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.

Key Features:

• Develops theory and pragmatic techniques based on simple models for designing amplifiers with bandwidths extending from DC to the multi-GHz frequencies while maintaining a good transient response (MFED)



• Uses a combination of simulation programs, including SPICE and Genesys, to compare real circuit performance to simulated data



• Develops highly accurate, simplified models providing insight into the behavior of all kinds of analog circuits, including wideband amplifiers, RF amplifiers, and circuits used for audio frequencies

• Chapter 1 Basic Network Theory


• 1.1 Introduction


• 1.2 RC Low-Pass Filter


• 1.3 Transient Analysis


• 1.4 Second-Order Systems—an RLC Low-Pass Filter


• 1.4.1 The Ideal Time-Delay Function


• 1.4.2 Phase Delay


• 1.4.3 Envelope Delay


• 1.4.4 The MFED Function


• 1.4.5 Series Peaking


• 1.4.6 Step Response—Series-Peaked Network


• 1.4.7 Bandwidth for a Series-Peaked Circuit


• 1.4.8 Bandwidth Improvement Factor


• 1.4.9 Series-Peaked Rise-Time�Bandwidth Product


• 1.4.10 Phase Delay for a Series-Peaked Circuit


• 1.4.11 Envelope Delay for an RLC Series-Peaked Circuit


• 1.4.12 What is �?


• 1.5 Cascaded Filters


• 1.5.1 Rise-Time�Bandwidth Product


• 1.5.2 Bandwidth For N-Cascaded Identical Filters


• 1.5.3 Nonidentical Cascaded Stages


• 1.5.4 Optimum Number of Cascaded Stages


• 1.5.5 Optimum Number of Stages to Optimize Gain�Bandwidth


• 1.6 Additional Peaking Techniques


• 1.6.1 Shunt Peaking


• 1.6.2 “T-Coil” Peaking


• 1.6.3 A Misadjusted Coefficient of Coupling, k


• 1.6.4 T-coil with MFA Response


• 1.6.5 T-coil with �= 0.5


• 1.7 Nonsymmetric T-Coils


• 1.8 Other Uses of T-Coils


• 1.8.1 Delay Lines


• 1.8.2 Reciprocity


• 1.8.3 An Analog SumBus Example


• 1.9 Physical Implementation of a T-Coil


• 1.10 Peaking Technique Summary


• 1.11 Chapter Summary


• References


• Chapter 2 Transistor Models with Application to Follower Circuit


• 2.1 Overview


• 2.2 High-Frequency Models


• 2.3 High-Frequency Models


• 2.3.1 Model 1


• 2.3.2 A Second High-Frequency Model


• 2.3.3 A Simplified Variant of the Second Model


• 2.3.4 A Third Model Appropriate for Op-Amps


• 2.3.5 Both Low- and High-Frequency Models are Necessary


• 2.3.6 Adding Back Stray Elements


• 2.4 Applying the Models


• 2.4.1 Input Impedance of the Emitter Follower


• 2.4.1.1 Solve For Zin Start by solving for Zin as defined in Figure 2�12:


• 2.4.2 Let Ze = Re, a Pure Resistor


• 2.4.2.1 Adding Back Rb a


• to Obtain Zin Total


• 2.4.3 Voltage Gain


• 2.4.4 Capacitive Loading


• 2.5 Cauer Series Expansion


• 2.6 Conditions for Stability for an Emitter Follower with a Capacitive Load


• 2.6.1 Routh�Hurwitz Criteria


• 2.6.2 Emitter-Follower Stability for a Capacitive Load


• 2.7 A Little Too Simple; Add Back REB and CJC


• 2.7.1 Adding Bulk Resistance to the Emitter


• 2.7.2 Computing the Base Resistor Combination to Eliminate Negative Elements


• 2.8 An Example


• 2.8.1 Applying Genesys to the Example


• 2.8.2 s-Parameters and Stability


• 2.8.3 Unconditional Stability


• 2.8.4 Apply These Concepts to the Circuit Example


• 2.9 Adding Resistance to the Base


• 2.10 Stopping Oscillations


• 2.10.1 Adding Positive Impedance in the Base to Cancel the Negative Elements Generated by the Transistor


• 2.10.1.1 Real Numbers for the Cancellation Network


• 2.10.1.2 Increase L1 from 0 to 10 nH; Is It Still Stable?


