Chapter 5 – Bipolar Junction Transistor

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Now that we have covered many aspects of semiconductors behavior, it will be much easier to cover another transistor type: a BJT (bipolar junction transistor).

A BJT is not as easy to control as a MOSFET or a JFET, which only required a voltage level at the gate. A BJT requires a controlling current, which is of a significantly large value. BJTs are harder to control, require more knowledge for proper operation, and require more circuit components for operation. But it is the most versatile semiconductor device, in areas other than digital logic and power switching (where MOSFETS are usually better).

While a lot of knowledge is required to design BJT circuits, the reader will be rewarded for the study with the ability to understand and control the most universal semiconductor device – a BJT.

5.1 BJT drive requirements

Fig 5.1

A very crude representation of BJT operation can be seen from Fig 5.1. What we see is a three-terminal device, just like other transistor types we have covered. One terminal is an input or control terminal, and current flows thru the other two terminals, controlled by the input terminal.

The three terminals are Collector, Emitter, and Base. They are somewhat equivalent to FET Drain, Source, and Gate. The base is the controlling or input terminal, and current flows thru the transistor from the collector to the emitter. Current IB flowing from base to emitter controls the amount of current IC flowing from collector to emitter. The amount of resulting collector current, in a crude approximation, follows the relationship:

hFE or β (beta) is a “gain” parameter, and it is specific to a transistor family (transistors of the same part number). Additionally, hFE parameter for transistors of the same part number will vary to some extent.

For small (TO-92) transistors, hFE of 100-200 is typical. However, large transistors have significantly lower current gain. TO-220 transistors switching 10A of collector current have typical gains of 10-20. That means a very large base current – 1A – is needed to drive a power BJT. This base current will be wasted in the transistor as heat. Compare this to a power MOSFET switching 10A at slow speeds: negligible static gate current is required, just a voltage potential at the gate. Current is needed to charge and discharge MOSFET gate capacitor quickly enough to avoid I*R losses of a partially open / closed MOSFET, but at slow speeds, the amount of MOSFET drive current needed is small.

The BJT is a current—controlled current source. How exactly do we supply a controllable amount of current to the base? We certainly could control a BJT like so:

Fig 5.2

However, four problems of such a circuit present themselves:

Producing a constant voltage in a circuit is easy. All that is needed is a resistor voltage divider. Producing constant current in a circuit is a little more involved – more components and devices such as JFETs are needed.

Our inputs are usually voltage levels, not current levels. In other words, we want a circuit to respond to a voltage level, without requiring current drive capability from that input.

hFE is an unreliable parameter – we can only assume the minimum value specified in a datasheet.

hFE, and other parameters of such a drive circuit will change greatly with such parameters as temperature. We would ideally prefer a circuit which had very predictable and certain parameters.

In essence, the remainder of this chapter will be trying to create a BJT circuit which will have none of the limitations listed above.

Let us see if we can control the base current with a voltage level. The BJT base-emitter section consists of a forward-biased Si diode, with 0.6V of forward voltage drop. That forward-biased diode is connected straight to circuit COM. Therefore with voltage and current applied to the diode, and with the diode in a conducting condition, base-emitter voltage potential will never rise above 0.6V. We can feed the base from a voltage source, and thru a base resistor. That resistor will produce a current of

Fig 5.3 Input equivalent and driving from a constant voltage source. RB will limit base current.

We would ideally like to not have to use two voltage sources, so we can tie a base resistor to the power supply instead. Since we are using a BJT, our power supply “+” connector can be referred to as VCC. Notice the difference from VDD.

Fig 5.4

If we can know VCC to be of a set and certain value, base resistor value can be calculated from the equation we have already discussed.

