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ANALOG ELECTRONICS - 2004

A Content of the Classes

A. PASSIVE ANALOG CIRCUITS

I. Passive Analog Converters Containing Resistive Elements

Class Exercise 1 (March 1 - 6, 2004)

1. Elementary Passive Converters with Current Output

1.1. The elementary voltage supplied electric circuit. Functional notion of voltage causes current phenomenon (direct causality in Ohm's law). Circuit building blocks and electric attributes. How to visualize the invisible electric attributes: potential bars, potential diagrams, current loops, superimposed IV characteristic curves.

1.2. Deriving elementary analog converters from the basic voltage supplied electric circuit.
1.2.1. Voltage-to-current converter.
Applications: producing a current from a voltage (compound voltage-controlled current source); indirect measuring a voltage by converting into a current (compound voltmeter); transistor switch (an input part); current interface (a transmitter). Imperfections caused by a real voltage source and a real current load. Discussions: May we say that the current source is a "bad" voltage source? How do we decrease the errors (a settlement by compromise - method 1)? How do we remove completely the circuit imperfections (an ideal solution)? How do we convert the imperfect passive circuits into almost ideal ones (looking for a universal principle)?
1.2.2. Resistance-to-current converter. Applications: producing a current controlled by a resistance (compound resistance-controlled current source); indirect measuring a resistance by converting into a current (compound ohmmeter); indirect measuring non-electrical quantities by resistive sensors. Discussion: How do we remove the imperfections?
1.2.3. Voltage-into-resistance divider. Application outlined: multiplying digital-to-analog converter (R-2R ladder) with a reference (an input) voltage and a current output. How do we remove the imperfections?

1.3. Deriving elementary analog converters from а multiple voltage supplied electric circuit.
1.3.1. Series voltage summer
(according to II Kirchhoff's law). Application: subtractor in electronic circuits with a series negative feedback (briefly mentioned). Imperfections and ideas for a remedy. Discussion: What is a "common ground" problem in circuitry?
1.3.2. Circuits with "incorrectly" connected voltage sources. Discussions: Might we connect to each other two voltage sources? What happens if we begin varying the source voltages (in opposite or in the same directions)? Ideas for future building "absurd" electronic circuits.

Class Exercise 2 (March 8 - 13, 2004)

2. Elementary Passive Converters with Voltage Output

2.1. The elementary current supplied electric circuit. Functional notion of current causes voltage phenomenon (reversing causality in Ohm's law). Circuit building blocks and electric attributes.

2.2. Deriving elementary analog converters from the basic current supplied electric circuit.
2.2.1. Current-to-voltage converter.
Applications: producing a voltage from a current (compound voltage source); indirect measuring a current by converting into a voltage (compound ammeter, analog-to-digital converter with current input); current interface (a receiver); current feedback. Imperfections caused by a real current source and a real voltage load. Discussions: How do we decrease the errors (a settlement by compromise)? How do we remove completely the circuit imperfections (an ideal solution)? How do we convert the imperfect passive circuits into almost ideal ones (looking for a universal principle)?
2.2.2. Resistance-to-voltage converter. Applications: producing a voltage controlled by a resistance (compound resistance-controlled voltage source); indirect measuring a resistance by converting into a voltage (compound ohmmeter); indirect measuring non-electrical quantities by resistive sensors. Discussion: How do we remove the imperfections?
2.2.3. Current-by-resistance multiplier. Application outlined: multiplying digital-to-analog converter (R-2R ladder) with a reference (an input) current and a voltage output. How to remove the imperfections.

2.3. Deriving elementary analog converters from а multiple current supplied electric circuit.
2.3.1. Parallel current summer
(according to I Kirchhoff's law). Application in electronic circuits with a pаrallel negative feedback (briefly mentioned). Imperfections and ideas for a remedy.
2.3.2. Circuits with "incorrectly" connected current sources. Discussions: Might we connect to each other or in series to the load two current sources? What happens if we begin varying the source currents (in opposite or in the same directions)? Ideas for future building "paradoxical" electronic circuits.

