Introduction to

Electronic Circuits

An informal self-study course

Written by Prof. C.K. Michael Tse
encktse@polyu.edu.hk

CONTENTS

1. Introduction
2. The bipolar junction transistor (BJT)
3. Amplifiers
4. Operational amplifiers
5. Feedback and oscillators

1 Introduction

1.1 Outline of Objectives

Some basic concepts of analogue signals are introduced in this section. You will learn the basic functions of an analogue electronic system, viz. transformation and generation of signals of continuous nature. Here, signal transformation refers to all kinds of manipulation such as filtering (selecting signals of a certain range of frequencies) and amplification (enlarging the magnitude of a signal). Signal generation in the context of analogue electronics can be taken to mean the construction of a signal with a specified waveform, as in the case of a sinusoidal wave generator. This section prepares you for the study of electronic amplifiers and oscillators in the later sections.

1.2 Signals

A. The concept of signals

For the purpose of this introductory course, it suffices to view signals as voltages that change in time in a particular manner. A sinusoidal voltage, for instance, is a signal. The definitions of frequency, amplitude and phase, are central to the description of a signal. The diagram below illustrates the meaning of these terms. (See Fig. 1.)

Fig. 1: Sinusoidal signal

The mathematical expression for this sinusoidal signal is

v(t) = A sin (2 π f t + α ).

The units of measurement should be noted. In particular, your attention is drawn to the unit of frequency which is cycle per second or hertz. It is also important to distinguish between peak values and root-mean-square values for the description of amplitudes of signals, as studied in an earlier section in the course.

Remarks:

A common misunderstanding is worth noting: the unit of frequency is NOT per second, as may be wrongly concluded from the dimension of frequency. In fact it is cycle per second! The consequence of this misunderstanding can be serious. 1 cycle actually equals 2π radian, with the radian being the truly dimensionless unit. Thus, writing 50 Hz as 50 per second would result in an unacceptable error! Alternatively, you may use angular frequency ω which has the unit of per second or radian per second.

B. Comparing signals

Before introducing the concept of amplification, it is important to explain how two signals of the same frequency can be compared. The simplest comparison is to take the ratio of the amplitudes of two signals, leading to the concept of gain. Moreover, it is important to mention that since the magnitude of gain is usually quite large, it is better to employ a "compressed" scale. This brings up the unit decibels (dB). When two voltages of amplitudes V₁ and V₂ are compared, their ratio (gain), in dB, is given by the formula:

dB

Another type of comparison between two signals of the same frequency is the phase difference. This can be expressed in either degree or radian.

Phase difference φ = α₂ - α₁

where α₁ and α₂ are the phase angles of the two signals relative to a fixed reference sine wave.

Class discussions:

What is the amount of gain or attenuation in dB when a signal is reduced by half in power or by a factor of 0.7071 in amplitude? (ans: 3dB)

C. What is analogue electronics?

At this point, it is worth mentioning, as a prelude to the study of analogue electronics, that the subject deals with signals of continuous nature. (At a later stage, you will contrast this with digital electronics which deals with signals of discrete nature.)

Remarks:

For the purpose of these introductory notes, it suffices to regard analogue electronics as systems that either transform or generate continuous signals. Here, the function of transforming signals may include filtering, amplification and phase shifting, and the generation of signals refers in particular to the creation of signals of certain specified waveforms, as in the case of oscillators.

1.3 Interim Review and Recapitulations

Upon completing this section, you should be well aware of the characteristic features of analogue electronics. More specifically, you should be able to

1. describe a sinusoidal signal (or more generally periodic signals) in terms of frequency, amplitude and phase;

2. compare two signals in terms of gain and phase difference;

3. name the basic roles of analogue electronics.

2 The Bipolar Junction Transistor (BJT)

2.1 Outline of Objectives

The Bipolar Junction Transistor (BJT) is introduced here as a crucial electronic device for the construction of amplifiers. The basic characteristics of BJT will be discussed, with minimal reference to semiconductor physics. The simplest application of a transistor as a switch brings up two operating conditions of a transistor, namely, cut-off and saturation. Without involving complex mathematical expressions, the input, transfer and output characteristics will be explained for active transistor operation.