The following is important to remember, so that the reader never makes the mistake: a voltage source, be it an input or whatever else, can never be connected directly to the base. A base resistor or a coupling capacitor (more on this later) must be used. Just like an LED, which is a forward-biased “diode” that has to be operated at limited current levels, so must the base diode not be driven from a voltage source which is not current limited. Passing an uncontrolled amount of current from a voltage source into the base will cause transistor overheating and destruction:

Fig 5.4

If we keep this in mind, that there is a diode which will conduct if a voltage of >0.6V will be applied to the base, then we can take care to limit that base current and not destroy the BJT.

Fig 5.5

The symbol for a bipolar transistor is:

Experimental circuit

A rudimentary control circuit can be made like

Fig 5.6

For the bulb, you can use RadioShack #272-1092, 272-1141, or 272-1099. Those bulb leads are very feeble – make sure they do not short to each other! Slide a piece of thin heatshrink over one of the uninsulated leads to prevent shorts.

Before you build the circuit and experiment, read “The case of the burning-out potentiometer” section in the first chapter.

Tweak that potentiometer R2, and record all findings in the lab notebook. Measure currents thru points 1 and 2 (by “breaking” the connection and inserting an ammeter there), and also voltages at points 1 and 2 with reference to COM, at half a dozen potentiometer positions. Plot your findings.

And with experimentation, we find that:

1) At voltage levels at the base of less than 0.6V, not much current flows thru either the base or collector ammeters. We will call this “cutoff” mode of operation.

2) At voltage levels somewhat higher than 0.6V, a small current starts flowing thru the base ammeter, and a large current thru the collector ammeter, which is enough to make the light bulb glow.

For control purposes, we can see that the base acts somewhat like an LED:

1) Any voltage below about 0.6V will be ignored

2) Slightly above 0.6V, a small current will flow which will cause transistor collector current.

3) A constant-voltage source at the base with an output voltage significantly above 0.6V will cause a very large current flow into the base, and destroy the transistor.

We must take care that a current-limiting resistor (like with an LED) is inserted at the base, as is shown on Fig 5.3 and Fig 5.4. Its value is calculated with the assumed base forward voltage drop of 0.6V, and the current thru the base being a fraction of current flow thru the collector. For now we will assume that this fraction is 1/100 of collector current.

Second task for the reader: Adjust the circuit so that it passes little current (bulb is only dimly lit). Now press your fingers against the transistor, warming it. Do you see lightbulb brightness change? Is this at all desirable transistor behavior?

BJT Datasheet

We are going to look at the MPS3904 datasheet. This device is sold by RadioShack as “2N3904”. Other small-power BJTs they sell do not have good datasheets for our purposes.

We see some parameters which I hope the reader will be able to decipher by now. Briefly, ratings to watch out for are:

VCE, which is the maximum voltage across the transistor (power supply in this case)

IC, maximum current thru the collector, and hence thru the load in this circuit

VBE (very small limit!) an absolute maximum voltage at the base above which the transistor will be destroyed

PD maximum power dissipation in the transistor, since there will be some voltage drop at the transistor

Maximum junction temperature

There are also some pretty plots. The reader should inspect Fig 8, 9, 10, 13, 14, and 20.

5.2 Large signal behavior

By “large signal behavior” I mean “a rough model of how a BJT operates”. A BJT in a circuit can be operating in one of four regions. This is a summary only, and the reader should not try to interpret what this says – everything will be explained shortly!

Cutoff. If VBE is <0.6-0.7V, the BJT is not passing any collector current, and is therefore OFF. Only a small leakage current ICEO flows.

Active. At VBE>0.7V and intermediate levels of base current, collector current is at some value between zero and maximum. Voltage at the collector must be above both base and emitter voltages, by at least a volt. In this region of operation, also called “linear mode”, transistor follows relationships VB = VE+0.6V, IC = hFE * IB. This region is used for amplification.

Saturation. If a large base current is applied, the transistor will attempt to pass a maximum amount of current thru the collector, by lowering voltage drop VCE as much as possible. If a load is attached, a BJT transistor will attempt to “open” fully by reducing the voltage drop thru itself. The lowest collector-emitter voltage drop a transistor can achieve is somewhat less than half a volt. This region is used for switching circuits.

