feedback circuits.
Video
Study
Chapter 10.2
Asymptotic-gain feedback model
The asymptotic-gain feedback model provides a solid base for relating controller imperfections such as:
to important performance limitations of the amplifier:
Presentation
The presentation “Asymptotic-gain model introduces the asymptotic-gain feedback model.
Video
Asymptotic-gain feedback model
Study
Chapter 10.3.1, 10.3.2
Selection of the loop gain reference variable
The analysis of feedback circuits with the asymptotic-gain feedback model gives the same result as network analysis techniques. However, if the loop gain reference is selected in a proper way, the asymptotic-gain model provides much more design information and it facilitates two-step design of negative feedback circuits.
Presentation
The presentation “Selection of the loop gain reference illustrates the way in wich the loop gain reference should be selected such that the model provides meaningful design information.
Video
Selection of the loop gain reference
Study
Chapter 10.3.3, 10.3.4
Port of impedance single-loop feedback amplifiers
The port impedance of single-loop feedback amplifiers can be expresses in tems of the asymptotic-gain feedback model.
Presentation
The presentation “Port impedance of single-loop feedback amplifiers shows the way in which this can be done.
Study
Chapter 10.3.6
Derive controller requirements from amplifier requirements
Bandwidth of a negative feedback amplifier
For design purposes it is convenient to decouple the definition of the bandwitdth of a negative feedback amplifier from its desired frequency characteristic. This can be achieved by defining the bandwidth of a negative feedback amplifier by that of its servo function.
Presentation
The presentation “Bandwidth of a negative feedback amplifier shows that the bandwidth of a negative feedback amplifier will be defined as that of its servo function.
Video
Bandwidth definition for negative feedback amplifiers (3:40)
Study
Chapter 11.4.1
Example: Bandwidth of a negative feedback transimpedance integrator
Presentation
The presentation “Bandwidth Transimpedance Integrator shows the bandwidth definition for a negative feedback transimpedance integrator.
Video
Example Bandwidth definition for an OpAmp Integrator Circuit (7:12)
study
Chapter 11.4
Butterworth or Maximally Flat Magnitude (MFM) responses
The -3dB cut-off frequency of systems with a Butterworth or MFM transfer equals the Nth root of the magnitude of the product of their N poles, where N is the order of the system.
In this course we will design the frequency response of a feedback amplifier in such a way that the servo function obtains an MFM or Butterworth filter characteristic over the frequency range of interest. Design procudures for other filter characteristics, such as, Bessel or Chebyshev do not differ. Only the numeric relation between the -3dB bandwidth and the gain-poles product of the loop gain will be different.
Presentation
The presentation “Butterworth or Maximally Flat Magnitude (MFM) responses shows the Laplace transfer functions, the pole patterns and the magnitude characteristics of first, second and third order Butterworth transfers.
Video
Butterworth frequency responses (4:07)
Study
Chapter 11.4.3
MFM bandwidth of an all-pole feedback amplifier
The product of the loop gain and the magnitude of the dominant poles of the loop gain is a design parameter for the -3dB MFM bandwidth of an all-pole negative feedback amplifier .
Presentation
The presentation “All-pole loop gain and servo bandwidth proofs the above.
Video
All-pole Loop Gain and Servo Bandwidth (5:13)
Study
Chapter 11.4.3
Determination of the dominant poles of the loop gain
Presentation
The presentation “Dominant and non-dominant poles in feedback systems illustrates the procedure for separating dominant poles and non-dominant poles on feedback systems.
Video
Dominant poles and non-dominant poles of the loop gain (8:53)
Study
Chapter 11.4.3
Determination of the requirement for the gain-bandwidth product of an operational amplifier
The requirement for the GB-product of an operational amplifier can be derived from the loop gain-poles product (for dominant poles only).
Presentation
The presentation “Determination of OpAmp GB-product requirement illustrates the procedure for deriving the requirement for the gain-bandwidth product of the operational amplifier from the expression of the loop gain.
Video
Determination of GB product requirements for operational amplifiers (5:35)
Study
Chapter 11.4.3
Frequency stability of negative feedback systems
A system is stable if its responses to bounded excitations are also bounded.
A lumped system is said to be stable if the solutions of its characteristic equation (the poles) all have a negative real part.
Presentation
The presentation “Frequency stability of feedback amplifiers presents three ways to determine the stability of feedback systems.
Study
Chapter 11.5
Frequency compensation
Introduction to Frequency Compensation
After the bandwidth of a negative feedback amplifier has been designed, the poles of the transfer are not necessarily in the desired positions.
Presentation
The presentation “Introduction to Frequency Compensation defines the term frequency compensation and presents strategies and methods for frequency compensation.
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Introduction to frequency compensation (9:01)
Study
Chapter 12.1
The Phantom Zero
Phantom zero frequency compensation is the most powerful frequency compensation technique.
Presentation
The presentation “Frequency Compensation: the Phantom Zero introduces the concept of the phantom zero.
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Study
Chapter 12.2.1
Phantom Zero Compensation of a 2nd-order System
Presentation
The presentation “Frequency Compensation: the Phantom Zero Compensation of a 2nd-order System applies the concept of phantom zero frequency compensation to the compensation of a second order system.
Video
Study
Chapter 12.2.2
Implementation of Phantom Zeros
Practical implementation of phantom zeros can be accomplishes in two ways:
Active implementation requires the use of active differetiating circuits in the feedback loop of the amplifier.
Passive compensation requires the insertion of loop gain zeros in:
Such passive zeros are called effective if:
This is usually the case if, before compensation, these feedback networks or coupling networks introduce a large attenuation in the loop gain at the phantom zero frequency.
Presentation
The presentation “Implementation of Phantom Zeros presents passive implementation techniques for phantom zeros and discusses the effectiveness of the frequency compensation.
Study
Chapter 12.2.4, 12.2.5, 12.2.6
Examples Phantom Zero Frequency Compensation
Presentation
The presentation “Examples Phantom Zero Compensation presents Examples 11.8, 12.8 and 12.9.
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Examples of implementation of phantom zeros (15:23)
Study
Examples 11.8, 12.8 and 12.9
Phantom zero compensation and interaction with other performance aspects
Presentation
The presentation “Phantom zero compensation and interaction with other performance aspects briefly discusses the interaction between frequency compensation with phantom zeros and other performance aspects, such as, noise, bandwidth, weak distortion, energy storage, power dissipation and overdrive recovery.
Study
Chapter 12.2.8.
