**V. I. Boyko, V. Y. Zhujkov, V. M. Spivak, A. A. Zori, ** **T. О. Tereschenko, V. D. Sheliagin **

**BASICS OF CIRCUITRY **

**OF ELECTRONIC SYSTEMS **

**ТRANSLATION FROM UKRAINIAN by E. A. BATINA **

*Approved by Ministry of Education and Science of Ukraine * *as textbook for students of institutions of higher education *

### Kyiv

*Norita-plus * *Avers *

### 2008

### UDK 621.382.2/ .3+004 (075.32) BBK 32.844.1я723

*Stamp is given by Ministry *

*of education and science *

*of Ukraine (protocol of 23 September 2003 *

*№ 1/11-4043) *

* Reviewers: O. V. Kirilenko, cor. mem. of NASU, d-r of techn. sciences, prof. *

### (Unstitute of electrodynamics of National Academy of sciences of Ukraine);

### U. E. Kuleshov, cand. of techn. sciences, prof. (Kyiv national university of technologies and design)

### **Basics of circuitry of electronic systems: Textbook / V. I. Boyko, ** V. Y. Zhujkov, V.M. Spivak and others; Translation from Ukrainian by E. A. Batina. – K.: Norita-plus:Avers, 2008. – 784 p.: graph.

### ISBN 966-8777-03-4

### Basics of circuitry are stated, principles of operation are considered, it is given calculations of analog, digital and pulse devices of electronic systems, based on semiconductor devices, integrated operational amplifiers and integrated logic circuits of TTL, MOS, CMOS types, construction principles of systems of control by electronics devices based on microprocessors and microcontrollers.

### For students of institutions of higher education. It can be useful for specialists on electronic engineering, specializing in the area of development, fabrication and maintenance of electronic systems and devices.

### UDK 621.382.2/ .3+004 (075.32) ISBN 966-8777-03-4 BBK 32.844.1я723

### © V. I. Boyko, V. Y. Zhujkov, V. M. Spivak , A. A. Zori,

*, T. О.Tereschenko, V. D. Sheliagin, 2008*

** © Computer make-up and design “Norita-plus”, 2008 **

© Тranslation from Ukrainian edition by E. A. Batina, 2008

### PREFACE

Electronics is the area of current physics and electrical engineering. It studies and applies phenomena, devices and systems, based on passage of electrical current through vacuum, gas and solid body, investigates and develops electronic measures and systems and the principles of their application. The information interchange in electronic systems is realized with the help of signals, which carriers can be represented by various physical quantities currents, voltages, magnetic states, light waves.

The analog (continuous) and discrete signals can be recognized. There are two types of discrete signals: the rst is got by the way of digitization of continuous signals by amplitude or time, the second one as a set of code combinations of signs.

The advantages of digital devices and systems comparatively with ana- log ones are increased interference immunity, high reliability, ability to store information for a long time without losses, economic and energetic eciency, compatibility with integrated technology, high manufactura- bility and reproducibility, and disadvantages slow operating speed and low accuracy.

The base of development of electronics is progressive complication of functions. It is impossible as for now to solve the new tasks by old elec- tronic measures with the help of available element base. The main factors are reliability increasing, decreasing of overall dimensions, mass, power consumption and depreciation.

The important assignment of high education is right orientation of future specialist at the stage of study of fundamental and professionally- oriented special disciplines, where the depth of important physical pro- cesses statement and their optimal volume are joined. The most of pub- lished textbooks and educational manuals on analog and digital circuitry or devoted to statement of only some parts of this discipline, either give common knowledge of the main parts or insuciently reect tendency of present-day electronics development. In oered textbook the authors made attempt to liquidate referred above failings.

The textbook consists of ve parts.

The part one "Electronic devices with continuous signals"

contains 12 chapters on analog circuitry, which consider questions, such as these:

main components of electron systems, subsystems and junctions, ampliers;

RC-voltage ampliers on bipolar and unipolar FET-transistors ac- cording to dierent connection circuits by common emitter, collector, drain, source;

frequency responses of audio RC-ampliers, amplier operation in the range of low, medium and high frequencies; logarithmic amplitude- frequency responses, computations examples; matching of signal source with load, single- and two-step power ampliers and ampliers without transformers;

through stage characteristics, temperature inuence on bipolar tran- sistor characteristics, origins and calculation methods of nonlinear dis- tortions;

classication of analog microelectronic structures, integrated circuit operational ampliers, their circuitry elements;

construction of solving structures on the operational amplier base, linear and non-linear functional generators, adders, integrators, dieren- tiators, frequency correction, taking the logarithm, multipliers, dividers, rectiers, detectors;

generalities of the theory of dierent type selective ampliers;

LC-generators of periodic oscillations at unipolar FET and bipolar transistors;

basics of theory of RC-generators with dierent type phase shifters and without them.

Part two "Pulse devices" contains 5 chapters, considering the follows question:

pulses passing through circuits of integration, dierentiation, divid- ing, clampers;

squarer, keys, limiters, models for large signal;

multivibrators and single-shot multivibrators; frequency regulation, thermostabilization (heatset) and improvement of circuits output voltage waveform; ramp generators;

coding devices analysis, ADC and DAC, sample-and-hold devices.

Part three "Digital circuitry" includes 6 chapters, viewing the questions:

mathematical fundamentals of digital circuitry, numerical systems, codes, binary arithmetic and forms of number presentation, logic algebra, method of Boolean functions minimization;

combinational circuits, multi- and demultiplexers, adders, coders, decoders, comparators, code converters;

trigger elements, FS-, D-, JR-triggers;

functional junctions of sequential logic devices: shift registers, coun- ters, digital phase shifters;

microcircuits of memory devices: static, dynamic operative, and mi- crocircuits of read-only memory (ROM);

digital integrated circuits application, interferences and interference immunity, digital integrated circuits mounting.

Part four "Microprocessors and microcontrollers" consists of 4 chapters, which exposes such issues:

main ideas of microprocessor technology: common principles of mi- croprocessor systems construction, buses organization, conception of mi- croprocessors architecture;

architecture of microprocessors: single-chip 8 (octal) and 16 (hex- adecimal) -bit microprocessors, features of architecture of Pentium and 64-bit microprocessors;

fundamentals of Assembler programming;

microprocessor systems hardware construction: of ROM and RAM module, of In/Out interfaces;

present-day microprocessors and microcontrollers: single-chip micro- controllers with CISC- and RISC- architecture, signal microprocessors, neuron computers and their functions.