Class Exercise 3 (March 15 - 20, 2004)

3. Compound Passive Converters with Voltage Output

3.1. Voltage divider - building by the more elementary voltage-to-current converter and current-to-voltage converter (resistance-to-voltage converter). Applications: voltage-to-voltage converter; resistance-to-voltage converter (a future application in the transistor stages); movement-voltage converter (sensor); resistance ratio-by-voltage multiplier. Imperfections and ideas for an improvement.

3.2. Parallel voltage summer - assembling from more elementary building blocks: voltage-to-current converter; current-to-voltage converter and parallel current summer. Visualizing the operation by a potential diagram. Future applications: subtractor in electronic circuits with a parallel negative feedback (briefly mentioned); converting a bipolar input/output into a unipolar and v.v.; resistive digital-to-analog converter. Discussion 1: Comparing the parallel voltage summer and the series one (imperfections and ideas for an improvement). Discussion 2: What is virtual ground? Is it inherent only for the future op-amp circuits with negative feedback?

3.3. Bridged circuits - building from more elementary voltage dividers. Exploring at differential and common input signals. Discussion: What is a differential and common input signal? Ideas for a future application in the bridged transistor stages.

3.3. Deriving elementary analog converters from а heterogeneous supplied electric circuit.
3.3.1. Series summer of a current and a voltage
. Application in electronic circuits with a pаrallel negative feedback (briefly mentioned). Imperfections and ideas for a remedy. Discussion: May we load a voltage source by a current source and v.v.? Ideas for future building odd electronic circuits.

II. Passive analog converters containing reactive elements

Class Exercise 4 (March 22 - 27, 2004)

4. Passive Integrators and Differentiators

4.1. Elementary capacitive circuits. Deriving a functional notion of an element storing potential energy from many everyday situations (analogies).
4.1.1. Capacitive integrator with current input and voltage output (C current-to-voltage integrator). Application - an elementary building block for
assembling more complicated integrators. Discussion: Is the circuit an ideal integrator? Imperfections caused by a real current source. Looking for a remedy.
4.1.2. Capacitive differentiator with voltage input and current output (C voltage-to-current differentiator). Application - an elementary building block for
assembling more complicated capacitive differentiators. Discussions: Is the circuit correct? What does a voltage source "like"? What does it "hate"? Is it an ideal differentiator? Imperfections caused by a real current load. Looking for a remedy.

4.2. Building compound resistive-capacitive converters with voltage inputs and outputs.
4.2.1. RC integrator. Building the circuit by using the more elementary voltage-to-current converter and C current-to-voltage integrator. Applications: imperfect ramp generator (assembling from an external square generator and RC integrator); filtering circuits etc. Imperfections and remedies.
4.2.2. CR differentiator. Building the circuit by using the more elementary C differentiator and current-to-voltage converter. Applications: pulse "shortening" circuits; dynamic potential "shifting" circuits (ideas for future applications in transistor bias circuits). Imperfections and remedies.

4.3. Elementary inductive circuits. Deriving a functional notion of an element storing kinetic energy from many everyday situations (analogies).
4.1.1. Inductive integrator with voltage input and current output (L voltage-to-current integrator). Application - an elementary building block for
assembling more complicated inductive integrators. Imperfections caused by a real current load. Looking for a remedy.
4.1.2. Inductive differentiator with current input and voltage output (L voltage-to-current differentiator). Application - an elementary building block for
assembling more complicated inductive differentiator. Discussions: Is the circuit correct? What does a current source "like"? What does it "hate"? Is it an ideal differentiator? Imperfections caused by a real current source. Looking for a remedy.

