Designing with Transistors

1.0   INTRODUCTION

When I first began circuit design I was overwhelmed with the theoretical nature of all the books on the subject, I just wanted to know how to design a few coupled transistor stages without needing to know about silicon doping and junctions and lattices and 'flow of holes' In 1974 I came across a superb series in the now extinct 'Practical Electronics' called "First Steps in Circuit Design" by AP Stephenson. It was the key I was looking for to unlock this mystery, I devoured it several times and it put me on the right track, and I have never looked back. I have been unable to acknowledge the magazine and author as they seem to no longer exist.

For some reason I never kept the first chapter in this series, probably because it was too elementary. I assume you are able to figure that out, undersatan Ohm's law and have a rudimentary grasp of arithmetic and can drive a calculator, so this series begins then with heading 2.0.

Here and there I have edited the original text to add more clarity. This first section (part2), which seems theoretical, has really been scraped to the bone, and attempting to design with any less theory would simply be guesswork. There is nothing here that you can skip over, if you get lost go back and start again. You need to grasp the fundamentals.
Part 3, 4 and 5 cover some roll-up-your-sleeves design theory, and part 6 and 7 do some real designing. I promise you that if you stick with it, you WILL be designing your own stages like a 'real engineer' by the end of the tutorial - it's really all here. Do not be put off that the original of this article was written in 1974, the design steps are still valid. And so we begin:

2.0   PART 1 THE ESSENTIAL THEORY

This series, specially written for the beginner, takes you step-by-step through transistor-circuit design in a simple non mathematical way. You do need to understand Ohm's Law, and that k means 1000 as in 3k9 = 3900 ohms, also mA is a thousandth of an Amp ie 500mA is a half of an Amp.

Design of a small signal amplifier will be followed by a Class A amplifier and the series will conclude with a constructional project so that your theoretical knowledge can be put into practice.

2.1   THE 0.6V VOLTAGE DROP V_BE

We begin by looking at some of the general principles of transistor circuit design and look more closely at the transistor itself and examine how the characteristics of this device influence circuit design. We shall also look at the main circuit components which influence voltage gain. The principles to be discussed initially, refer only to small signal amplifiers, power amplifiers requiring a different approachwill come later.

The transistor requires the base/emitter diode to be forward biased. ln the case of silicon transistors the voltage drop across the junction will appear "locked" at about 0.6V. Germanium "locks" at about 0.3V. This voltage is an intrinsic value and is predictable from a rather involved discussion on the physics of the pn junction.

EFFECTS OF TEMPERATURE

V_BE refers to the voltage measure between the base and emitter of any transistor.
The 0.6V figure is almost, but not quite, a constant because at normal ambient temperature (usually specified as 25 °C) the variation is typically between 0.55V and 0.72V. The effect as temperature increases is a reduction in this voltage according to the following scale:
For every °C rise, V_BE falls by 2mV.
For example, a transistor operating at 125 °C will have a V_BE of about 200mV less than normal, i.e. 0.4V. For the majority of design work, however, transistors are running at the 25 °C norm, the only exception being the larger power stages.

V_BE AND CIRCUIT DESIGN

It is very important for the amateur designer to fully appreciate the significance of the 0.6V V_BE lock, and to ram home this point the circuit in Fig. 2.1 may be used.

Large variations in VR1 will not have much effect on the voltage V_BE. However, if VR1 is reduced to too low a value, the dreaded thermal runaway" will soon cause the death of the transistor.

In fact, if you are measuring V_BE with a voltmeter and you notice a reading approaching, say, 1V the transistor is either already dead or soon will be! When fault finding, this is the first thing you should measure, and if the 0.6V is not correct something is not right. Changes in VR1 will have very little effect on the base-emitter voltage

2.2.   THE COLLECTOR SATURATION VOLTAGE V_CE(sat)

It is easier to define collector saturation voltage by reference to the demonstration shown in Fig.2.2. As the slider of VR1 is moved towards the 12V line, I_c increases and the collector voltage falls because of the voltage drop across RC. At some point adjusting the slider the collector output voltage stops falling, becoming locked at a certain lower limit. At this limit the collector current can rise no further, in spite of rises in the slider.