Part ve "Systems of power supply and control" the next aspects are considered:

circuitry of the main blocks of switched power supplies (SMPS), power electronics element base;

control systems of power complex of beam processing station; con- trol systems and their junctions computation, microprocessor control systems.

The problems for current monitoring and testing are given; exercises for independent and individual solving are listed.

All parts of bachelors training program for "Electronics", "Power engi- neering", "Radio engineering" and others, according to Ukrainian stan- dard are stated in the textbook in a compact and available form, which should promote increasing eciency of both auditorium lessons and in- dependent work of students. Material was arranged with each next part being logic continuation of previous.

The result of course study is learning by students of principles of func- tioning, choice, practical realization of devices and electronic systems of dierent purpose, principles of development of electronic devices control systems. Students must know: principles of analog and digital circuitry devices construction and functioning; principles of microprocessor and microcontroller systems construction and functioning.

The textbook has been written based on experience of teaching of dis- ciplines according to bachelor training program for "Electronics" at the National Technical University of Ukraine "KPI", Donetsk National Tech- nical University and Dneprodzerzhinsk State Technical University.

Course is provided with main disciplines: mathematics, physics and ba- sics of electrical engineering.

Authors would like to thank collaborators of departments of "Industri- al electronics", "Audio engineering and data logging"of NTUU "KPI",

"Electronic engineering"of Donetsk NTU and "Electronics and auto- matics"of Dneprodzerzhinsk STU for their assistance during mechanical preparation and teaching material discussion.

Authors are grateful to associate professors Bagrij V. V. and Peterge- ria U. S., senior teacher Batina E. A. for their teaching and methodic assistance during textbook composition and to reviewers for their invalu- able remarks and recommendations on development of some manuscript parts, taken into consideration during revision, which has contributed to improvement of textbook contents.

### INTRODUCTION

Industrial development of electronics possesses two directions:

1. Informational, embracing electronic instrumentation and systems of measurement, control and monitoring by dierent technologi- cal processes at fabrication, scientic research, biology, medicine.

Signals ampliers, generators of voltages, currents and power of various waveforms and frequency, logic circuits, counters, indicat- ing devices all these are devices and systems of informational electronics, based on integrated circuits application.

2. Power direction, concerned with transformation of alternating and direct currents for electrical power engineering, metallurgy, chem- istry, transport electric motive power and so on. The main types of electronic systems are rectiers, inverters, frequency converters, controlled converters.

Electronic systems are divided into two classes by the way of electric signals formation and transmission analog (continuous) and discrete (discontinuous), being divided in-turn into pulse, relay and digital.

Analog electronic devices and systems are destined for reception, trans- formation and transmission of electric signal, changing according to con- tinuous (analog) function. Unique, completely dened value of chosen electrical parameter of direct or alternating current corresponds to each specic value of real physical quantity at the input of electronic system of analog type. It can be voltage or current at electrical subcircuit, fre- quency, phase and others. Both the physical quantity and its electric equivalent at that, being possessed of innite number of values, can be determined at any moment and change on the same time scale. It should be noted, that electric equivalent contains full information about real process, though in a common case the moments of real quantity possess- ing specic value and its electric equivalent appearing, can mismatch, i.e. there can be some delay between these moments. The advantages are theoretically obtainable accuracy and operating speed, system sim- plicity, lacks low interference immunity and parameters instability, caused by considerable device behavior dependence on external destabi- lizing factors, for example temperature, time (elements ageing), external elds action and others, considerable distortions during transmission at

a great distance, diculties in a case of results' long-term storage, low energy eciency.

Discrete electronic devices (systems) are destined for reception, conver- sion and transmission of electric signals, obtained in result of quantiza- tion (process of continuous signal's change by its values in some points) by time or (and) by amplitude of given analog function. Therefore, sig- nals acting in them, are proportional to limited number of values, chosen by specic law, of real physical quantity, represented by various parame- ters of pulses or drops of voltages (currents) (amplitudes, pulses rise and fall time, pulse duration, period and frequency of pulses propagation, spacing interval and so on). Discrete electronic systems (DES) use only part of information about real physical quantity, i.e. information partial losses take place during its supply. Pulse and mean power are dened by means of pulse ratio, which also can be referred to advantages, there- fore it's possible to get essential power redundancy in pulse, allowing mass and overall dimensions indices improvement; power dissipation is minimal in a switch mode, which increases device coecient of utiliza- tion; the discrete devices behavior less depends on instability of utilized devices parameters; interference immunity is higher, since time interval, when interference can inuence on signal decreases; monotypic element base is used, causing reliability rise, providing cheapness.

DES discrete signals are divided into pulse, relay and digital according to quantization type. Pulse electronic systems realize quantization of initial signal. Output sequence pulses waveform remains constant during pulse modulation. Pulse-amplitude, pulse-width, pulse-phase modulations are spread. Relay systems realize initial signal quantization by amplitude and transform it into step function, with each level height being proportional to some quantity given in advance.

In the near future digital electronics will occupy most likely the lead- ing place in the market of electronic devices and systems. Now digital personal computers and controllers practically displace analog ones, cre- ated earlier. The same takes place with equipment of radio communica- tion, broadcasting (TV-sets, radio sets, video recorders, devices of audio recording, photo-apparatus).

However, digital technique is not able to displace fully analog in principle, because physical processes, providing electronic system with information, is analogous by nature; in that case, analog-digital and digital-analog

devices are required at the input and output.

Industrial development of electronics for almost century of its existence numbers four generations, characterizing by following microminiaturiza- tion of electronic components, devices and systems based on application of large-scale-integration (LSI) and very-large-scale-integration (VLSI) circuits. Some functional blocks are fabricated in one integrated cir- cuit, being nished electronic device or system of information reception, transformation and transmission. Such electronic devices allows entire providing required algorithm of initial information processing and essen- tial increasing reliability of their functioning. Mounting compactness of electronic devices of the forth generation comes to nearly 1000 el/ñm3 and more (for comparison: the third generation electronic devices 50 el/ñm3). Integrated circuits application in modern electronic systems essentially increases system reliability and lowers their cost, overall di- mensions and power consumption.

### PART I

### Electronic devices with continuous signals

### CHAPTER 1. AMPLIFYING DEVICES

### 1.1. Electronic systems, subsystems and units

The subject of electronic technique is the theory and practice of applica- tion of electronic, ionic and semiconductor apparatuses in devices, used in dierent elds of national economy. Its exibility, operation speed and accuracy give it the great possibilities of application in science and engineering.

