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ANALOG ELECTRONICS  2004
What we do at the Class Exercise 1 (March 1  6, 2004)
Elementary Passive Converters with Current Output
First Viewpoint: Voltage Causes Current ...
At every class exercise we will derive, build or even "invent" a few circuit building blocks which we will gradually accumulate in a library. Being initially empty, it will continuously grow and grow ... At the current exercise we will derive the first 10 elementary blocks as follows:
indivisible building blocks  sources/loads  voltage source  current load 
converters  voltagetocurrent converter  resistancetocurrent converter  
compund building blocks  current sources  voltagecontrolled current source  resistancecontrolled current source 
measuring devices  voltmeter  nonlinear ohmmeter  
multiinput devices  voltageoverresistance divider  series voltage summer 
PHILOSOPHY. In the beginning of the course, we try to reveal the causalitiy in ... Ohm's law. First, using a lot of analogies, we introduce an intuitive notion of the general attributes pressure, flow, impediment. Then, we concretize them into electrical attributes of voltage, current, resistance. Next, we discuss a bit philosophical question  What causes what? This is, so to say, the electrical version of the wellknown question Which came first, the egg or the hen? troubling philosophers from the remote past to the present :). As it is hard for us to answer this primary question we just assume ... the both alternative answers are possible. Well, let's first begin with assumption that pressure causes flow i.e. voltage causes current in the most elementary voltage supplied Ohm's circuit.
Answer the questions: What is pressure? What is flow? What is impediment? What is pressurelike attribute? What is flowlike attribute? What is impedimentlike attribute? What is voltage? What is current? What is resistance? Which came first, the egg or the hen :)? What is the causality between the pressurelike and the flowlike attributes in life? What causes what in Ohm's law  voltage causes current or current causes voltage? Add more questions ...
VARYING voltage or/and resistance as input variables and taking current as an output one we, figuratively spoken, "invent" the first three most elementary indivisible circuit building blocks: passive voltagetocurrent converter, resistancetocurrent converter and voltage/resistance divider (see also vtoi minitutorial). In order to visualize the invisible electrical attributes, first we draw circuit diagrams in a most suitable way. Then, we present voltages by potential bars with heights corresponding to their values, potential diagrams and superimposed IV curves; also we present current by a corresponding thickness of a current loop.

A resistor acting as a voltagetocurrent converter (see also a flash animation). Compare with the opposite currenttovoltage converter (Class 2). 

A resistor acting as a resistancetocurrent converter (see also a flash animation). Compare with the opposite resistancetovoltage converter (Class 2). 