4.4. Building compound resistive-inductive converters with voltage inputs and outputs.
4.4.1. LR integrator. Building the circuit by using the more elementary L integrator and current-to-voltage converter. Imperfections and remedies.
4.4.2. RL differentiator. Building the circuit by using the more elementary voltage-to-current converter and C differentiator and L differentiator. Visualizing the operation by means of potential bars. Imperfections and remedies.

B. ELECTRONIC ANALOG CIRCUITS WITHOUT FEEDBACK

Class Exercise 5 (March 29 - April 10, 2004)

5. Diode Circuits

5.1.1. Series diode limiter (clipping circuit). Applications: signal former; rectifier; separating element; reverse polarity protector etc. Error caused by the forward voltage VF. Discussion: How do we decrease the error (a settlement by compromise)? How do we remove completely the error (looking for an ideal solution)?
5.1.2. Parallel diode limiter (clipping circuit). Applications: signal former; reverse polarity protector (with series connected fuse); transient protector etc. Error caused by the forward voltage VF. Decreasing the error. Completely removing the error (looking for an ideal solution)?

5.2. Diode as a voltage-stable non-linear element. Functional notion of RV non-linear element. Characteristic curves of an ideal RV element. Simplified IV characteristic curve of kind 2.
5.2.1. Circuits with parallel connected diode elements. Applications: voltage stabilizer (regulator); overvoltage op-amp input protector; current self-switching circuits (LED indicators, emitter-coupled circuits; differential amplifiers, TTL logic circuits etc.). Temperature influence (is it harmful or useful?). Discussion 1: How do we make good voltage source in electricity? What are its imperfections? How do we overcome the imperfections by using electronic components? Discussion 2: Is it feedback circuit? Might we imagine that it is? What is the benefit of this approach?
5.2.2. Circuits with series connected diode elements. Applications: static potential "shifting" circuits in transistor circuits (biasing in push-pull amplifiers).

5.3. Diode as a logarithmic non-linear element. Real IV characteristic curve of kind 3.
5.3.1. Logarithmic converters.
5.3.1.1. Diode logarithmic converter with current input and voltage output
(D log converter). Applications: an elementary building block for assembling more complicated integrators. Imperfections caused by a real current source. Looking for a remedy.
5.3.1.2.
RD log converter. Building the circuit by using the more elementary voltage-to-current converter and D log converter. Applications: signal compressing circuits. Imperfections and remedies.

5.3.2. Antilogarithmic converters.
5.3.1.1. Diode antilogarithmic converter with voltage input and current
output
(D antilog converter). Applications: an elementary building block for assembling more complicated antilog converters. Imperfections caused by a real current source. Looking for a remedy.
5.3.1.2. DR antilog converter. Building the circuit by using the more elementary D antilog converter and current-to-voltage converter. Applications: signal expanding circuits. Imperfections and remedies.

Class Exercise 6 (April 12 - 17, 2004)

6. Transistor Circuits without Feedback

6.1. Functional notion of amplification. Discussions: Is it possible to amplify energy? What does an amplifier really do? Block diagrams: series and parallel connection (advantages and disadvantages). Functions of the constituent parts. Characteristic curve of an ideal "amplifying" element.

6.2. Bipolar transistor as an "amplifying" element (grounded-emitter stage). Functional notion of the input base-emitter part (RV non-linear element), of the output collector-emitter part (electrical controlled RI non-linear element) and of the direct input-output connection (current-to-current converter).
6.2.1. Circuits with series connected transistor to the load. Versions: amplifier with grounded transistor and "flying" load; amplifier with "flying" transistor and grounded load. Discussions: What is the big problem of the series circuit in relation to the common ground? Is the circuit inverting? Does the load influence the circuit operation and how?
6.2.2. Circuits with parallel connected transistor to the load. Solving the problem of the common ground. Circuit versions. Discussion: Is the circuit inverting? How does the load influence the circuit operation?
6.2.3. Applications: transistor switch (assembling from more elementary voltage-to-current; current-to-current and current-to-voltage converters. Discussion: What kind of analog device is the transistor switch - digital or analog? Do digital elements really exist?