Breakdown. Operating a transistor beyond the voltage breakdown limits, maximum current, or power dissipation limits will result in device destruction.

Graphically,

Fig 5.7

Where:

Area under the horizontal line A is the cutoff region, with VB<0.6V.

Area to the left of the line B is non-linear area. We will see that the BJT operates here in saturation mode.

Lines C is the linear mode of operation, with collector current being dependent on base current, but not on collector-emitter voltage.

A line D, to the right of which the VCE*IC product exceeds the PD specifications. The circuit cannot be operated to the right of the line.

Area E of higher VCE voltages, at which point a breakdown will occur.

5.3 BJT as a switch

One of the easiest things to do is to operate a BJT as a switch. The thing to keep in mind is that the BJT is a current-controlled device; therefore sufficient base current is required.

As we have seen in the MOSFET chapter, a good transistor switch is one which drops a minimal voltage across itself (therefore creating minimal power dissipation in the transistor). We have seen that a MOSFET acts as a switch by being a low resistance. A BJT acts as a switch by exhibiting a “saturation voltage” drop – the transistor, when driven with enough base current, will attempt to reduce its VCE as low as possible, with typical voltages being 0.3V-0.5V or so. A good power BJT transistor can go as low as VCE = 0.2V in the open condition.

BJT switch saturation

We already know that the transistor should drop zero volts and present a resistance of zero ohms for an ideal switch. How will the BJT manifest itself in the “open” condition? How good are BJTs at the task? Let us examine the I-V plot:

Fig 5.8

How much base current is required? Theequation is only valid for the active region of operation. Somewhat more current is required to drive the BJT into saturation.

In order for the BJT to switch ON, VCE must be low, and we must operate to the left of the dashed line (plot taken from datasheet Figure 10). We are out of the linear area, and into the “saturation” region.

The plot on the right of Fig 5.8 is VCE, at several given IB values. Notice that in order to get a low VCE value, base current must:

Be higher than value given by linear mode equation .

Be higher at higher collector currents. The reader should look at datasheet Figure 8.

Be high enough to ensure the lowest VCE value.

We can see that for a controlled current of 50mA, for example, 1mA of base current would drop VCE to 0.2V. In saturation mode, hFE drops at low VCE voltages.

BJT as a switch example circuits

Fig 5.9

This circuit can be used as a basic control. When the switch SW1 is OFF, the BJT presents a high VCE drop and little collector current. Turning the switch ON will cause a low VCE drop, and high IC. The RB value is calculated from the maximum current that the load may require and the lowest gain that the transistor might have (due to device to device variations, and due to the amount of collector current).

RP is a pull-down resistor, there just to ensure that base is at 0V with the switch open. Its value is not critical. Something like 100k can be used.

If the BJT needs to be controlled from LOW-HIGH voltage levels, perhaps from digital logic, then we can use the circuit:

Fig 5.10

Ensuring a sufficient amount of collector current

It is a good idea to supply plenty of base current, enough to ensure that the BJT will open fully at any combination of temperatures, current gains, and load currents. This is usually called "over-driving".

We have the luxury of having a good datasheet. If the reader is in a situation that only hFE is given, but switch characteristics of the transistors are not specified (and you cannot find the datasheet at AllDatasheet.com), then as a rule of thumb, to make sure the transistor drops little VCE voltage, it is always a good idea to supply much more (3x-10x) base current than by using linear-mode equation and hFE specification alone.

Remember: hFE is an unreliable parameter, and it varies with circuit operating conditions.

We can also see a reason to use a BJT switch instead of a MOSFET in some applications. At high voltages and currents, and at fast switching speed, that super—low MOSFET RON might not look so great anymore. Compare an RON of 0.02Ω vs. VCEsat of 0.2V at 500V power supply voltage and collector current of 50A. In a high-power application like this, and at a switching frequency of perhaps 10kHz, a BJT will perform much better. BJTs are easy to control in high-speed switching (there is no dynamic gate capacitance and current). A special hybrid device, called an IGBT, is actually used in such applications.