A. S. Popov's discovery of radio (May 7, 1895 report and demonstration of radio transmission) is considered to be the beginning of electronic tech- nique development. Five main periods can be emphasized in electronics development:

1. radiotelegraph (1895-1925);

2. radio engineering (1925-1945);

3. electronics (semiconductor) (1945-1965);

4. microelectronics (from 1965);

5. nanoelectronics (modern tendency).

The last achievements in the eld of microelectronics creation of in- tegrated circuits from small to very large-scale integration allowed to obtain the basic elements with very high reliability characteristics, op- eration speed and small required power, on their base not only modern microprocessor devices and systems are created, but also modern com- puters and elements of measuring, control and computing systems.

Under the term electronic system, we mean a number of blocks and devices of electronic technique that have some kind of connection with each other and make a certain functional integrity.

The model, representing the function, fullled by each element, describes its operation. In each electronic system, a number of subsystems (blocks)

can be emphasized. Subsystem is a group of elements fullling denite (simplest) function in a system.

Subsystems consist of more simple devices (units). Units, in their turn, consist of elements. The accepted classication is relative and depends on the division criteria.

### 1.2. The main components of electronic devices

Among the components of electronic devices, we can distinguish pas- sive and active. One-port networks (resistors, capacitors, inductors) and some multi-ports, composed of passive one-port networks, are referred to passive elements.

Consider the basic passive components resistor, inductance and capac- itor (see Fig. 1.1 a, b, c).

Fig. 1.1. The main passive components of electronic circuits:

a resistor; b inductance; c capacitor

Relations between currents and voltages for these elements are described by the next expressions:

U =R·i, U =Ldi

dt, U =CdU

dt . (1.1)

One-port networks, for which cause-and-eect relations are dened by the equations (1.1), are called linear. The next relations are true for them:

U =R·i, ψ=L·i, q=C·U. (1.2) where ψ magnetic ux; q capacitor charge. The characteristics of linear elements are shown in Fig. 1.2.

Fig. 1.2.The characteristics of linear elements

If we know the elements characteristics, we can dene their parameters:

R= dU(i)

di = U(i)

i , L= dψ(i) di = ψ(i)

i , C= dq(U)

dU = q(U) U . (1.3) The values of these parameters are constant for linear one-port networks, and superposition (overlay) principle can be applied to them.

A number of one-port networks possess nonlinear characteristics.

Active elements are the elements with controlling electrode that are simu- lated by active voltage and current sources. They are mainly intended for amplifying and generation of electrical signals with required waveform, amplitude and frequency. They include transistors, electronic tubes, op- erational ampliers, multilayer structures of p-n junctions and so on.

### 1.3. Amplifying devices. The main denitions

Amplier is a device, which allows the input signal transforming into the signal of greater power without considerable distortion of its waveform.

A mention should be made that the amplifying of signal power can be done at the expense of current or voltage amplication.

The eect of amplication is possible only in the presence of source of controlled energy, transformed by the amplier into the energy of amplied signals. Such source is a power supply source (see Fig. 1.3).

The energy of the power supply (voltage E_{S}) is transformed into the
energy of useful signal by means of amplier with amplier gainK.
The device, which is a consumer and to which the output voltageUout

is applied, is called the load (Zload), and the amplier circuit, to which

Fig. 1.3. The block diagram of electrical signals amplifying

it is connected, is called the output circuit (clamps 3, 4). The energy
ow from the power supply (PS) to the load (Zload) is controlled by the
input signal, represented by the input voltage U_{12} =U_{in}.This voltage
depends on the value of the electromotive force source (EMF) E_{in}, its
internal resistanceR_{int}and amplier input resistanceR_{in}.The signal to
be amplied is called the input signal, and the amplier circuit, to which
it is connected, is called the amplier input circuit (clamps 1, 2). The
clamps 2 and 4 are often unipotential and they are called the common
bus (mass) of the amplier.

The classication of ampliers is done according to:

purpose;

character of amplied signals;

bandwidth of amplied frequencies;

type of used active elements.

According to the purpose, we distinguish:

1. voltage ampliers, K_{U} =Uout

U_{in} voltage amplier gain;

2. current ampliers,K_{I} =I_{out}

Iin current amplier gain,I_{in} input
current, Iout output current;

3. power ampliers,K_{P} = P_{out}

Pin power amplier gain,P_{in}andP_{out}
powers on the input and output of the amplier.

In the power ampliers it is required to provide given or maximum power in the load (Zload), and in the voltage (current) ampliers it is required to

provide given values of amplier gains and output parametersUout(Iout). According to the character of amplied signals, we distinguish:

ampliers of harmonic signals. These devices provide amplifying of continuous harmonic signals;

ampliers of impulse signals. These devices provide amplifying of impulse signals with given waveform.

According to the band of amplied frequencies, we distinguish:

direct current ampliers, the bandwidth of amplied frequencies is

∆f = 0÷fup,wherefup the upper cuto frequency of amplication;

alternating current ampliers, with frequency band ∆f = flow÷

÷fup,where flow the lower cuto frequency of amplication.

The alternating current ampliers, in their turn, are divided into:

low frequency ampliers;

high frequency ampliers;

pass-band amplier f_{low}
fup

≈1,1.

According to used active elements, we distinguish the next ampliers:

vacuum-tube;

transistor;

diode;

parametric.

The amplier block diagram is given by Fig. 1.4 and includes input and output devices, preamplication and power amplier stages.

Fig. 1.4. The amplier block diagram

The input device performs the signal transmission from the signal source to the input circuit. It is used if the signal source is impossible or inex- pedient to connect directly to the amplier input.

The preamplication amplier stages are intended for the voltage, cur- rent and power amplication of signals to the required level, which pro-

vides normal operation of the next block.

The power amplication stages provide required power values in the load, at the permissible levels of waveform distortion and signals noise.

The output devices are required for the signal transmission from the power amplier to the load. They are used if direct connection of the load is impossible or inexpedient.

### 1.4. The main technical attributes of ampliers

The data that characterize the ampliers properties are called its at- tributes. They include:

input and output data;

amplier gain;

coecient of eciency (CE);

frequency responses;

amplitude characteristic.

Consider these factors in detail.

Input and output data.

Input data areUin, Iin, Pin, Zin.The input signal source can be presented by EMF and current source. The model of the EMF source is shown in Fig. 1.5.