6.3. FET transistor as an "amplifying" element (grounded-source stage). Functional notion of the input gate-source part (-), of the output drain-source part (electrically controlled RI non-linear element) and of the direct input-output connection (voltage-to-current converter).
6.3.1. Circuits with series connected transistor to the load - as 6.2.1.
6.3.2. Circuits with parallel connected transistor to the load - as 6.2.2.
6.3.3. Applications: FET transistor switch (assembling from more elementary voltage-to-current and current-to-voltage converters.

6.4. Biasing circuits. Functional notion of the "bias" idea (necessity). Presenting the biasing using the operation of summing and scaling.
6.4.1. Dynamic biasing - "shifting" potential variations by blocking capacitors. Applications: an ac amplifier (the input and the output part). Visualizing the operation using potential bars.
6.4.2. Static biasing.
Applications: diode "shifting" circuits in transistor push-pull amplifiers; resistive "shifting" circuits in the op-amp circuits, ADCs and DACs. Visualizing the operation using potential bars.

6.5. Transistor as a current-stable non-linear element.
6.5.1. Functional notion of the RI non-linear element. Characteristic curves of an ideal RV element. The output collector-emitter part as a current-stable element. Simplified IV characteristic curve.
6.5.2. Constant current source.
Discussion 1: How do we make a constant current source (possible ways)? How did we make very good and even an ideal current source in electricity (remember method 1? What are its imperfections? How do we overcome them by using electronic components? Remedy: Keeping constant the overall circuit resistance by changing the current internal source resistance (method 2). Discussion 2: Is it a circuit with feedback? May we imagine that it is? What is the benefit of this notion?
6.5.3. Transistor constant current source/sink. Applications in analog circuitry: building a transistor amplifier from electrically controlled current source and current-to-voltage converter; dynamic load in differential amplifiers; ramp generator - building the circuit by means of transistor current source and C integrator. Discussion: Is the transistor current source in the circuit of a ramp generator a common-base or a common-collector stage (revealing a misconception)?

Spring Vacation (April 12 - 17, 2004)

C. ELECTRONIC ANALOG CIRCUITS WITH IMPERFECT NEGATIVE FEEDBACK

Class Exercise 7 (April 26 - May 1, 2004)

7. Transistor Circuits with Feedback

7.1. Elementary system with negative feedback (active follower). Negative feedback (NFB) principle: deriving the idea from many everyday situations (analogies); generalizing in a block diagram. Behaviour presented through the operations of comparison and regulation. Constituent components: comparator and regulating element.
7.1.1. Emitter (source) follower unloaded. Building the circuit by using the block diagram. Visualizing the operation by a potential diagram. Discussion: What does act as a comparator in the circuit of the emitter follower?

7.2. NFB system disturbed. Discussion: How do the active followers react to the harmful disturbances in the day's routine? What are their advantages in comparison with the passive followers? What do they have to have in order to compensate big disturbances?
7.2.1. Emitter (source) follower loaded. Applications: transistor voltage regulator (stabilizer) - building from RD stabilizer and emitter follower. Discussion: How does the transistor transmute from a current source into a voltage source? Exploring the circuit at a varying load and voltage supply (in comparison with common-emitter stage.

7.3. NFB amplifying system. Discussion: Are there useful disturbances? May we use the reaction of an active follower to the disturbances as an input? Converting the active follower into an amplifier by deliberately disturbing.
7.3.1. Common-emitter amplifier. Converting the emitter follower into an amplifier by introducing a "disturbing" resistor RC. Discussion: Can the circuit act as a follower and even as an attenuate?
7.3.2. NFB transistor current source. Converting the emitter follower into a current source/sink. Exploring at a varying load and supply voltage.
7.3.3. Common-base amplifier. How do the active followers react when we try to change "brutally" their output value? "Inventing" the circuit by disturbing an emitter follower in the output. Discussion: What is the function of the collector resistor RC? To what extent may we change the circuit output voltage? Why is the circuit non-inverting?