In all other applications, BJT transistors should be used in low-power switch circuits only, because small-power BJTs are more common than small-power MOSFETs. Compared to a MOSFET switch, BJTs have low base voltage (depends on RB, as low as 0.8V) to turn the transistor ON.

High power BJTs switches use the same principle, but will not be covered in this book. The reader should use a MOSFET instead. High-power BJTs are worse than power MOSFETs because MOSFETs have no “secondary breakdown”, and have low gate current at slow switch speeds.

For circuit analysis purposes, transistor voltages in saturation mode follow the relationship of VC < VE + 0.6V.

Watch out maximum ratings of the transistor and resistor RB in switch circuits. V(BR)EB, IBmax, and base resistor power ratings cannot be exceeded.

BJT switch circuit analysis

Assume VCC = 12V, hFE = 30, RL = 50Ω. Calculate everything.

Among the RadioShack devices, 2N2222 and 2N4401 from the NPN assortment can handle this collector current, but only the 2N2222/MPS2222 has a usable datasheet.

Figure 7 of that datasheet shows that about 5mA of base current (typical value) will cause the transistor to saturate with VCE < 0.6V. Let's check this against the device hFE specification. The datasheet lists hFE to be about 30 at this collector current. We know that to ensure complete transistor saturation with a very low VCE, plenty of current must be supplied to the base. We should supply from 10mA to 20mA to ensure this switch works with minimal I*R losses, works for any device with worse individual parameters, and ensures transistor operation if the load draws current higher than 0.24A (such as a light bulb which has a very low resistance until its filament heats up, and so on).

Note that the switch contacts must be able to handle 10-20mA. Base resistor value is easy to calculate:

RP will be 100k.

Power dissipations:

at RL:

at RB:

If a resistor is used for experimentation, it must be able to dissipate the heat. RadioShack part number 271-133 is a 10W resistor, and is able to dissipate more heat than the minimum 2.9W.

For RB, although a 1/8W (0.125W) resistor can be used, it will get hot. A 1/4W resistor should be used instead.

Unlike a MOSFET covered in first chapter, a BJT will need a relatively significant control current. And in this crude case, a fraction of total circuit power will be lost in the base resistor, and in the transistor, instead of the load.

Let us calculate power lost in the transistor itself, which will manifest as heat. We must make sure this power dissipation amount does not exceed our chosen device limitations.

PD across transistor due to collector-emitter drop: VCE x IC = 0.6 x 0.25 = 150mW

PD across transistor due to base-emitter drop: VBE x IB = 0.6 x 0.02 = 12mW

Total power dissipated: 160mW. Notice that I have used worst values for the calculations. This power dissipation is within the capability of a MPS2222. Task for the reader: how high will transistor case temperature rise from a 40°C ambient?

CAUTION: The VCE value used in calculations is only valid for a fully open transistor. If not enough control current will be supplied to this transistor, more power will be dissipated in the transistor. For example, if the load, due to a miscalculation, actually requires double the current, then our transistor will get out of saturation, VCE will be higher, and power dissipation will be high.

If the load fails and becomes a short circuit, then a large current will flow thru the device. So much heat will be dissipated that the case temperature will exceed the maximum in a few seconds. If a fuse was not used due to negligence, then a burned-out device will be the result. Note that the transistor may “fail closed” – that is, unlike a fuse, it will keep conducting current, this time uncontrollably. Even if base current is ceased, a “failed closed” device will still conduct current, making the device extremely hot and smoking.

Let's do a thought experiment. If we are to adjust IB, at some values of control current, transistor may be “half-open”, dropping 6V across itself. Calculate power dissipated in the transistor and the load resistor in this condition. Answer: 0.72W for both. For supplying just 0.72W to the load resistor, transistor itself will dissipate just as much power as heat, making the circuit 50% efficient.

