Wideband Amplifier Design
In this book, the theory needed to understand wideband amplifier design using the simplest models possible will be developed. This theory will be used to develop algebraic equations that describe particular circuits used in high frequency design so that the reader develops a 'gut level' understanding of the process and circuit. SPICE and Genesys simulations will be performed to show the accuracy of the algebraic models. By looking at differences between the algebraic equations and the simulations, new algebraic models will be developed that include parameters originally left out of the model. By including these new elements, the algebraic equations provide surprising accuracy while maintaining simplicity and understanding of the circuit. While the emphasis is on wide bandwidth (DC to several GHz) amplifiers with good transient response, the techniques presented are also quite useful to people doing classic analog design. For example, the same things that cause certain one-transistor amplifiers to oscillate at 5 GHz can also explain the behavior of an op-amp loaded into a capacitor. The term 'high frequency' is relative. As such, this book is of interest to anyone doing analog design. Both op-amp designers (Integrated Circuit) and op-amp users will find the material useful. Other applications include fast digitizers, analog to digital converters (A/D), and digital to analog converters (D/A), as well as the emerging area of Ultra Wideband (UWB) radio. Narrow bandwidth (classic Radio Frequency (RF) design) is either similar to, or a subset of the techniques presented in this book. As such, classic RF designers will also find the contents of this book useful.
Inspec keywords: wideband amplifiers; network synthesis; passive networks
Other keywords: circuit modeling; passive network theory; high-frequency transistor models; wideband amplifier design; wide-bandwidth applications
Subjects: Passive filters and other passive networks; Amplifiers; General circuit analysis and synthesis methods
- Book DOI: 10.1049/SBCS010E
- Chapter DOI: 10.1049/SBCS010E
- ISBN: 9781891121517
- e-ISBN: 9781613530573
- Format: PDF
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Front Matter
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1 Basic Network Theory
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In this chapter, you will learn about various kinds of low-pass filters, such as Butterworth filters and maximally flat envelope delay (MFED) filters. You will see the small-signal bandwidth these filters exhibit as well as how they respond to step response. You will learn that all high-frequency circuits are eventually limited in their bandwidth because of output resistance driving an input capacitance. And then you will observe that it is possible to increase bandwidth by the judicious use of inductance added in the right place. You will find that it is possible to obtain as much as 2.72 times the bandwidth of a simple RC (resistance/capacitance) low-pass filter while maintaining good transient response. These techniques are referred to as 'peaking' networks.
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2 Transistor Models with Application to Follower Circuit
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Before we can do any high-frequency designs, we need simplified high-frequency models for active devices; BJT (bipolar junction transistors) and FET (field effect transistors) that are (1) generic, i.e., applicable to just about any active device, (2) simple, in order to allow algebraic manipulation that is easy enough to perform, and (3) a model that provides easy-to-understand results. Generalized, hybrid-π models are too complicated to meet this need, although that is where we will start. They contain information needed for analysis at low frequencies, which is not needed for high-frequency analysis. We want to create a model that contains only the information needed for high-frequency analysis - and nothing more. The model we will create is based on frequency-dependent sources with DC gains set to infinity. It will work so long as the active device can be modeled with one pole in its frequency response, and it will work for frequencies above the point where the gain begins to roll off with frequency (sometimes called the fβ frequency). Once created, the model will first be applied to follower circuits. Follower circuits provide unity voltage gain from input to output while keeping the input impedance at ∞ and the output impedance at zero. At first glance, these circuits seem simple. Unfortunately, these circuits tend to oscillate freely at high frequencies when loaded into certain kinds of loads (principally capacitive). In some cases, the only sign that the circuit is oscillating is a distorted waveform that changes as you move your finger toward it. Because of this circuit's unique character, we will study it in detail. The analysis will prove quite useful for understanding other circuits described in future chapters, such as differential amplifiers.
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3 The Difference Amplifier
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This chapter develops the concept of difference amplifiers as applied to high-frequency design. The author has used the models developed in the last chapter to analyze these circuits. The author found that by setting the time constant of the parallel combination of ReCe to the transistor Tt, the input impedance at the base would look like a pure capacitor that could be series-, shunt-, or T-coilpeaked. The authors developed the concept of a level-shift PNP transistor that allowed a complete gain block to be created. The gain block is designed so that it has zero DC volts at both the input and output along with the same impedance levels (usually 50-100 Ω). This allows gain blocks to be directly cascaded.