7.4. Differential amplifying system. Discussion: How do the active followers interact (aid or oppose) in life? Examples (popular games): arm fighting. How can we apply the phenomenon of conflict in the electronic circuits? How can we cause a conflict of potentials?
7.4.1. Transistor differential amplifier.
7.4.1.1. Building the circuit.
SCENARIO 1:
Assembling the circuit from a voltage comparator with current output (a transistor controlled by the base and by the emitter + current-to-voltage converter + boosting emitter follower.
SCENARIO 2: Assembling the circuit from emitter followers with a common output. Discussion: Why is the emitter resistor RE needed? Can we make the circuit without RE (hint - try to use heterogeneous transistors)?
7.4.1.2. Exploring the circuit (visualizing with potential bars) at:
* single-ended input signals. Presenting the circuit as consecutively connected emitter follower and common-base stage. Linking with digital electronics. What is emitter-coupled circuit?
* differential input signals. Presenting the circuit as contrary connected emitter followers. Discussion: Might we name the common emitter point virtual ground? Is the resistance of the common emitter resistor RE crucial in this case? Is the resistor RE necessary?
* common-mode input signals. Presenting the circuit as cooperatively connected emitter followers. Discussion: What is the role of the common emitter resistor RE in this case? May we take a single-ended output from the one of collectors?
7.4.1.3. Improving the circuit by replacing the resistor RE with a current source. Revealing the phenomenon of aiding in electronic circuits. Discussion: How does an emitter follower (voltage source) behave when it is loaded with a current source? Is the emitter element really a current source?
7.4.1.4. Improving the circuit by replacing the collector resistor RC with a current source. Revealing the phenomenon of current conflict in electronic circuits. Building an amplifying stage with dynamic load. Discussion: How does a transistor current source behave when it is loaded with another current source?

7.4.2. An operational amplifier. Building the circuit by improving the differential amplifier with additional building blocks. Functional notin of an operational amplifier as voltage controlled voltage source. Discussion: What is the role of the bipolar supply in the op-amp circuits? Applications: The op-amp as a comparator.

D. ELECTRONIC ANALOG CIRCUITS WITH PERFECT NEGATIVE FEEDBACK

Class Exercise 8 (May 10 - 15, 2004)

8. Op-amp Amplifiers with Negative Feedback

8.1. Op-amp followers. Discussion: Why do we convert a very good amplifier ( with K > 100000) into ... a follower (K=1)?
8.1.1. Op-amp follower with series NFB. Building the circuit by using the block diagram. Discussion: What does act as a subtractor (comparator) in this circuit? Why is the circuit inverting? What have to be the op-amp in this circuit (regarding the inputs)? To what limits may we varying the input voltage?
8.1.2. Op-amp follower with parallel NFB. Building the circuit by using the block diagram: assembling from a parallel voltage summer. Visualizing the operation by a potential diagram. Discussion: What does act as a subtractor (comparator) in this circuit? Why is the circuit inverting? What have to be the op-amp in this circuit (regarding the inputs)? To what limits may we varying the input voltage? May we connect the virtual ground to the real ground since it is a kind of ground?

8.2. Op-amp follower disturbed. Discussion: Where have to be connected the "disturbing" element in order to be compensated its harmful influence? When a virtual ground is not a ground?
8.2.1. Multiplicative (proportional) disturbances caused by the op-amp output resistance ROUT, lead resistance and load resistance. Applications: eliminating the ROUT; "hiding" a current limiting resistance; voltage carrying without losses over a long line. Visualizing the applications by potential bars.
8.2.2. Additive disturbances caused by "voltage-shifting" diode and transistor elements.
Applications: eliminating the forward voltage drop VF across a diode in the circuit of series diode limiter (ideal diode); eliminating the base-emitter voltage drop VBE0 in the circuit of emitter follower (booster) connected in the op-amp feedback loop. Visualizing the applications by potential bars.