Exercise: Calculate power supplied to the load, and power lost in the transistor if transistor drops 3V, and 9V across itself. At which point (0, 3, 6, 9, or 12V across transistor, dropped) is the circuit least efficient?

Darlington transistor

The 10-20mA base current is approaching source current limit of common digital logic and microcontroller outputs. And we are only able to switch 0.25A! If any more current control is needed, higher-power transistors must be used, hFE of which will be even less.

There is a way to control more current with less base current. There's a special type of a BJT, called a Darlington transistor. We will have to wait until a later section to see what it is made out of. For now, we will just note that its hFE is more than a hundred and is typically up to several thousand or more. Unfortunately, its VCE is always higher than that of a regular BJT. RadioShack sells a TIP120. Explore its datasheet. As an example, for 4A collector current, a typical hFE of 3,000 is shown. At saturation, a base current of 5mA is needed, but VCE does not go below 1.3V.

Paralleling BJTs

If required current or power dissipation cannot be met with a single transistor, BJTs can be paralleled.

Just like with LEDs, if we simply connect several transistors together,

Fig 5.11 Without emitter resistors

then one of the transistors is bound to happen to conduct more current than the others (due to different gain, temperature, parameters, etc from other transistors). When it does so, it will heat up more than other transistors. As it heats up, it will conduct even more current, stealing more of the share of the total current from the other devices. It will continue to increase its current as a share of total, and its junction temperature, until that transistor destroys itself.

We can remedy the situation by inserting a low-value resistor in the emitter path of every transistor:

Fig 5.12 With emitter resistors

This time, whichever transistor happens to conduct more current than the others will also see a larger resulting resistor drop, which will reduce voltage across that transistor, relative to others. Emitter resistors will automatically adjust current values to be exactly the same across the paralleled transistors.

For choosing resistor value, there is a tradeoff. Larger resistance stabilizes the transistor better, but wastes more power as a voltage drop. A resistance which produces 0.6V drop at a typical circuit current is an acceptable value.

Temperature effects and SOA

We will need to wait until a later section to discover that temperature has a large effect on BJTs in switch mode. For now, we will only look at thermal dissipation concerns.

For any semiconductor device, the VCE*IC product of maximum parameters greatly exceeds the specified maximum power dissipation. What are safe transistor operating conditions, especially near the limit of one of the parameters?

Datasheets usually supply a SOA (safe operating area) plot. We will look at one for MPS3904, datasheet Figure 20.

Fig 5.13

As you can see from the plot, there are many things going on at the same time!

The top portion is the ICmax constraint. The right portion is the VCEO constraint. Plots with time labels (1ms, etc) are pulse ratings, and are of no concern to us. We are going to use the “maximum ratings” specified in the beginning of the datasheet, where continuous collector current maximum is specified to be 100mA.

Notice the only two diagonal lines labeled “dc”. The lines are showing a power dissipation product IC*VCE limit (625mW at 25°C). Test conditions for this plot are Tjunction=150°C, Tambient =25°C. The second dc diagonal line, specifying a condition of transistor case being at 25 ° C is not realistic. We are therefore left to only one plot of relevance to our discussion.

This device was designed to dissipate all the heat it generates thru its case as-is. More powerful devices cannot dissipate enough power all by themselves, and require to be mounted on a heatsink. In those cases, their datasheets will specify operation with a proper heatsink. More information about selecting a proper heatsink is in Appendix A.

Secondary breakdown

Notice also the “second breakdown limit” plots of the SOA. These are extremely important for high-power BJT devices. Let us take a look at the datasheet of TO-3 2N3055.

Fig 5.14

At DC, we see a diagonal line of the IC*VCE limit. However, at VCE = 40V, slope of the diagonal line changes to a faster drop-off. This is the secondary breakdown in action. Restricting operation to a limit even lower than that of IC*VCE, secondary breakdown is an effect which causes irreversible failure of the device. The effect happens when small regions of the semiconducting material inside warm up more than other areas of the device. Thereafter, the same condition happens as the one we have seen with paralleled BJTs without emitter resistances.