Fig. 1.5. The EMF source model Fig. 1.6. The current source model

For the amplier normal operation providing,Uinmust tend toEg. But, as Zg>0, so there is a voltage loss on it, and therefore,Uin< Eg, and

Uin is dened by the expression:

Uin= Eg·Zin

Zg+Zin

. (1.4)

As it follows from the above mentioned expression, in order to getUin≈

≈ Eg, the fulllment of condition Zg << Zin is required. In practice Uin= 0,5Eg is permitted, butUin<0,2Eg is inadmissible.

The current source model is shown in Fig. 1.6.

For given circuit we can write:

Iin=Ig· Zg

Zg+Zin

. (1.5)

Therefore, in order to getIin≈Ig, Zg>> Zinis required.

The output data are U_{out}, I_{out}, P_{out}, Z_{out}, Z_{load}.The output circuit can
be depicted as in Fig. 1.7, whereKU_{OC} is the amplier gain under open
circuit conditions,Zoutis the amplier output impedance. For agreement
between the signal sources and the load the next conditions must be
fullled:

for voltage ampliersZ_{load}>> Z_{out},thenU_{load}≈E_{out}=K_{U}_{OC}·U_{in};
for current ampliers Z_{load}<< Z_{out},thenI_{load}=I_{out};

for power ampliers Z_{load}=Z_{out},thenP_{L}→max.

Fig. 1.7. The model of amplier output circuit

Fig. 1.8. The graphical presentation of the amplier

signals

The amplier gains.

We can mark out the next amplier gains:

by powerKP = P_{out}
Pin;
by voltageKU = Uout

Uin;
by current K_{I} = Iout

I_{in}.

In a general case the amplier gain is:

K_{U} =K_{U}·e^{j(ϕ}^{out}^{−ϕ}^{in}^{)}=K_{U}·e^{jϕ}, (1.6)
where ϕ=ϕ_{out}−ϕ_{in} is the phase shift between the input and output
voltages or currents,K_{U} is the complex amplier gain.

This can be shown graphically on the complex plane in the following way (see Fig. 1.8).

For the multistage amplier that contains n stages, the common amplier gain is dened by the expression:

KU =KU1·KU2·. . .·KU_{n}=

n

Y

i=1

KU_{i}. (1.7)

Sometimes the logarithmic scale ofKU presentation is more convenient.

Its unit is decibel, which is dened by one tenth of the decimal logarithm
of the output and input powers ratioK_{P(dB)}= 10 lgK_{P}. For the voltage
and current amplier gains, the formulas for conversion of relative values
into logarithmic are:

K_{U(dB)}= 20 lgKU; K_{I(dB)}= 20 lgKI.

At that, the multistage amplier gain in logarithmic units will equal to:

Amplitude-frequency (AFR) and phase-frequency (PFR) responses.

Dependence of amplier gain modulus on frequency represents the amplitude-frequency response (AFR).

The phase-frequency response (PFR) reects dependence of phase shift angle between the input and output signals on frequency.

Fig. 1.9 shows the graphical presentation of given responses for the al- ternating voltage amplier.

K_{U(dB)}=K_{U1(dB)}·K_{U}_{2(dB)}·. . .·K_{U}_{n}_{(dB)}=

n

Y

i=1

K_{U}_{i}_{(dB)}. (1.8)

Fig. 1.9. AFR a and PFR b of RC-amplier

Fig. 1.10. The amplier i-v characteristic Volt-ampere (i-v) characteristic.

i-v characteristic depicts the dependence of the output signal steady- state value on the input sine signal|Uout|=f(|Uin|)at certain constant frequency (Fig. 1.10).

In the operating range of input signal amplitudes, the i-v characteristic
must be linear (section ab), and its slope angle is dened by the ampli-
er gain value at given frequency. The minimum input signal |U_{in}|_{min} is
dened by the intrinsic amplier noises level, and the maximum input
signal |U_{in}|_{max} by the transition to the nonlinear part of the charac-
teristic, which causes nonlinear distortions, at the expense of amplier
gain decrease.

The voltage range of the input signal, amplied without considerable

distortions, is characterized by the amplier dynamic range
Dsig=|Uin|_{max}

|Uin|_{min} or Dsig= |Uout|_{max}

|Uout|_{min}. (1.9)
The dynamic range of input signal distortions must not exceed the am-
plier dynamic range.

### RESUME

It is necessary to understand It should be memorized 1. Concepts of electronic systems,

subsystems and units.

2. Dierence between passive and active elements.

3. Physical basis of resistors, ca- pacitors and inductors operation and their purpose.

4. Dierence between linear and nonlinear passive elements.

5. Purpose of power supply source in amplier construction.

6. Dierence between voltage, cur- rent and power ampliers.

7. Concepts of amplier input and output parameters.

8. What is graphic presentation of amplier input and output signals on complex plane.

9. Denition of multistage ampli- ers gains in non-dimensional and logarithmic units.

10. Amplier frequency responses:

AFR, PFR, APFR, their physical sense and presentations.

1. Graphic representation of re- sistors, capacitors, inductors and voltage and current sources.

2. Models of EMF and current sources.

3. Purpose of ampliers of dierent types.

4. The main parameters of am- pliers and their denitions (Rin, Rout, KU, KI, KP).

5. The main frequency responses and their denitions (AFR, PFR, APFR).

6. Purpose of amplier amplitude response and denition of amplier dynamic range.

7. Formulas:

U=R·i;U=Ldi

dt;i=cdU

dt connec- tions between currents and volt- ages of passive elements;

KU=Uout

U_{in} , KI=Iout

I_{in},
K_{P}=P_{out}

Pin voltage, current and power amplier gains;

### RESUME

11. Amplier amplitude response and dening of dynamic range on its base.

KU=

n

Q

i=1

KU_{i} multistage ampli-
er gain;

D_{c} = U_{in max}
Uin min

= U_{out max}
Uout min am-
plier dynamic range.

K = |K|e^{jϕ} complex amplier
gain;

You should be able to:

1. Dene the concepts of: passive, active, linear and nonlinear elements;

voltage, current, power ampliers and their main parameters; frequency and amplitude responses of ampliers.

2. Write the main formulas for passive R, L, C elements; for voltage, current, power and multistage ampliers.

3. Solve problems on amplier main responses and parameters denition.

### 1.5. Task for current testing

1.5.1. Questions for monitoring

Give the denition of electric signal amplier and explain the require- ment of power supply in its construction.

X Name the main classication types of ampliers.

X Explain the conditions of optimal coordination between the amplier output stage and the load for voltage amplier.

X Explain the conditions of optimal coordination between the amplier output stage and the load for current amplier.

X Explain the conditions of optimal coordination between the amplier output stage and the load for power amplier.