• 2.10.1.3 Series Peaking: Voltage Gain with Compensation


• 2.10.2 What If We Did Have Control over L?


• 2.10.2.1 Using T-coil Peaking for the Emitter-Follower Circuit Example


• 2.10.3 Overview of Results


• 2.10.4 Emitter Cancellation of Negative Elements in an Emitter Follower


• 2.10.4.1 Series-Peaking the Sample Circuit with Emitter-Cancellation Network


• 2.10.4.2 T-coil-Peaking the Emitter Follower with Compensation Network in Emitter


• 2.10.5 T-coil-Peaking the Load Capacitor in the Emitter


• 2.10.5.1 Optimizing the Value of RL for Maximum Bandwidth


• 2.10.5.2 Example


• 2.10.5.3 Stopping Oscillation with a Resistor Added to the Emitter


• 2.11 Package Parasitics


• 2.11.1 Simulation Results


• 2.12 Emitter-Follower Output Impedance


• 2.12.1 Output Impedance Summary


• 2.13 FETs


• 2.13.1 A Sample FET Follower


• 2.13.2 Determining Component Values for the Device Model


• 2.13.3 Determining Component Values for the FET Follower Circuit


• 2.13.4 Simulation Results for the FET Follower


• 2.13.5 Using the Negative-Element-Cancellation Network in the Gate
• 2.13.5.1 A Second Pole


• 2.14 Negative Elements


• 2.15 The Grounded Base Amplifier


• 2.16 Chapter Summary


• References


• Chapter 3 The Difference Amplifier


• 3.1 Difference Amplifier Basics


• 3.2 High-Frequency Gain of the Difference Amplifier


• 3.2.1 Low-Frequency Current Gain


• 3.2.1.1 Approximation for High gm


• 3.2.2 Case 1: Ze= Re


• 3.2.3 Example: Resistor in Emitter


• 3.2.4 Case 2: Ze as a Parallel RC Network


• 3.2.5 Add Effects of Emitter Bulk Resistance, Reb


• 3.2.5.1 Total Capacitance Seen at the Base Node


• 3.2.5.2 Input Impedance


• 3.2.5.3 Voltage Gain, Base to Emitter


• 3.2.6 Voltage Gain, Base to Collector


• 3.2.6.1 Gain from Emitter to Collector


• 3.2.6.2 Miller Effect and Junction Capacitance


• 3.2.6.3 Summary


• 3.2.6.4 Example: Bandwidth for Circuit with Complete NE851M03


• 3.2.6.5 Simulation Results


• 3.3 Series Peaking


• 3.3.1 Optimizing Rs to Yield Maximum Bandwidth


• 3.4 Adding a PNP Level-Shifter


• 3.4.1 PNP-Level-Shifter DC Characteristics


• 3.4.2 AC Performance of the PNP-Level-Shift Circuit


• 3.4.2.1 Total System Bandwidth


• 3.4.3 Simulations Results for PNP Level-Shifter


• 3.5 Full Differential Amplifier Driven Differentially


• 3.6 A Single-Ended Difference Amplifier


• 3.7 The ft Doubler


• 3.7.1 Cascading Stages


• 3.7.1.1 Three Cascaded Gain Stages


• 3.8 Noise Figure


• 3.8.1 What Is Noise Figure?


• 3.9 A Capacitive Load


• 3.9.1 A “Spiking” Network


• 3.9.2 Deriving the Values for RR, CR, Rx, Cx, Ce, and Ls


• 3.9.3 Base Network


• 3.9.4 Adding Reb and Low gm to the Spiking Network


• 3.9.5 Taking into Account the Effects of Finite reb and gm in Designing a Spiking Network


• 3.9.5.1 A Base Network to take into Account Reb and Low gm


• 3.9.6 Deriving the Output Voltage-Gain Function with the Spiking Network


• 3.9.7 Selecting Components for MFED Response


• 3.9.8 Bandwidth and Frequency Scaling


• 3.9.9 T-coil-Peaked High-Capacitance Driver


• 3.9.10 Spiking-Network Summary


• 3.9.10.1 Series Peaking


• 3.9.10.2 T-coil Peaking


• 3.9.11 Example; a Spiking Network


• 3.10 FET Differential Amplifier


• 3.11 Chapter Summary 234 References


• Chapter 4 Low-Frequency Nonlinear Performance


• 4.1 Overview


• 4.2 Basic Models


• 4.2.1 Gain and Impedance Functions


• 4.2.2 Let � Approach Infinity


• 4.3 gm Modulation


• 4.4 Nonlinearity in Difference Amplifiers


• 4.4.1 Differential Drive Equations


• 4.4.2 An Example


• 4.4.3 A Second Example


• 4.5 A Low-Distortion Difference Amplifier


• 4.5.1 Assume That Reb Equals Zero and � Equals Infinity. How Well Does This Circuit Work?