Load requirements

Since BJT switch base current somewhat depends on load behavior (if the load requires a lot of current, large current will be needed from base control circuitry), it is necessary to consider load requirements. The best load is a resistive load and one which does not draw a lot of current. Real loads are almost never resistive – they can combine inductance, capacitance, have non-linear resistance, and have other requirements. I have summarized this in a table:

Incandescent light bulb – Exhibits a low cold-filament resistance before the bulb warms up, which may be as little as one tenth of bulb specification or . Therefore, before the bulb filament warms up, it draws a considerable amount of current from the transistor switch. Filament-based light bulbs should also not be cycled on and off quickly, because that leads to a shorter life.

LED – requires constant-current power source with a limited voltage.

MOSFET gate – current increases with increasing frequency, gate sends back dV/dt voltage spikes to the driver when drain swings from large voltage.

Relay – Requires activation current, stated in the specifications. Less current is required to maintain the relay ON condition. Current must drop to a still lower amount to turn the relay OFF.

Inductor or Capacitor – High inrush current to turn the load ON. In case of inductor, large kickback voltage spike across inductor terminals as it is turned OFF.

Speaker – DC current is not allowed thru the speaker.

Motor – behaves as an inductor, and also has mechanical inertia. Under load, requires large current to start rotating. If it is shorted or braked, high current must be dissipated. Brushed DC motors create large voltage spikes and lots of electrical noise.

5.4 Linear BJT operation

Being a switch is the most mundane thing a transistor can be. It is much more interesting to use it as an amplifier, which can amplify an arbitrary voltage level, even if it is a negative voltage. For this, a “forward bias” is required. This section will discuss methods of biasing and operation in the "intermediate" linear region.

Class-A DC quiescent point biasing

As we have seen from our discussion of JFET amplifiers, most input signals are a varying voltage phenomena. That varying voltage usually has a center point around which the varying occurs. That may be 0V, in case of which the signal can go from a positive voltage to a negative voltage, or any other offset positive or negative voltage.

In designing a linear BJT circuit, we want it to do three things: a) accept any expected voltage levels and polarities, b) reproduce that input linearly, i.e. without any distortion, and c) amplify the signal, (produce gain).

If the input signal has to drop to less than 0.6V, or even go negative (sine wave), we also need isolation to ensure that biasing works.

Now, the unfortunate thing for us is that only one of the small-power BJTs sold at RadioShack even has enough datasheet information for us to be able to look at base current vs. collector current characteristics. That's because whoever created those small-power BJTs decided they should be "switching type", and measured its parameters for switching applications. And all other companies which have taken over manufacture of those devices did not bother to include any extra information in the datasheet themselves.

We will look at the MPS3904.

Fig 5.14

The reader should know by now that if a statement such as "TA=25 °C, pulse width = 300 μs, duty cycle ≤2%", then all information which follows such unrealistic test conditions will be irrelevant for steady-state operation. Nevertheless, this is all we have. Also, keep in mind the parameter spread of semiconductor devices, and do not expect exact values from the plot. Look at the general behavior instead.

Task for the reader: what is the significance of the plots not being parallel? What would it mean if they were parallel? Stop reading and think about this for a while!

What we see is a plot which looks like a FET ID vs. VDS plot, with several specified VGS. The difference is that a base current is given as an input to the device under test, and collector current is measured. This explains the "current-controlled current source" part!

We also see that instead of several volts' worth of VGS spread (up to 10V spread for a power MOSFET), transistor base controlling current spread is very small. This will be true for power BJTs we will study later, as well. A much smaller range of controlling base current is needed to control a BJT, compared to a large range of voltages needed to control a FET.