X Dene the voltage amplier gain.

X Dene the current amplier gain.

X Dene the power amplier gain.

X What is amplitude-frequency response?

X What is phase-frequency response?

X What is amplitude-phase-frequency response?

X What is amplitude characteristic?

1.5.2. Problems for independent and individual solution Dene the connections between currents and voltages for linear elements:

resistor, inductor and capacitor.

XDene the parameters of linear elements (resistor, inductor and capacitor) knowing their characteristics, give the graphic presentation.

X Present the block diagram of electric signals amplifying.

X Present the block diagram of electric signals amplier.

XGive the graphic presentation of amplier signals on com- plex plane.

X Dene the multistage amplier gain in ordinary and loga- rithmic form.

X Present AFR of audio frequency amplier.

X Present PFR of audio frequency amplier.

X Present the amplier amplitude characteristic. Dene the main parameters and the dynamic range of amplier signals.

X Knowing the amplier amplitude characteristic Uout =

=ϕ(Uin)present it in such form:|K|=ψ(Uin).

### CHAPTER 2. RC-VOLTAGE AMPLIFIERS ON BIPOLAR JUNCTION AND

### FIELD-EFFECT TRANSISTORS

### 2.1. Bipolar junction transistor amplier, switched by the common base circuit

Input transistor transition is always switched in the direct direction, output transition in inverse direction for ampliers on bipolar junc- tion transistors. Amplier circuit on bipolar junction transistor, switched with a common base (CB) is shown in Fig. 2.1. Alternating current source Iinhas to provide low resistance to the direct currentIg.

Fig. 2.1. Common base amplier circuit

Resistor RC is transistor's load by direct current and denes its am- plication properties. If RC = 0, voltage amplication eect doesn't happen, because Uin = EC = const. WhenRC increases, voltage gain grows, however, there is a restriction onRC from above.

Gains approximate values for the given circuit can be determined:

kU =UCB

UEB

= PC·RCB||RC

PE·REB

,

whereRin andREB resistances of the collector-base and emitter-base junctions.

As for the CB circuit:PC ≈PE, RCB||RC ≈RC, REB << RC (because input transistor junction is switched in conducting direction), that's why the voltage gain moduluskU ? 1.

Current gain modulusk_{I} is less 1 (CB):

k_{I} =Pout

P_{in} = IC

I_{E} <1, k_{I} ≈(0.5. . .0.95).

Therefore, CB circuit amplies voltage, power, but does not amplify current.

1. Circuit's calculation by direct current.

Circuit's operating conditions by direct current is dened by the ele-
ments: R_{C}, R_{E}, E_{C}, E_{E} and transistor's VA characteristics. There are
Kirchho equations for output circuit:

(E_{C}=I_{C}·R_{C}+U_{CB};
U_{CB}= Ψ(I_{C}, I_{E}).

(2.1) (2.2) Equation (2.1) represents equation of straight line, that is named a load line; equation (2.2) gives a set of common base transistor output char- acteristics.

Two regimes are recommended for load line building (2.1).

Open circuit conditions: IC = 0,then from (2.1) we get UCB =EC

point 1 (Fig. 2.2)

Short circuit conditions: UCB = 0, so, ICG = EC

RC point 2 (see Fig. 2.2).

Trace a load line throw two got points, then choose an idle point on it, for example point Î (Fig. 2.2). To use transistor characteristics more fully, point "O" is located at the central area of output characteristics.

This point is characterized by two coordinatesI_{C}_{Q}, U_{CB}_{Q} depending on
chosenI_{E}_{Q}.

To provide amplier's operation in idle point "O", input currentIE_{Q} has
to be provided. Describe input circuit similar to the output circuit by
the equations system:

Fig. 2.2. CB transistor output characteristics

(E_{E}=I_{E}·R_{E}+U_{EB};
U_{EB} =ϕ(I_{E}, U_{CB}).

(2.3) (2.4) Equation 2.3 is the input load line, equation 2.4 input transistor char- acteristics. To build a load line we use open circuit and short circuit conditions (look Fig. 2.3):

Open circuit conditions: I_{E}= 0, U_{EB} =E_{E};
Short circuit conditions: UEB = 0, ICG= E_{E}

RE.

We can determine operating point (Q-point) location on the load line by
current I_{E}_{Q} and by voltage U_{CB}_{Q}. Operating point coordinates dene
voltage between base and emitter by direct currentUEB_{Q} (see Fig. 2.3).

2. Amplier's calculation by alternating current.

VoltageUin amplier schematic circuit is shown in Fig. 2.4.

Blocking capacitorsC_{coup1} andC_{coup2} are needed for:

• Input signal source and load don't change transistor operating mode by direct current;

• Not let passing direct component in the load.

Build the oscillograms, showing the amplier operation. Let input eect is represented by sinusoidal current source:

iωt =Im·ωt.

Oscillograms, illustrating amplier's operation are as in Fig. 2.5. Typical

Fig. 2.3. CB transistor input characteristics

Fig. 2.4. CB amplier schematic diagram
points for I_{C}, U_{CB} at argument's valuesωt= 0; π

2;π; 3π

2 ; 2πof input
currenti_{in}(ωt),and also for argument arbitrary valueωt_{i}of input eect
i_{in}(ωt)are shown in gure.

Amplier is supposed operating in characteristic linear area for input
current oscillations, which values vary not more than on25÷30% rela-
tively idle point coordinate "O"; that provides output current(I_{C})and
voltage(U_{CB})sinusoidal values at sinusoidal input eect.

Input voltage Uin =iin(ωt)·Rin amp coincides with current iin(ωt) by phase. As it follows from Fig. 2.5 phase shift between input and output voltage is equal to zero(ϕU = 0), and phase shift between currentsIC

and IE is 180^{◦}(ϕi = 180^{◦}). It can be explained by negative values of
UCB andIC, and are really located in the third quadrant.

### 2.2. Bipolar junction transistor amplier, switched by the common emitter circuit

Amplier's circuit is presented in Fig. 2.6. Elements assignments are similar to shown earlier circuit with RB fullling RE function taking into account.

Fig. 2.5. Common-base transistor amplier's oscillograms 1. Amplier calculation by direct current.

Amplier operating mode by direct current is determined by elements EC, RC, RB and by transistor VT parameters.