DEFINITION

The collector saturation voltage, V_CE(sat) may be defined as follows:
The collector becomes "saturated" or "bottomed" when the collector current has reached its maximum possible value - because its voltage has reached its minimum possible value. This minimum voltage to which the collector can fall is called the collector saturation voltage or V_CE(sat). A typical figure to indicate the order of magnitude would be 0.5V The actual value for V_CE(sat) is dependent on the value of I_c at this voltage which, in turn is clearly dependent on R_C.

MANUFACTURERS' FIGURES

It is inconvenient for a transistor manufacturer to give V_CE(sat) values in terms of R_C, because the supply voltage would also have to be quoted. Instead the V_CE(sat) figures are quoted for a given Ic. For example in the case of the BC108:
V_CE(sat) = 90mV for I_c at 10mA
V_CE(sat) = 200mV for I_c at 200mA
measured with I_c/I_b = 20
Note that V_CE(sat) rises with larger collector currents; which may be taken as a general rule. It also rises with increase in temperature.

As the slider of VR1 is moved upwards, the V_CE falls to minimum of V_CE(sat) The academic way of explaining and measuring what goes on inside a transistor is to use a set of "network parameters" which are supplied by the manufacturer for each type of transistor. known as 'h-parameters', the term "h" meaning hybrid. To reassure the amateur designer, we shall try to avoid any further reference to any of them with the exception of h_fe which is the most generally useful of all h-parameters and r_e, which is still a most useful term because it can so easily be calculated from the collector current. We discuss r_e in section 2.5. The design of any circuit, within the capabilities of the amateur, can be carried out with these two alone, the rest of the tribe will be left to the academic types.

2.4.   THE RATIOS h_FE and h_fe

The ratio h_FE is one of the important pieces of information given in the manufacturers' literature. Its full title is "large signal forward current transfer ratio in a grounded emitter configuration" which is a bit of a mouthful and is simply collector current divided by base current thus:
h_FE = I_c/I_b
It is useful in setting up the dc bias conditions because for a given collector current and h_FE the required base current can be found.

RANGE OF VARIATION

Unfortunately it is not a very reliable constant and should not be taken at its face value. This is not to say that manufacturers issue false information, in fact they always stress that their figures for h_FE are typical and often give minimum and maximum expected values. The production line spreads however are very large as can be seen from the example of the BC108 where h_FE = 125 to 500 which means that picking one of these at random the h_FE could be anything within this range. In addition to the production line spreads there is also another variation which is an added annoyance for the designer. The mean collector current also affects h_FE. This means that manufacturers always specify the mean collector current when stating h_FE. In the above example for the BCI08 the collector current was taken at 2mA. In general the h_FE increases as mean collector current increases up to a certain upper limit and then tends to fall again.

THE RATIO h_fe

The ratio h_fe is similar to h_FE but is strictly a small signal ratio. All the remarks above apply except for this difference. The values given for hfe and h_FE are usually about the same anyway.

2.5.  THE 25/Ic EQUATION

The base-emitter junction in a transistor must be forward biased in order to operate the device as an amplifier. What "forward biased" means is there is sufficient current going in to the base to set up the 0.6V voltage, also called the "forward bias" Since forward bias causes the junction to pass current it is a relevant question to ask what is the resistance across the base-emitter junction when it is conducting?

THE INTERNAL EMITTER RESISTANCE

The answer is not straightforward, because most of the emitter current ignores the base altogether and flows upwards to the collector. It is not altogether surprising therefore to learn that the value for r_e is not a constant but depends on the collector current I_c.
(By the way here is another stumbling block for the beginner namely current flow and electron flow) Actually you really don't need to get lost in what to understand, I just imagine current flowing in the direction of the arrows, so current flows down from the collector and out of the emitter and this is also joined by some of the current flowing in from the base. Purist will beat me up over this but it will work for you if you just accept that.