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4 Low-Frequency Nonlinear Performance
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So far, the author has not been overly concerned with low-frequency effects. Unfortunately, there are several issues that operate at DC or low frequencies that cause problems at higher frequencies. The changing of gm with some circuit parameter (gm modulation) and the thermal effects as a function of signal level and power are two such examples. Fortunately, a variety of circuits and techniques have been developed to either correct or greatly alleviate these problems. This chapter is devoted to these concepts. The authors begin this chapter using the basic hybrid-π model to derive low-frequency gain equations. While some of this repeats information from the previous chapters, a more coherent flow should make the concepts a little easier to follow.
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5 Shunt Feedback and Other Nifty Circuits
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Up to now, all the circuits the author has talked about have used series feedback, where the local feedback element is in series with both the input and output currents. In this chapter, the author looks at shunt feedback, where some of the output voltages are sampled and shunted back to the input. This is the technique used by almost all op-amp circuits. However, since the same technique can be applied successfully to high-frequency circuits, the authors need to investigate this important concept. Moreover, there is another important circuit that does not fit well into the other categories. This is a circuit made up of three transistors that produces the equivalent of a single transistor. This composite circuit has a higher equivalent ft and twice the β of the devices making up the circuit. Because it can be used almost anywhere a single transistor can be used, it is an extremely useful circuit - especially handy when designing integrated circuits, because it is easy to add transistors to an integrated circuit. This circuit provides almost the same bandwidth-improvement factor as series peaking. But because series peaking requires inductors, the composite circuit is much easier to implement on an integrated circuit.
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6 Book Summary
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Apart from showing how wide bandwidth amplifiers and some of the resulting circuits are designed, the author wanted to explore the techniques used for designing these circuits. While not every circuit invented can be shown in one book, the techniques used here are applicable to any circuit. If you understand these techniques, then you will have added a powerful new tool to your arsenal. These techniques are not limited to broadband amplifiers. They can be easily adapted to narrowband applications or, in a general sense, to low-frequency applications. A major aspect of the technique is to recognize that SPICE and the other simulation programs 'throw the book' at a problem by using every conceivable transistor parameter under the sun to model the problem.
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Appendix A: Gummel-Poon Models and ft
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Another reason to change the actual Gummel-Poon parameters (while keeping ft the same) is to see the effect on the circuit of a particular parameter (the usual one being Cjc) without upsetting the over ft of the device. Cjc affects things outside the immediate transistor. For example, it is the main component in s12; typically, if Cjc were zero, s12 would be zero. It is also the principal contributor to preshoot. It supplies the capacitive sneak path that causes preshoot. To see if these effects are dominant in your circuit, it is sometimes necessary to absorb the effects of Cjc on ft into one or both of the other parameters (Cje or τf) so that the transistor ft does not change if Cjc is set to zero. The outside circuit effects will be changed with Cjc equal to zero. In this way, a valid comparison can be made and we can determine the importance of Cjc. The author used this technique when talking about preshoot in earlier chapters to illustrate certain points.
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Appendix B: Two Port Parameters for the Simplified Models
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It is useful to have two-port models available for the simplified transistor models introduced in Chapter 2. The model shown in Figure B-1 does not include any reference to Cjc or Rbb, but these items are easily added later, and there are times you would want to perform an analysis without them. Cjc is included in the equation for ft (and therefore Tt ) so the frequency response for the model has not been compromised. The author has included Reb because it is an important factor, and it is not always easily added. From this model, we want to derive the two-port h-parameter and the two-port s-parameter model.
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Appendix C: More on T-coils
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The following was contributed by Dr. Allen Podell (he teaches Advanced Wireless Microwave Techniques at Besser Associates and is an expert in microwave engineering). It is a discussion of how T-coils can be derived from a lattice network with two baluns and more importantly, how their 'ideality' (their frequency response) can be extended by including an extra shield wire.
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Back Matter
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