When amplier designing, Uoutm, Rload are specied. Hence: 2EC >

Fig. 2.6. CE amplier schematic diagram

> Uoutm;Iloadm = U_{outm}
Rload

;IR_{Cm} = U_{outm}

RC , we get IR_{Cm} = (3÷5)ICm

with Rload ∼= (3÷5)RC taking into account, this implies: ICmax ≈

≈ 5ILmax. Transistor amplication cuto frequency fcutof f has to be 3 ÷ 5 times higher than upper cuto frequency of amplied signal fup. Transistor is chosen by boundary-permissible parameters values ICmax, UCEmax, Pdis.ad andfcutof f.

Amplier operating mode by direct current is described by the equations system.

(EC=IC·RC+UCE; UCE= Ψ(IC, IB).

(2.5) (2.6)

(E_{C}=I_{B}·R_{B}+U_{BE};
U_{BE} =f(I_{B}, U_{CE}).

(2.7) (2.8) By output transistor characteristics, with restrictions (see Fig. 2.7) tak- ing into consideration, load line's location by direct current is chosen.

ECis recommended to be taken of an order (0.8-0.9)UCEmax. Load line is built via two points (NL and SC).

From equation (2.5):

• For OC mode,IC= 0; UCE=EC (point 1);

• For SC mode,U_{CE} = 0;I_{CG}= E_{C}

RC (point 2).

Fig. 2.7. CE transistor output i-v characteristics and maximum permissible parameters

The operating point should be located in characteristic's operating area center (point "O"), when amplier is working in small signals mode.

Two coordinates IKQ, UCEQ for selected base current IBQ determine
it. Point "O", determined by coordinatesI_{B}_{Q}, U_{CE}_{Q} corresponds to this
point on input transistor characteristics (look Fig. 2.8). Let us set voltage
valueU_{BE}_{Q} (look Fig. 2.8) to calculate resistorR_{B} value (according to
equations (2.7) and (2.8)). Since this voltage value has an order (0.4÷

÷0.7) V, it is not convenient to trace load line accordingly to equation (2.7), because voltage C has an order (10÷20) V. Calculate required resistorRB value having written down equation (2.7) for point "O":

EC=UBE_{Q}+IB_{Q}·RB;→RB =EC−UBE_{Q}

I_{B}_{Q} .

Resistors RC and RB values are approximately units and dozens of kΩ correspondently for law-power transistors.

2. Calculation by alternating current.

To calculate by alternating current, it is necessary:

• Origin of coordinates on transistor characteristics should be re- placed into operating point "O" by direct current. Transistor param- eters for innitesimal increments are to be determined in operating point. H-parameters are the most common. With transistor working in small-signals condition about the operating point taking into ac- count, superposition principle is applicable for amplier calculation in that case.

•Build an amplier's linear model for voltage and current alternating components with transistor linear model taking into consideration.

Fig. 2.8. CE transistor input i-v characteristics

With the source internal resistance being small for voltage and current alternating components (pointsEC and−EC are supposed to be unipo- tential) and transistor operating in active region in small-signal condition taking into account, we'll get a next linear electric amplier model (see Fig. 2.9).

Fig. 2.9. CE amplier equivalent circuit

Having described this model by equations in correspondence with elec- trical engineering laws we determine:

1. Amplier input resistance required for taking into account ampli- er matching with input signal source.

2. Amplier by output circuit is represented as a Thevenin generator relative to load resistanceRload. Output amplier resistanceRout

and voltage gain in open circuit condition kOC are dened for this.

3. Amplier voltage and current gains kU and kI and their depen- dence on frequency to build amplitude-frequency response (AFR),

phase-frequency response (PFR) and amplitude-phase-frequency response (APFR).

4. Nonlinear distortion factor at set value of input signal and frequen- cy distortion coecients Mlow andMup on the cut-o frequencies flow andfup.

This bandwidth is symbolically divided into 3 sub-bands, when audio amplier is calculated (look next chapter 3.1):

Low frequencies (10÷300 Hz);

Medium (mid) frequencies (300÷5000Hz);

High frequencies (5000÷30000 Hz).

Amplier general parameters are dened in the band of mid frequencies.

The assumptions on blocking capacitors resistances in this region being small in comparison withRinandRload, switched in series and possible to be neglected, while capacitor resistanceloadΣbeing considerably more than RL,|XC| =

1 jωCLΣ

>> Rload, switched in parallel and can be also neglected, are fullled. Here:

C_{loadΣ}=C_{CE}+C_{M}+C_{load},
WhereCCE output transistor capacitance,
Cload load capacitance,

CM mounting capacitance.

CloadΣis about tens hundredspF, as a rule.

When collector voltage absolute value is more 5 V, input i-v character- istics interow in one, stipulatingh21E →0,this implies:

Rin.tr ≈h11E.

Here, amplier input resistance is dened by resistances, switched in
parallel toR_{im.t}andR_{B}:

R_{in.amp} = R_{in.tr}·R_{B}
Rin.tr+RB

.

Because RB >> h11E, the amplier input resistance Rin.tr >> h11E. Whenh12E→0 we get:

kU ≈ − h12E

h_{22E}+_{R}^{1}

C +_{R}^{1}

L

·h_{11E}
.

Last expression's analysis shows, that|KU|>>1,while sign "−" points Uout andUinbeing antiphased. Expression in brackets is about 1

RC and amplier simplied gain value is:

kU ≈h21E·RC

h_{11E} .
Amplier current gain is determined as:

ki =Iout

I_{in} =Iload

I_{in} ,
wherePload= Uout

R_{load},whilePin= Uin

R_{in.amp}.Therefore, we get:

ki = U_{out}
Rload

·R_{in.amp}
Uin

=k_{U}·R_{in.amp}
Rload

.

It follows from expression, that current gain ki >> 1. To increase ki, Rload is to be decreased, however beginning from some Rload value, kU decreases, and that can lead to opposite eect.

Assuming, thath12= 0,which is almost always true, we get:

R_{out} ≈ 1
h_{22}+_{R}^{1}

C

.

Since 1 h22E

>> RC,thenRout≈RC.

As input and output CE circuit resistances are commensurable, the series
CE ampliers stages connection is possible, provided their satisfactory
agreement. For example, we get a general amplier gain K = K_{1}·K_{2}
for two-stage amplier with a gainsK1andK2an equalityRout1=R2in2.

3. Voltage amplier by the common base circuit.

Similarly we can examine an amplier on transistor, switched by the cir- cuit with CB (look schematic diagram Fig. 2.4), that is described without determination of main parameters in chapter 2.1. Its linear electric mod- el (equivalent circuit) is the same as CE circuit model (see Fig. 2.9), in which h-parameters have common base indices (h11B, h12B, h21B, h22B) and resistorRE is on the place of resistorRB.