We also see that the lines are not as parallel as we have seen with FETs. Go back to our MOSFET and JFET plots and see for yourself. What can this mean? In case the reader has not realized himself, we can analyze this as follows. Picking any one single plot with a portion of VCE > 5V, we see that collector current thru the device increases somewhat if a larger voltage VCE is applied across the device. Would that be a much desired property of "controlling collector current with base current"? No, of course it would not be! We don't want our collector current to be dependent on applied voltage. That does not make a good "current source". BJTs are worse at being a stable current source than a FET.

We should also examine spacing between the horizontal plots. Remember that we are building a linear circuit. We want it to respond linearly. We see a wider separation between plots on the bottom of the plot, compared to plots in the upper section. What it means is that a change in base input current from 100μA to 200μA would have a different effect than a change from 400μA to 500μA. That is not a linear BJT response! We therefore have to constrain our circuits to areas of the plot where the response is as linear as possible.

Obviously, we will also avoid the left part of the plot, where VCE < 5V. We see a huge collector current dependence on voltage across the device, making device highly non-linear. That area, as we have seen already, is only used for saturated switch circuits.

What about power dissipation limits, due to the IC*VCE product? At a realistic TA = 60°C, PD is specified to be 450 mW. Putting all of this on the plot, we get:

Fig 5.16

The safe and linear area of operation is between the two fine-dot lines. If we wanted to select a region where the biggest IC variation could be made, we can perhaps select a quiescent point of VCEQ = 6V, IC = 35mA. At this point, base current can vary ±200μA, and the resulting collector current variation would be about ±30mA. Note: if the reader does not understand the reasoning behind the choice of this quiescent point, then JFET chapter sections “JFET Class A low-power amplifier” and “Range of permissible IDQ and VDSQ levels” should be revisited.

Simplest BJT DC Q-point biasing

The simplest circuit to place a BJT at a Q-point is:

Fig 5.17

Calculating all values is similar to our JFET class-A amplifier circuit calculations.

Resulting collector current from BJT amplification of input current is, of course, IC = hFE*IB. Looking at the datasheet of MPS3904, we see hFE specification at several collector currents, and also a plot of hFE vs. IC. We will pick the minimum value of 60. We need to watch out so that both IB and IC stay within the linear range which we have picked for our Q-point. For example, if we had a known input current source, and transistor gain was low, then we would not be able to produce ±30mA. On the other hand, if the input current was a large value, and the device had a large value of hFE gain, then we cannot blindly apply the IC = hFE*IB relationship, if the resulting IC was larger than ±30mA. For ease of experimentation, we will set the circuit up so that the biggest collector current variation is seen, and we will then find out the necessary input supply requirements to achieve that big collector current variation.

A BJT does nothing if less than 0.6-0.7V is applied to the base (since no current would flow at a voltage lower than this). However, at any voltage higher than this forward voltage drop, a base current-limiting resistor RB, like the one we used for LEDs.

Its value is .

RC must place collector voltage and current at a certain point, by dropping voltage across itself.

Its value is Ω

Its power dissipation is

We can apply the input signal to the VBE point, and see the change at the VCE point. Since the circuit will be changing about a Q-point, we will need to apply the input and extract the output thru DC blocking capacitors.

This circuit suffers from many limitations, the biggest ones being:

Dependence of the circuit to transistor gain. Typical hFE for small-signal transistors is 50-200. Our MPS2904 lists the gain as being anywhere from 30 to 300. If you built this circuit as an audio amplifier for your customers in a production environment, then some of the amplifiers will sound five times as loud as some others. You could tweak each built circuit by hand, but that would not be affordable even in China.

Variability of hFE parameter. Since our circuit depends on hFE (because we have based our calculations on what was given in Fig 5.16), as you have seen from the datasheet, hFE is specified at several collector currents, because gain depends on collector current.