• 4.5.2 Using the Complete Model


• 4.5.3 Reduce Power, Keep Linearity the Same


• 4.5.4 High-Frequency Response


• 4.5.5 A Second Example


• 4.5.6 Cascaded Amplifiers


• 4.6 Feed-Forward Correction in FET Amplifiers


• 4.6.1 Improving Linearity by Increasing Current


• 4.6.2 High-Frequency Performance


• 4.7 Linearity Correction for ft Doublers


• 4.7.1 The ft Doubler


• 4.7.2 ft Doubler Linearity-Correction Circuit Type 1


• 4.7.2.1 An Example.


• 4.7.2.2 A Second Example


• 4.7.3 Comparisons Between the ft Doubler Circuit and the Difference Amplifier with Feed Forward


• 4.7.4 A More Power-Efficient Circuit for Improving Linearity in ft Doublers


• 4.7.4.1 An Example


• 4.7.4.2 Reducing Current to Save Power


• 4.7.5 FET Implementation


• 4.8 Summary of Linearity-Correction Circuits


• 4.9 Thermals [5]


• 4.10 Frequency-Dependent Dielectric Constants


• 4.11 Problems with Attenuators


• 4.11.1 An Aside


• 4.11.2 Hook!


• 4.11.3 Solutions


• 4.12 Chapter Summary 306 References


• Chapter 5 Shunt Feedback and Other Nifty Circuits


• 5.1 Overview


• 5.2 Composite Circuit


• 5.2.1 A Composite Circuit


• 5.2.2 Look More Closely at the Circuit


• 5.2.3 What Is the ft of the Composite Device?


• 5.2.4 Finding Zin with an Impedance in the Composite Devices Emitter


• 5.2.5 Example of Composite Circuit Used in a Difference Amplifier


• 5.3 Shunt Feedback


• 5.3.1 Derive the Low-Frequency Zin, Zout, and Gain for the Shunt Feedback Amplifier


• 5.3.2 Voltage Gain


• 5.3.3 Input Impedance


• 5.3.4 Output Impedance


• 5.4 High-Frequency Performance


• 5.4.1 Transresistance Gain


• 5.4.2 Output Impedance


• 5.5 Some Examples


• 5.5.1 Look at Output Impedance


• 5.5.2 Use RL to Control �


• 5.5.3 Use Cjc to Control �


• 5.5.4 Use Rf to Control �


• 5.5.5 RL is Finite and Fixed. Use Cjc to Control �


• 5.6 Driving High Capacitance Loads


• 5.6.1 Example 5�2: a Shunt Feedback Amplifier Driving a 25 pF Load


• 5.6.2 Use the Composite Circuit


• 5.6.3 Transresistance Gain and Reb


• 5.7 Op-Amps


• 5.7.1 Example 5�3


• 5.7.2 Transfer Function


• 5.7.3 Input Impedance


• 5.7.4 Output Impedance


• 5.7.5 SPICE Results for Sample Circuit


• 5.7.6 A Final Point about Shunt Feedback


• 5.8 NonLinear Effects in Op-Amps and Slew Rate


• 5.9 Chapter Summary 364 References


• Book Summary 365 Appendix A: Gummel-Poon Models and ft


• Appendix B: Two Port Parameters for the Simplified Models


• B.1 h-Parameter Two-Port Model


• B.2 s-Parameter Two-Port Network for the Simple Model


• Appendix C: More on T-coils
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About the Author / Editor


Allen Hollister has over 30 years experience in digital, analog, and RF engineering design and development. He has 14 patents either granted or in the patent pending process including four in the last year related to RFID. He has over 12 years of senior level engineering management experience and was one of the founders (and chairman) of the VXIbus consortium. He is a founder and Vice President of Engineering for Identifi Incorporated, a pioneer in RFID technology.

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