Its main parameters R_{in}, R_{out}, K_{U}, K_{I} examination allows to nd the
follows:

• Amplier input resistance, as well as for CE, Rin.amp =

= h_{11B||R}_{E}_{≈h}_{11B}. However, h11B value is tens times smaller, then
h11E,that's why CBRin.amp is about the tens-hundreds Ohms.

• CB circuit output resistance is dened similarly to the CE circuit Rout= 1

h22B

||RC≈RC.

•CB circuit voltage gainKU >>1,as in CE circuit, but is positive, that stipulates null phase shift between input and output voltages.

Unlike CE circuit CB stage doesn't amplify the current (KI <1), because h21B <1 (h21B =a).

4. Conclusions:

Voltage amplier circuit (CE) has almost equal input and output resis- tances, that allows agree by voltage input resistance of the next stage with output resistance of the previous, when they are connected in se- ries in multistage ampliers. CB circuit doesn't allow this connection, because Rin.amp << Rout.amp. For the series CB stages connection, matching stages have to be switched between them, built by the CC circuit (see next chapter 2.3).

CE and CB circuits voltage gains K_{U} >> 1 (dozens) and are diered
only by phase relationsϕ_{CE}= 180^{◦}, ϕ_{CB}= 0^{◦}.

CE circuits current gains (KI >>1), for the CC circuit (KI <1). As power gainKP =KU ·KI, so the CE circuit has the biggest gain.

CE voltage amplier circuit is widely used in electronics, but the CB cir- cuit, in spite of the pointed disadvantages, is applied in compliance with its advantages. The most high temperature stability and less nonlinear distortion should be referred to them (see next chapter 5).

### 2.3. Bipolar junction transistor amplier, connected by the common collector circuit

1. Direct current circuit calculation.

Direct current circuit operating mode is determined with the elements:

R_{E}, R_{B}, E_{C} and transistor's parameters. Amplier schematic diagram is
shown in Fig. 2.10. Similarly, as for common emitter circuit, input and
output circuits can be described with next set of equations:

(E_{C}=I_{E}·R_{E}+U_{EC};
U_{EC}= Ψ(I_{C}, I_{B}).

(2.9) (2.10)

(EC =IB·RB+RE·(IC+IB) +UBE; UBE =f(IB, UCE).

(2.11)
(2.12)
I_{E}=I_{C}+I_{B}, I_{B} << I_{C} that's why equation (2.9) can be written:

EC≈IC·RE+UEC.

Fig. 2.10. Bipolar junction transistor CC amplier schematic diagram As for the CE circuit (see Fig. 2.11), build a load line (1), corresponding to the system of equations (2.9), (2.10):

By analogy with the CE circuit choose idle point "O", and dene resis- tancesRE andRB values (see Fig. 2.11).

R_{E}≈ E_{C}
ICG

, R_{B} =E_{C}−R_{E}· I_{B}_{Q}+I_{C}_{Q}

−U_{BE}_{Q}
IB_{Q}

.

Present CC amplier equivalent circuit (look Fig. 2.12).

Fig. 2.11. Determination of the direct current operating mode:

a on the output transistor characteristics;

b on the input transistor characteristics

Fig. 2.12. CC amplier equivalent circuit

Studying the model, we get the voltage gain:

kU = Uout

Uin

= h21E·Req

h21E·Req+h22E·h11E·

Req+ 1 h22E

.

Since denominator k_{U} is bigger then numerator, then k_{U} < 1.k_{U} ≈

≈0.9÷0.99provided the rightly designed stage.

Since kU ≈ 1, then Uout ≈ Uin, therefore an CC amplier is called emitter Input transistor resistance can be dened as:

R_{in.tr}= U_{in}
PB

= h_{11E}
1−kU

. Hence, input amplier resistance is expressed:

R_{in.amp}=R_{in.tr}||R_{B}.

Since kU ≈ (0.9÷0.99), then Rin.tr = (10÷100) ·h11E, therefore,
R_{in.amp} ∼= (10÷100kΩ). Therefore, CC circuit has the highest input
resistance, and it has to be applied if signal source with high internal
resistance is used.

Dene similarly current gain:

kI =
U_{out}
Rload

U_{in}
Rin.amp

=kU ·Rin.amp

Rload

≈ Rin.amp

Rload

.

As allowed values R_{load} are of order of units kΩ hundreds Ω, then
k_{i}>>1 and makes up about tens- hundreds.

Output transistor resistance can be dened as:

Rout.tr= U Icom

= U

U

1 + h_{21E}
h11E·h22E

·h22E

= h_{11E}

h11E·h22E+h21E

.

Sinceh_{11E}·h_{22E} << h_{21E},then we getR_{out.tr} ≈h11E

h_{21E}. For the typical
parameters values of these low-power transistors we'll getRout.trof order
of tensΩ.

Emitter follower's full output resistance is equal to: Rout.suf =

=Rout.tr||RE≈Rout.tr, asRE is usually much larger then Rout.tr. 2. Conclusions:

Common collector circuit possesses the lowest output resistance and the highest input resistances from the three circuits of transistor connection.

That's why this circuit is used as a matching stage between input signals
source with the highR_{in}and low-resistance load. The given circuit has
the highest current gaink_{i},but doesn't amplify voltage (k_{U} ≈1), there-
fore it is called emitter follower, as output signal repeats input signal
both by phase and amplitude. Common collector circuit is used as input
and output stages to provide a large input and small output amplier
resistances. It also is used as a matching stage between amplier stages
CB-CB or CE-CB.

### 2.4. Bipolar junction transistor amplier, switched by the common base circuit

Amplier schematic diagram is shown in Fig. 2.13.

Fig. 2.13. Amplier schematic diagram

Circuit construction concept is similar to bipolar transistor CE amplier
circuit. Resistor R_{D} is similar to R_{C}, automatic bias chain works as
resistorRB or as divider (look Fig. 5.5, 5.6).

In this circuitRS, RG and CS form an automatic bias chain. There is a voltage drop onRS,stipulated by the drain current, transmitted to the

gate through the resistor RG, and denes an operating point position, i.e. transistor direct current operating mode. ResistorRS is bridged by the capacitanceCS in the alternating current mode, not disturbing thus idle point location, determined in the direct current mode.

1. Direct current calculation.

Field-eect transistor is chosen similarly to bipolar one by the maxi-
mum permissible values ofE_{DSmax}, I_{Dmax}, P_{max} andf_{cutof f}. Amplier
output circuit can be described by the next system of equations:

(EDC=ID·(RD+RS) +UDS; UDS =ϕ(ID, UGS).