8.3. Op-amp NFB amplifier. A principle attenuation causes ... amplification. Discussion: Where have to connect the deliberately disturbing element in order to obtain an amplification?
8.3.1. Non-inverting amplifier. Converting the op-amp follower into an amplifier by introducing a "disturbing" voltage divider. Visualizing the operation by potential bars. Building a circuit with T-bridge in the feedback loop by using a "double disturbing".
8.3.2. Inverting amplifier. Converting the op-amp inverter into an amplifier by "troubling" the op-amp (changing the ratio R2/R1). Visualizing the operation by potential diagram. Can the circuit act as an attenuator? Building a circuit with T-bridge in the feedback loop by using a "double disturbing".
8.3.3. Differential amplifier. Assembling the circuit from an inverting and a non-inverting amplifiers. Exploring the circuit at single-ended, differential and common-mode input signals. Discussion: Why do we convert a very good transistor differential amplifier into an operational amplifier and then ... again in a "bad" op-amp differential amplifier with gain only of 1?
8.3.4. Instrumentation amplifier. Assembling the circuit from two interacting non-inverting amplifiers (stage 1) and a differential amplifier (stage 2). Exploring the circuit at single-ended, differential and common-mode input signals. Discussion: May we take a single-ended output from the first stage? Why we need the stage 2? How are the instrumentation and transistor differential amplifier alike? How are they different?

8.4. Disturbance as an input in the NFB circuits. Discussion: How do the active followers react to the varying disturbances in the day's routine? May we use this phenomenon in order to find additional inputs to the circuits? Applications: "Strange" circuits (without inputs) containing resistive sensors (photo-, thermo-, pressure-, displacement- etc.) placed in the feedback loop. Formulating a common rule for putting disturbances into the feedback loop.

8.5. Modification the circuit attributes by negative feedback.
8.5.1. Virtually increasing a resistance and decreasing a capacitance by series NFB. Deriving the idea of bootstrapping from many situations. Application 1: ramp generator - building the circuit from an external square generator, passive RC integrator, emitter follower and voltage "shifting" element. Application 2: Widlar current source. Discussion: Is it a circuit with feedback?

Class Exercise 9 (May 17 - 22, 2004)

9. Op-amp Converters with Parallel Negative Feedback

9.1. Converting passive circuits into active ones (a universal principle). Deriving the idea of removing disturbance by antidisturbance from many situations of our life. Concretizing into a principle of removing voltage by antivoltage (parallel negative feedback).

9.1.1. Converting resistive passive circuits into op-amp circuits.
9.1.1.1. Op-amp converters with current output: voltage-to-current converter, resistance-to-current converter and voltage-into-resistance divider. Keeping a constant current by supplementing the input voltage in order to compensate the losses in the load (method 3). Future application in ramp generators.
9.1.1.2. Op-amp converters with voltage output: current-to-voltage converter, resistance-to-voltage converter and voltage-into-resistance divider.
9.1.1.3. Compound converters with voltage inputs/output: inverting voltage divider (inverting amplifier); inverting voltage summer.

9.1.2. Converting reactive passive circuits into op-amp circuits.
9.1.2.1. Capacitive circuits: integrators; differentiators. Application 1: ramp generation. Building ramp generator from an external square generator and an op-amp RC integrator.
9.1.2.2. Inductive circuits: integrators; differentiators.

9.1.3. Converting imperfect diode circuits into op-amp circuits: parallel diode limiter (an ideal diode), logarithmic and antilogarithmic converter.

9.2. Virtually decreasing a resistance and increasing a capacitance by parallel NFB. "Bottomless" capacitor (another view point at op-amp RC integrator).

9.3. Transforming NFB op-amp circuits into negative impedance circuits. Applications: negative impedance converters (NIC).