In fact the formula is complex involving logs to the base e, Boltzman's constant and various other unpleasant things including the absolute temperature. Fortunately, for most practical purposes at room temperature the formula can be reduced to a very simple form:

re = 25/I_c where I_c is in milliamps, and r_e in ohms.
For example:
I_c = 1mA,
r_e = 25Ω
I_c = 10mA, r_e = 2.5Ω
I_c = 0.lmA, r_e = 250Ω

DYNAMIC RESISTANCE

It is important to note, that one should not make the mistake of thinking that r_e is a simple resistance which can be measured with multi meter set to ohms. It is a "dynamic small signal value" which only comes to life when the transistor is passing collector current.

From the designer's viewpoint, the equation is very useful because it shows how to make re any desired value by suitable choice of collector current.

however, it is not r_e itself which is important but the fact that it appears in equations for voltage gain and input resistance.

2.6.   THE LOAD WHICH THE SIGNAL SEES

For a grounded emitter amplifier circuit the signal is applied between the base and ground (see Fig. 2.3). The input resistance, r_IN, is the load which the signal sees. Superficially this would appear to be simply r_e. However, it must be remembered that only a small fraction of the total emitter current is supplied by the base, the actual fraction being I/h_fe. The apparent input resistance, as far as the signal is concerned is therefore much higher than r_e, in fact the equation is:
r_IN = h_fe * r_e


For example if the collector current is 1mA, r_e = 25Ω which makes r_IN = hfe * 25Ω.
If the transistor has an h_fe of 100, the input resistance is 2k5Ω.
It is unusual in practice to ground the emitter directly. For stability purposes, an external emitter resistor R_E is commonly employed, see Fig. 2.4.
Since r_e and R_E are in series across the signal, the modified equation for r_IN is
r_IN = h_fe(r_e+R_E)

2.7   THE STAGE INPUT RESISTANCE

Although the equation r_IN = hfe(re + RE) - will describe the load presented to a signal by the transistor, this is not the complete story. Before an amplifier can amplify, the base must be supplied with forward bias, which means extra resistive networks. These extra resistors are a nuisance because they form an additional load on the signal. For example the forward bias is often provided by a voltage divider chain R1, R2 as shown in Fig. 2.5 The problem now is to obtain an. overall equation for the total resistive load on the signal, in other words the stage input. resistance R_IN.

SERIES OR PARALLEL?

It appears fairly obvious that r_IN and R2 are in parallel but the position of R1 is not quite so easy. Is it in series with R2 or in parallel? From the d.c. bias viewpoint there is no doubt that R1 is in series with R2. From the signal viewpoint, however, R1 is in parallel with R2 because of the large smoothing capacitor Cs (shown dotted in the diagram because it is part of the power supply). The capacitor is a short circuit as far as varying signals are concerned, which makes the supply rail a (signal) ground line as well. The input circuit which the signal finally sees is shown in Fig. 2.6. From this it is clear that R_IN = R1,R2 and r_IN all in parallel

2.8.   VOLTAGE GAIN EQUATIONS

The voltage gain of a grounded emitter stage is the ratio of the output voltage swing (measured between collector and around) to input voltage swing (applied between base and ground). The symbol "A" will in future be used to represent this ratio thus A = Vout/Vin The strictly relevant components which decide this gain are shown in the skeletal diagram of Fig. 2.7. An equation for finding the voltage gain which has the merits of simplicity and reasonable accuracy is the following:
A = RC/(re+RE)
Although this equation is true as far as the amateur design is concerned there are times when an even simpler pair of equations are good enough. If RE is chosen to be very much larger than re, then the following equation is allowable:
A = RC/RE
If RE is not there at all, either short circuited or bypassed the equation reduces to: A = RC/re