A voltage/resistance divider. Compare with the opposite currentbyresistance multiplier (Class 2). 
"Provoking" questions: Is it worth to "invent" the most elementary circuit building blocks? If yes, how do we do that? Did Ohm invent the elementary passive circuits? What is an ideal VtoI converter? Does it exist? What does it really do? What is the relation between the input and output value of the ideal VtoI converter (RtoI converter)? Is a VtoI converter a reversible device? What happens if we swap its input and output? Is an RtoI converter a reversible device? Is the RtoI converter a linear device? What is a quiescent point of a VtoI (an RtoI) converter? How do we visualize it?
COMBINING the elementary blocks into more complicated compound blocks we build useful devices: voltagecontrolled current source; compound voltmeter made from an ammeter; resistancecontrolled current source; compound ohmmeter made from an ammeter; future devices (briefly)  multiplying R2R ladder DAC with an input (reference) voltage and a current output.
We can even write building "formula" for each compound building block:
voltagecontrolled current source = voltage source + voltagetocurrent converter,
compund voltmeter = voltagetocurrent converter + ammeter,
resistancecontrolled current source = voltage source + resistancetocurrent converter,
compund ohmmeter = voltage source + ammeter. Give more examples ...
May we say that the current source is a "bad" voltage source? How to take the current as an output? Are all the passive circuits ideal devices? What is an ideal current load? Can it really exist? Is it possible to measure something not consuming energy?
A small project: Dynamic curve tracer. Design a setup consisting of a transformer, resistor and a diode (ordinary, zener, LED) in order to visualize the diode's IV curve (VMAX = 5.6V, IMAX = 10 ma) on a oscilloscope. Can you connect the components in a way that will allow to trick the scope into showing a display of I versus V without any errors? What is the function of the resistor in this arrangement? Can we say that it functions as a perfect voltagetocurrent converter? What is the function of the diode? Can we say that it functions as a currenttovoltage converter?
IMPERFECTIONS. All the passive circuits with current output we have build are, curiously enough, ideal devices!? Well, more precisely speaking, they work at ideal load conditions (with "shorted" output). Once we try to consume their output current with a real load, they change for the worse.
What kind of input source does a VtoI converter "like"? What is the input resistance of the VtoI converter? What happens if we drive the converter with a real voltage source? When does аn ideal VtoI converter act as a real one? What kind of load does a VtoI converter "like"? What is the output resistance of the VtoI converter? What happens if we load the converter's current output with a real load?
IMPOVING. We begin looking for a remedy  how do we reduce the errors caused by the real voltage source and the real current load? Thus, a quite strange and even absurd idea of suppressing flashes on us  to reduce the error by introducing ... another higher error ?!? If we bring this idea to an end we will get the well known from electricity definition of an ideal current source.
How do we decrease the error (a settlement by compromise)?
IDEALIZING. This is a settlement by a compromise. That is why we begin right now, in the kingdom of pasive circuits, looking for an ideal solution which will enable us to convert the imperfect passive circuits with current output into almost ideal ones. What is more ...
GENERALIZING. At the next classes (2, 3, 4 and 5) dedicated to the rest passive circuits we will continue looking for a universal principle (a philosopher's stone :) for converting every imperfect passive circuit into an almost ideal one. What do you think, is there such a principle? And where do we look for it?
Questions: What is the difference between the passive and the active versions of the current output converters? Is there any relationship between them?
ENLARGING. We have derived many useful 1input passive devices from the most elementary Ohm's circuit. Why don't we try to derive multipleinput devices from Kirchhoff's circuits (laws)? Well, let's begin with Kirchhoff's voltage law ...
If we connect a few voltage sources in series to the load we get so useful series voltage summer (quite later on, using this building block, we will assemble electronic circuits with negative feedback  first imperfect, then almost ideal). Here, we strike the problem of common ground in circuitry which will make us "invent" later on the famous differential amplifier.
Finally, a great idea dawns on us  to connect (incorrectly?) two voltage sources to each other (don't do that with different car batteries :) and then to begin varying their voltages in opposite or in the same directions. Thus we get powerful ideas for future building "absurd" electronic circuits.
Presenting Class 1 as a Table
Why don't we present Class 1 in a form of table? Let's try! Here is a basic table. Add additional rows and columns to enrich it!
Block  Potential bars, current loops  Potential diagram  Working point (IV intersection) 
Transfer characteristic 
Function  Imperfections 
1. V > I  Animation  IOUT = f(VIN) curve 
IOUT = f(VIN)  Animation  
2. R > I  ? 
? 
?

IOUT = f(RIN) curve 
IOUT = f(RIN)  IOUT = f(RIN) 
3. V/R > I  ?

? 
?

IOUT = f(VIN,RIN)  IOUT = f(VIN,RIN)  
...  ...

... 
...

... 
...  ... 
Related web sites
Finally, let's see what the others say about this topic. Browsing the web for related resources, we may find excellent materials.
We may find related interesting problems in Lab 1 of Physics 123 electronics course taught by Tom Hayes at Harvard University (e.g. "show how to use the movement, plus whatever else is needed, to form a 10mAfullscale ammeter"). Tom Hayes is an author of Student Manual for the Art of Electronics  a student version of the famous The Art of Electronics.
Dynamic curve tracer. Design a setup consisting of a transformer, resistor and a diode (ordinary, zener, LED) in order to visualize the diode's IV curve (VMAX = 5.6V, IMAX = 10 ma) on a oscilloscope. Can you connect the components in a way that will allow to trick the scope into showing a display of I versus V without any errors? What is the function of the resistor in this arrangement? Can we say that it functions as a perfect voltagetocurrent converter? What is the function of the diode? Can we say that it functions as a currenttovoltage converter? Well, let's see how Tom Hayes has solved this problem in the Student Manual for the Art of Electronics (page 118). 
Look at Page 1 of Colin's Basic Electronics Course located on Talking Electronics site to see how he has solved the problem of current limiting.

. . . Question 6: How do you connect a LED to a supply voltage? Question 7: Why do you need a current limiting resistor?

Now, let's also see what Tony Kuphaldt (Bellingham Technical College, Washington) says in his Lessons In Electric Circuits. In Chapter 2 he reasons how voltage, current, and resistance relate; then he introduces a fluid analogy for Ohm's law. Browse also Topical worksheets from his great project of Socratic electronics; you may find there interesting questions.
Let's see also the more practical basic electronics course of Basic Car Audio Electronics maintained by Perry Babin. This course shows many applications in the cars. Perry has dedicated a separate page to various resistor applications (e.g. including current limiting) which we may apply in the class 1.
In his Intuitive electronics Glen Williamson shows how a resistor may act as a passive voltagetocurrent converter.
An interesting DCcircuit water analogy is presented in hyperphysics by Rod Nave.
Send your questions, views and suggestions about this topic to cyril@circuitfantasia.com
Last updated June 28, 2004
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