2.2 The Transistor Model and Operation

A. Basic transistor model

A BJT is viewed as a three-terminal device available in two flavours: npn and pnp.

Fig. 2: Simple models for BJTs

At this point, you should note the following properties of an npn transistor (with reverse polarities for a pnp):

Property 1: The collector must be more positive than the emitter.

Property 2: The base-emitter and base-collector junctions behave like diodes, as shown above.

Property 3: Collector current is roughly proportional to base current , and can be written as , where is the current gain of the transistor and is typically about 100. Both and flow to the emitter. An important observation should be made here: The collector current is not due to forward conduction of the base-collector diode; that diode is in fact reverse-biased. This situation may be viewed as "transistor action".

Remarks:

1. The npn transistor should be the initial focus of discussion in order to avoid obscuring the essentials. You may forget about pnp for the time being. When you have mastered the npn transistor, you should be able to extrapolate the ideas to the pnp transistor by merely reversing signs and polarities.

2. Property 3 gives the transistor its usefulness: a small current flowing into the base controls a much larger current flowing into the collector.

3. You should be warned that is NOT a "good" transistor parameter because its value can vary from 50 to 250 for different specimens of the same transistor type. Hence, any circuit that relies on a particular value is a bad circuit. Details will be postponed to a later time when DC biasing is studied.

4. Property 2 implies that an operating transistor has . (Here, polarities are given for the npn transistor. They should be reversed for the pnp transistor.)

Discussions:

The following question is interesting. Is the collector current a result of diode conduction? The answer is "no". The collector-base diode is normally reverse-biased, and the collector current does not vary much with the collector-emitter voltage. In most cases of active operation, the collector current is fairly constant, in opposition to the usual V-I relationship of a diode junction.

Fig. 3: Transistor as a switch

B. Cut-off and saturation: application as a switch

Use of a BJT in switching is typically illustrated by Fig. 3. This will conveniently explain the concepts of cut-off and saturation.

Since this is probably the first transistor circuit you have ever met, it is worthwhile to study this circuit in depth.

Situation 1: The idea can be put in a very simple way. Referring to Fig. 3, the collector current should be times the base current. Also, collector current causes voltage drop across the lamp (assuming that the lamp is a resistance). Proportionality between collector current and base current is maintained only if the voltage drop across the lamp is less than the total available voltage (10V). In this circuit, the max collector current is 100 mA. So, if the base current exceeds 100/ mA, the collector current is saturated at 100 mA.

In this situation, since the collector-emitter voltage is less than a diode drop, the collector-base diode is not reverse biased, invalidating the "transistor action" stated in Property 3. The transistor is said to be in saturation.

Situation 2: As shown in Fig. 3, the base is effectively grounded. Since both base-emitter and base-collector diodes are not conducting, the base current is zero. The collector current is zero, according to Property 3. The lamp is off.

In this situation, the transistor is said to be cut-off, having no base current to control the collector current.

Remarks:

The case of cut-off is usually more easily understood by you than the case of saturation. Indeed, you will find it confusing when trying to determine the validity of Property 3. Here, a simple rule will help you understand this idea: Property 3 is true only if Property 1 is true.

C. BJT characteristics for active operation

There are many possible views of an npn transistor. The usual view is to consider the base-emitter terminals as input terminals, and the collector-emitter terminals as output terminals. This view will conveniently give the various voltage-current relationships.

1. From Property 2, the input characteristic resembles that of a simple diode, i.e., exponential function. It may be helpful to give the characteristic curve of as shown in Fig. 2.4.

2. From Property 3 and the input characteristic, the transfer characteristic is likewise an exponential function relating and . (Mathematical expression may be optionally shown.)

3. Regarding the output characteristic, it is important to point out that is independent of . The curve of versus is simply a flat straight line under this condition.

The above characteristics remain valid when the transistor is in active operation.

You may put together the previously described saturation and cut-off conditions to obtain a complete picture of transistor operation.

Remarks:

Instead of a detailed examination of the mathematical expressions, you should have a strong intuitive feeling about the characteristics.