E. ELECTRONIC ANALOG CIRCUITS WITH POSITIVE FEEDBACK

Class Exercise 10 (May 24 - 29, 2004)

10. Op-amp Circuits with Positive Feedback

10.1. Systems with positive feedback (PFB). Positive feedback principle: deriving the idea from many everyday situations (analogies); generalizing in a block diagram. Discussion: How are the negative feedback and positive feedback alike? How are they different? How do we convert a negative feedback system into a positive one and v.v.?

10.2. Comparators with hysteresis. Examples of the phenomenon - mechanical, thermal, electrical etc. Generalizing. Discussion: Is the hysteresis useful or harmful phenomenon in electronic circuits? How do we do a hysteresis (including a hysteresis into a comparator without hysteresis)? Can a comparator with hysteresis memorize (i.e. can we convert the comparator into a RS trigger)?
10.2.1. Inverting comparators with hysteresis. Converting non-inverting amplifier into inverting comparator. Visualizing the operation by potential diagram.
10.2.2. Non-inverting comparators with hysteresis. Converting inverting amplifier into non-inverting comparator. Visualizing the operation by potential diagram. Discussion: Why the circuit do not ever work properly?

10.3. Pulse generators.
10.3.1. Self-generating circuits of triangle and square signals. Deriving the idea from many everyday situations (analogies). Generalizing the idea in a block diagram containing an integrator and a comparator with hysteresis.
10.3.1.1. Square-wave generator. Assembling the circuit from a RC integrator and comparator with hysteresis. Linking with digital electronics - is it comparator with hysteresis timer 555? Discussion: Is the non-linear waveform a problem in this circuit?
10.3.1.2. Square- and triangle-wave generator. Assembling the circuit from an active RC integrator and comparator with hysteresis. Linking with digital electronics - assembling the circuit from RC integrator and timer 555.

F. MIXED (ANALOG & DIGITAL) CIRCUITS

Class Exercise 11 (web version only)

11. Components and Sub-systems for Analog-Digital Signal Processing

11.1. Digital-to-Analog Converters (DAC). Deriving the operation from many everyday situations (analogies). Presenting as reference summing (materializing abstract digital code). Generalizing in a block diagram.
11.1.1. Building a DAC: from reference voltage sources and inverting voltage summer with binary-weghted inputs; from a reference current sources, current summer and an active current-to-voltage converter (R-2R ladder DAC). Exploring the circuit at constant reference voltage VREF and varying digital code. Transfer characteristics at different values of VREF. Discussion: What is the function of the reference voltage? What is depend on VREF?
11.1.2. DAC as a digital-controlled resistor and voltage divider (amplifier). Exploring the circuit at varying input voltage VIN and constant digital code. Transfer characteristics at different values of the code. Discussion: What is the function of the code? What is depend on it?
11.1.3. DAC as a digital-analog multiplier (2- and 4- quadrant). Exploring the circuit at varying input voltage VIN and digital code. Transfer characteristics.

11.2. Analog-to-Digital Converters (ADC). Presenting the operation by the negative feedback principle. Generalizing in a block diagram.
11.2.1. Building a ADC from a DAC and a comparator. Exploring the circuit at constant reference voltage VREF and varying input voltage VIN. Transfer characteristics at different values of VREF. Discussion: What is the function of the reference voltage? What is depend on VREF?
11.2.2. ADC as an analog-digital measurer of two voltages (divider). Exploring the circuit at varying input voltage VIN and constant digital code. Transfer characteristics at different values of the code. Discussion: What is the function of the reference voltage? What is depend on it?

11.3. Other building components of the analog-digital sub-systems.
11.3.1. Sample-and-hold circuits.
Capacitor as an analog memory. Discussion: What is the basic contradiction in the circuit?
11.3.2. Analog multiplexors.

11.4. Analog data acquisition sub-systems.
11.4.1. System structure. Block diagrams.
11.4.2.
Special features. Double buffering of multiple byte codes in DAC and ADC.

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