Anand Udupa - Zen of Analog Circuit Design
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From 2011 till 2013, I taught a course titled Analog Design for all which covered concepts starting with MOS transistors and progressed till the design of two-stage amplifiers. The course introduced concepts in a manner that led the student to the synthesis of new circuits, not merely their analysis. But I still felt that there was a more intuitive way to introduce Analog Circuit Design, one that would bring out the beauty of the subject so that the student could stop and smell the roses.
But why a Zen of Analog?
Because the foundational concepts in Analog closely mirror human relationships! The purpose of this book is to take a simplified and intuitive path to unlock some profound secrets of Analog. The protagonist of this book is Ang-Lao, a medieval monk who brings his insights into the Analog world to solve the challenges in human relationships.
The book addresses a problem statement that much of Analog Circuit Design tries to solve - how do you realize an ideal buffer? It starts with the simple concepts of voltage sources and current sources. From the I-V curve of the MOS transistor, we see how it behaves much like a Voltage controlled current source (VCCS). The inherent challenge in getting even a simple two-transistor circuit to work is the conflict arising from having two such current source-like elements in series. The digital inverter is shown to be one such circuit that can function like an analog amplifier, albeit over a narrow range of input voltage. The effect of loading on such a circuit is illustrated graphically and is shown as an added challenge in getting it to work in an analog manner.
Having understood the complications involved, we see how through the strikingly simple but immensely powerful concept of feedback, one of the two transistors can be modified subtly to make it behave like a voltage source. In that process, we realize our first approximation to an ideal analog buffer. We then see how manifestations of the same concept leads us to the synthesis of a whole bunch of two transistor circuits - source followers, common source amplifiers with gm-load and with diode-connected load, and differential amplifiers . The concepts used in synthesis of such elegant circuits are also extended to the analysis of much more complex circuits, for example, a Voltage to Current (V2I) conversion circuit. We introduce the concept of small signal parameters, gm, gds, showing the calculations for the gain and output impedance of our circuits, and quantifying how good each of our buffers really are.
The narrative switches between concepts of Electronics and the story of Aman-Ra, an engineer from Medieval Egypt. Struggling with his relationships, his guiding light is Ang-Lao, who teaches him the secret to happy relationships.
For some, this book will signal the end of the fear of Analog. For others, it will be the start of a love story.
Concepts covered
oI-V characteristics of Voltage & Current sources
oIdeal & non-ideal sources
oControlled sources
oActive and passive elements
oI-V characteristics of a MOSFET
oMOS transistor as a Voltage controlled current source
oDigital inverter as Analog amplifier
oOperating point
oCommon source (CS) amplifier
oEffect of loading on a CS amplifier
oFeedback
oHow can you make a MOSFET behave like a voltage source?
oSynthesis of a CS amplifier with diode-connected load
oAnalysis of a V2I circuit including an introduction to current mirror
oSynthesis of CS amplifier with gm-load
oSynthesis of source follower circuit
oSmall signal parameters: gm, gds
oSmall-signal gain and output impedance
oSynthesis of a differential amplifier
oSynthesis of an Operational amplifier
oRealizing the buffer using the Operational Amplifier
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Zen of Analog
Why a Zen of Analog?
Because the foundational concepts in Analog closely mirror human relationships! The purpose of this book is to take a simplified and intuitive path to unlock some secrets of Analog Design a path similar to Zen.
For some, this book will signal the end of the fear of Analog. For others, it will be the start of a love story with a new subject. For some others, it is hoped, this book will trigger a quiet moment of reflection into ones relationships.
After all, is not the intent of all Education that it should lead one to the betterment of ones life?
Contents
I want to know Gods thoughts the rest are details.
- Albert Einstein
The Holy Grail of Analog design can be summed up as a quest for an elusive component the Ideal buffer.
But what exactly is an ideal buffer?
The simplest definition of an ideal buffer is one where the output follows the input.
In other words, an ideal buffer is one where VOUT=VIN .