1. The base current increases exponentially with . Typically, remains zero until rises to about 0.6 V. Thereafter increases very rapidly. It may be assumed that stays around 0.6 V for all practical values of .

Fig. 4: Transistor characteristics

2. Although it may NOT be necessary to mention the characteristic equation , it is important to draw your attention to the fact that the incremental change of is proportional to the incremental change of , i.e., , where the proportionality constant k is numerically equal to the slope of the transfer characterisric curve (i.e., versus ) measured at a given . This incremental transfer characteristic is probably the MOST IMPORTANT transistor characteristic. You are advised to memorize it.

3. The term incremental transconductance or small-signal transconductance, , may be introduced here as an important transistor parameter. Here, the formula = may be helpful, where 25 mV at room temperature.

Class discussions:

Some calculations of the value of may improve understanding of its meaning. Here, a difficult (perhaps new) concept has to be explained. While is the ratio of the change of to the change of , its value depends on the actual value of the . For example, try to calculate how much would fluctuate if there is a 10 mV fluctuation of , given that the value of is set at 10 mA. Now, can you see the possibility of signal amplification?

2.3 Interim Review and Recapitulations

At this point, you should be well aware of the basic characteristics of an npn transistor (forget about pnp if you find it hard to swap polarities). These include:

1. an intuitive model of a BJT, i.e., the three properties;

2. operations in cut-off and saturation;

3. application as a switch;

4. active operation, with (a) base-emitter voltage more or less kept at 0.6 V; (b) base current proportional to collector current; (c) the change of collector current proportional to the change of base-emitter voltage; and (d) collector current independent of the collector-emitter voltage.

3 Amplifiers

3.1 Outline of Objectives

In this section, you will be introduced to the concept of amplification and the basic technique of constructing an amplifier using a BJT. The main transistor circuit to be studied is the common-emitter (CE) amplifier. A simple graphical technique is used to explain the operation of a CE amplifier and to deduce the voltage gain. The factors affecting the gain value will be considered using the graphical technique.

3.2 Amplification: Concepts and Implementation

A. The basic idea of amplification

The idea of amplification is introduced here as a gain of amplitude when a signal passes through an assembly of electronic devices known as an amplifier. Alternatively, an amplifier can be considered as an electronic circuit with an input port to which a signal enters, and an output port from which an enlarged signal emerges. The diagram shown in Fig. 5 may help explain this notion.

Fig. 5: Voltage amplifier

Two aspects of practical amplification should be highlighted. The first aspect is, of course, the enlargement (reduction) of signal amplitude. The second aspect is the phase shift of the output signal relative to the input signal. It is important here to point out that a practical amplifier does not give the same gain and phase shift for signals of all frequencies. Usually, a practical amplifier maintains a fixed gain and phase shift for a range of frequencies only. For example, an amplifier with a first-order low-pass cut-off should be adequate for this purpose. Your attention should be drawn to the gain and phase shift variation as frequency increases.

1. The use of semi-log scale is recommended. The x-axis is log f, and the y-axis is the gain in dB. Real figures may be given to clarify the usage. For instance, if Hz corresponds to on the x-axis, then Hz corresponds to on the x-axis as shown in Fig. 6.

2. The amplifier maintains a gain of A dB for low-frequency signals up to Hz. Thereafter the gain starts to drop. Here, is called the cut-off frequency or the bandwidth of the amplifier.

3. At , the gain is exactly 3dB below the intended low-frequency gain which is A dB. Therefore, the output signal amplitude at this frequency is reduced by a factor 0.7071 in comparison with the intended amplitude at low frequencies. In terms of power, the output power at this frequency is reduced to half the power for low frequencies.

Fig. 6: First-order frequency response of amplifier

4. The gain continues to drop, beyond the cut-off frequency, at a rate of 20 dB every ten-fold rise in frequency. See Fig. 6.

5. The phase shift between the input signal and output signal increases (actually getting more negative) as frequency increases. At the cut-off frequency, the output signal is exactly 45 deg lagging the input voltage, i.e., phase shift = -45 deg. At about 10 times the cut-off frequency, the phase shift stabilizes to -90 deg.