(2.13) (2.14)

The rst equation is the load line equation, and the second transis-
tor output characteristics. Graphic-analytical solution of this system of
equations is shown in Fig. 2.14. Here UDS_{Q}, ID_{Q}, UDS are the voltage
between the drain and source, drain current and gate-source voltage at
the idle point "O".

Fig. 2.14. Field-eect transistor output characteristics

Load line extreme points are determined at the OC and SC conditions.

OC conditions:I_{C}= 0;U_{DS} =E_{DS}.

SC conditions:UDS = 0;ID=ICG= EDS

RD+RS

.

At stage designing, the load line is traced correspondingly, and having

knownICGthe total resistanceRCD+RS to be dened.

R_{D}+R_{S} =EDS

I_{CG}.

Voltage drop on R_{S} is created at the expense of the current I_{D}, "+"

of this voltage is transmitted to the gate through resistor R_{G} (look
Fig. 2.13), "−" is applied to the source, that stipulates bias voltage.

Therefore, voltage loss on RS has to provide voltageUGS:

CapacitanceCS is selected such, that with input alternating signal sup- plying, the next inequality is true:

1

ω_{min}·C_{S} << RS,

whereωmin minimum amplied input signal frequency.

As the bias voltage is transmitted to the gate through the resistorRG, with the knownIG(stipulated in the Handbook) we can determine max- imumRG,value, such that IG·RG =UGC.RGmax is of the order of 1 MΩfor the eld-eect transistors withp−njunction.

Amplier full linear model is shown in the Fig. 2.15. CapacitorsC_{coup1}
and Ccoup2,and also capacitors C, Cin and CloadΣ can be neglected in
the band of mid audio frequencies, similarly to bipolar transistors RC
ampliers. Hence, amplier model for mid audio frequencies is represent-
ed in Fig. 2.16.

Output voltage can be written as:U_{out} =−S·U_{in}·R_{eq},
whereReq=Ri||RDRload, UGS =Uin, S= dID

dUGS

_{U}

DS=const

.

Fig. 2.15. Amplier equivalent circuit

Fig. 2.16. Amplier model in the mid audio frequencies band
Since R_{i}= dU_{DS}

dID

_{U}

DS=const

for low-power eld-eect transistors is of order of hundreds kΩ, RL units ofMΩandRC dozens ofkΩ, then Req ≈RD.

Hence, we can nd voltage gain:

kU =Uout

Uin

=−S·Req ≈ −S·RD.

At characteristic slope typical valuesS ≈1÷10mA/V, get|kU|>>1. Current gain is determined similarly to the bipolar transistor stages:

ki=I_{load}
iin

= Uout

RL

Uin

RG

=kU· R_{G}
Rload

.

Analyzing this expression we'll get|ki|>>1. Compared tokifor bipolar transistor CE circuit, the eld-eect transistor CS circuit has consider- ably higher gain. As follows from the model:

Rin=RG.

CandC_{in}inuences have to be taken into account on the high frequen-
cies, herewith input resistance is determined as:

Rin=RG||Cin||C·(1 +kU).

There is domination ofC action overCin, which values are about units ofpF,at big gains (10÷100) and typical values ≈1pF.

Amplier output resistance is dened traditionally as:

Rout = R_{i}·R_{D}
Ri+RD

≈RD.

Hence, by the set parametersk_{U}, k_{i}, R_{in}, R_{out} values, their parameters'
similarity with bipolar transistor CE amplier parameters is traced.

### RESUME

It is necessary to understand It should be memorized 1. System of calculation of CB volt-

age amplier by direct current.

2. How to build the loading line by direct current and choose operat- ing point position

3. System of calculation of CB volt- age amplier by alternating cur- rent.

4. How to build graphically the oscillograms of input and output voltages and currents and deter- mine relationships between them and CB amplier.

5. System of calculation of CE volt- age amplier by direct current.

6. Permissible (maximum) param- eters UCEmax;ICmax;Pmax bound the transistor output characteris- tics area for circuit calculation by direct current.

7. System of calculation of CE volt- age amplier by alternating cur- rent.

8. How to build graphically the os- cillograms of input and output

1. CB, CE, CC ampliers' circuit diagrams.

2. CB, CE, CC transistor and am- plier linear electric models.

3. Phase relationships be- tween voltages and currents of CB, CE, CC ampliers.

4. Parameters' typical values of CB, CE, CC ampliers:

R_{in}, R_{out}, K_{U}, K_{U}_{OC}, K_{I}, K_{P}.
5. Common source FET ampli-
ers' circuit diagram. 6. Common
source transistor and ampli-
er linear electric models.

7. Parameters' typical values of common source ampliers:

Rin, Rout, KU, KU_{OC}, KI, KP.
8. Formulas for CE circuit:

Rin.amp

Rin.tr·RB

Rin.tr+RB, Rin.tr =h11E, KU ≈−h21E·RC

h_{11E} >>1,
K_{i}=KU·Rin.amp

R_{L} >>1,
Rout ≈ 1

h22E+_{R}^{1}

C

,

### RESUME

voltages and currents and deter- mine relationships between them and CE amplier.

9. Features of CC amplier circuit calculation by direct current.

10. System of calculation of CC voltage amplier by alternating current.

11. System of calculation of FET ampliers by direct current.

12. Features of self-bias circuit cal- culation.

13. System of calculation of FET ampliers by alternating current.

Rout ≈RC; for CC circuit

Rin.amp = Rin.tr·RB

Rin.tr+RB,
R_{in.tr} = h11E

1−k_{U},
K_{U} =

=h ^{h}^{21E}^{·R}^{eq}
h21E·Req+h22E·h11E·

Req+_{h}^{1}

22E

i<

<1,

Req = RE·RL

R_{E}+R_{L},
K_{i}=K_{U}· R_{in.amp}

RL

>>1, Rout.amp= Rout.tr·RE

Rout.tr+RE,
R_{out.tr} ≈h11E

h_{21E}.

It is necessary to be able:

1. To determine concepts: common base, emitter, collector, source ampli- ers by direct current, alternating current, ampliers' critical parameters and their typical values.

2. To write formulas for voltage, current gains, input and output resis- tances of dierent types ampliers.

3. To solve tasks on amplier critical parameters determination.

### 2.5. Tasks for current testing

2.5.1. Questions for monitoring

X Dene common-base amplier input resistance.

X Dene common-emitter amplier input resistance.