To put it more verbosely, an ideal buffer is one where the Response (Output) tracks the Stimulus (Input).
But there is one more attribute to an ideal buffer. The response (output) should continue to match the stimulus (input) even when the buffer gets loaded as shown below. Here the load is shown as a resistor drawing a DC current of ILOAD from the output of the buffer. But the load could also be a capacitor that draws a switching current or the load could draw a combination of a DC and a switching current.
So an ideal buffer is one which responds in an appropriate manner to a stimulus and this response is unaffected even if the buffer is loaded.
Now let us strike an analogy with one of the most important facet of human existence our relationships.
Lets say a couple has been contemplating taking a long overdue vacation. The wife makes a fervent appeal to the husband to take a break so that they can plan a vacation to Bali a place which serves as the setting for her favourite 9 PM soap opera. The husband agrees and works hard to get all his work completed so he can take off. The wife surfs the Internet, planning out every detail of the vacation. On the day the couple is supposed to fly out on their vacation, an important customer of the husband calls and reports a production-stop issue.
I suspect you get an inkling of where I am headed. So let me come straight to the point. The expectations from an ideal relationship bear some striking similarities to those from an ideal buffer. There is a stimuli - in the above example, it is the wifes request for a vacation. The response the couple taking off for the vacation was appearing to be an appropriate response to the stimuli. Until the point where the husband received that fateful customer call Well, every relationship has to deal with several types of loading be it demanding customers, a painful boss, hyperactive kids, or interfering in-laws. And similar to our expectations from an ideal buffer, we can state an ideal relationship as one where every stimulus elicits an appropriate response - irrespective of the effect of the loading factors!
But before we move further in our journey of Analog (and relationships), let me introduce you to the cast of our story.
Our story starts in ancient Egypt 3300 years ago. Our hero is Aman-Ra , a civil engineer who works in the VLSM industry. That is short for Very Large Scale Mummification . In layman terms, Aman-Ra builds pyramids. His companys clients are the hard-to-please Pharoahs. He has an equally hard-to-please boss called Gamen-Ra . Aman-Ra dreads the weekly meetings he has with his boss.
Aman-Ra is a happy and single but that is going to change soon I meant the part about being single. The one destined for him is a beautiful girl called Uman-Ra . She works for the Pharoahs wife in the role of a CFO (Chief Fanning Officer).
I want to tell you how they met, but we will have to wait a bit for that.
To get started with the language of Analog, we start with a recap of two of the most basic elements of Electronics. The first one is the ideal voltage source.
The ideal voltage source
I have shown below a voltage source, connected to a node in a circuit. It tries to impose the voltage (depicted by the symbol Vs) on the node it is connected to. The circuit in turn loads it with a current Io.
If the voltage source is ideal, then it continues to drive the node (of the circuit it is connected to) to the same value Vs irrespective of how much the current loading (Io) from the circuit is.
We can capture this graphically as an I-V curve as shown below.
Another property of the ideal voltage source is that it has zero output impedance. What this means is that if you load it with any current, however high, it will still impose the same voltage (equal to Vs) across the load. This is depicted below.
A non-ideal voltage source would have Ro> . This would lead to the voltage Vo to keep reducing as more current gets drawn from the voltage source.
While the voltage source is a good starting point, we will use a different element to start off on our Analog journey.
The ideal current source.
As shown below, the ideal current source is one that draws (or pumps) a constant current from (or into) the node of a circuit.
As before, the operative word is ideal. In this case, the current remains the same (equal to Is) irrespective of the voltage Vo imposed by the circuit across the current source. We will call Vo as the terminal voltage of the current source.
The I-V curve of an ideal current source is shown below.
Another property of the ideal current source is that it has an infinite output impedance as shown below. What this implies is that irrespective of the voltage across it, the full current Is will flow into the load. This is shown below.
If the current source current had a dependence on the terminal voltage across it, then it would a non-ideal current source with characteristics as shown below. This would be characterized by a finite value of output impedance, Ro.
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