Remarks:

1. The study of the amplifier concept is centered around voltage signals. This should be sufficient for the purpose of studying transistor amplifiers later on in the course.

2. Details of frequency response of electronic systems may be omitted for the time being. It suffices for you, at this stage, to appreciate the usual drop of gain and phase shift in most practical amplifiers as frequency increases.

Class discussions:

Some of you may question the universality of the gain-phase features mentioned above. To clear up ambiguity, it is worth pointing out that some amplifiers do exhibit higher-order responses in which the gain drops off more rapidly and the phase shift increases to a larger extent.

B. Concept of loading

It is appropriate at this point to discuss the importance of loading effects. The phenomenon can be well motivated by the requirements of a "good" voltage amplifier which draws almost no current from the input signal and can supply very high current to the load. This concept is best explained in terms of input and output resistances. The input resistance can be viewed as the equivalent load of the amplifier as seen by the input signal. If the output of the amplifier is regarded as a voltage source supplying an enlarged version of the input to a load, then the output resistance can be viewed as an internal resistance of this voltage source. A "good" voltage amplifier will need to have a large input resistance and a small output resistance. This can be explained using a simple voltage divider concept. The model shown in Fig. 2.7 is convenient for explaining this situation.

This model can also be used to present the Maximum Power Transfer Theorem. The theorem states that maximum power transfer takes place when the load resistance is chosen to have the same value as the output resistance. Mathematical derivation is optional.

Fig. 7: Amplifier model

Remarks:

1. A simple way to illustrate the Maximum Power Transfer Theorem is to derive the expression for the power dissipated in the load and to examine how this power varies with the load resistance. The derivation involves first finding the current and then using the formula . Upon differentiating the power with respect to the load resistance, the maximum power transfer can be shown to occur when .

2. The Maximum Power Transfer Theorem must be treated with care. It may give a wrong impression that the output resistance should be designed to equal the load resistance. In fact, maximum power transfer takes place when the output resistance is zero. This seems to contradict the theorem, but it certainly makes sense to have zero output resistance in order to maximize the output. So, what is wrong with the theorem? In fact, nothing is wrong. The theorem assumes that the output resistance cannot be changed and suggests the value of the load resistance for achieving maximum power transfer. You will benefit from a careful reading of the statement of the Maximum Power Transfer Theorem and a thorough examination of its meaning.

Class discussions:

You can appreciate loading effects easily if you try to calculate the actual input voltage of the amplifier when are 50W and 1kW respectively and to repeat the same calculation using 50W and 100W instead. Likewise, you can try to calculate the actual output voltage when are 100kW and 50W respectively and to repeat the calculation with 100W and 50 W instead.

C. Basic operating principles of transistor amplifiers

The operation of transistor amplifiers is unarguably an important topic of Analogue Electronics. It will be helpful for you to get a quick glimpse at the whole construction process before probing into details. The following "golden trio" will serve this purpose well.

1. Before the transistor can be made to amplify signals, it must be given a set of DC currents and voltages around its terminals. This is called biasing.

2. Once the transistor is biased, its transfer characteristic is exploited to do amplification. Basically, when the transistor is in active operation and has a certain fixed , a small change of will give a wide swing of about the fixed value.

3. If a resistor is connected to the collector, the voltage across this resistor will swing too, according to the swing of . This gives voltage amplification.

D. Biasing a BJT

The process of biasing a transistor can be viewed as an assignment of a set of DC values for , in such a way that active operation is maintained, i.e., ensuring the transistor is neither cut-off nor in saturation. The specific objectives are:

1. to set collector current to a desired value; and

2. to set collector voltage to about (for max voltage swing).

Fig. 8: Biasing arrangements

Biasing is best illustrated with the two examples shown in Fig. 8. The objective, for both arrangements, is to work out the values of the resistances.

It is important to understand the design procedure and the difference of the two biasing methods.

Circuit (a): For this circuit, the objective is to find and , in order to achieve the target and . Normally, you can work out the design by assuming . With little difficulty, can be calculated for any given and . Finally, can be chosen to make equal to .