Very large temperature effect on the circuit. Many BJT parameters change with temperature. If you built this circuit for a customer, it would work fine in a heated room in the winter. When the customer takes your product outside in a cold winter, the circuit would stop working. Perplexed, the customer would get in the car, and turn the heater on. As the car warmed, the circuit would start working as normal. Half a year later, in a sun-heated car, the circuit would stop working again. Actually, you can see this by saturating the circuit with your bare fingers! Build the circuit, measure its collector current to ensure it is at the Q point you want, and then press your fingers around the device, warming it up. What happens to collector current? Is that a desirable behavior?

This circuit, called a “grounded emitter amplifier”, is actually worthless. The only reason I have used it was to illustrate biasing for Q point. We now need to see what we can do to create a BJT amplifier circuit which would not depend on variability of parameters, especially hFE and temperature.

Reverse ICBO leakage

Fig 5.18 Two-diode representation

For the purposes of this section, a BJT can be thought of as having two equivalent diodes inside. One is the base-collector junction, with the other being base-emitter junction. A BJT is not made with two separate diodes inside, however. This is just an equivalent representation for temperature effects discussion. By drawing an NPN amplifier schematic and writing down voltage levels on the three BJT terminals (a task for the reader), we can see that base-collector voltages reverse-bias that “equivalent diode”. However, any diode has reverse leakage. And, just like with any diode, reverse collector current ICBO increases rapidly with temperature.

For every 10°C increase, ICBO leakage current goes up 2.5 times. The situation is even worse, however, since the power supply is connected across the collector-emitter terminals. Any collector leakage current will also flow thru the base-emitter junction. When it does, it will obviously be amplified by hFE current gain of the transistor, making the amplified version of that leakage current appear on the collector. Increasing temperature will lead to more leakage current, and a higher amplified collector current added to the already existing collector current flow, and so on. With a slight temperature increase, the BJT will have its current increase so much, that it will turn completely ON and saturate. Not even with a signal applied!

The hFE increase with temperature rise will only add insult to the injury.

5.5 Improved Class-A BJT biasing

Fig 5.19

We are going to add two components to our circuit: RB2, and RE. In the previous simplistic grounded-emitter circuit, we have fixed the base current. For a stable circuit, we will now fix collector current instead.

Fig 5.20

We need to find out the value of the two base resistors first. If we assume that the base-emitter junction, with RE in series, is a large resistance Rin, then the voltage VB is simply due to the two base resistors acting as a voltage divider.

What should their resistances be? We want the voltage divider to provide enough current to keep the transistor at Q-point. Larger resistances will allow larger variations of ICQ with hFE (voltage divider will not be as stiff). That sets the upper resistance limit for both resistors. However, we also want the voltage divider to be able to be over-ridden by the input signal, which controls the BJT amplifier by moving its base up and down from the Q-point. And we do not want a large current to flow thru the two dividers, because that would be a waste of electrical energy. Resistances should be low enough to keep the voltage, but to not present a low resistance to input source. This sets the lower resistance limit.

As a rule of thumb, choose resistances that set the base current at . Remember that whatever the input signal source is, it would need to be “powerful” enough to be able to move the base current up and down from its Q point set by the divider. That input signal source would see an “input resistance” of Rin = RB1 || RB2, where “||” means parallel.

Voltage at the emitter will then be , where VBE is, of course, 0.6-0.7V. Emitter current can be calculated as . Voltage offset VE is a temperature stabilization feature.

Emitter resistor RE provides better bias stability, compared to our previous circuit. This circuit shows less variation if supply voltages, temperature, and hFE gain, all change. How does it work? As collector current increases with increasing temperature, voltage drop VE across RE increases. Since the VB point of base voltage divider does not change its voltage with increasing temperature, if voltage RE increases then the differential voltage VBE decreases, decreasing collector current, and canceling its increase due to the temperature. As a rule of thumb, voltage offset VE should be about 1V at Q-point, to minimize effects due to VBE variations, which allows us to calculate RE at a chosen quiescent IC.

The collector current is approximately equal to emitter current. Exact value of emitter current is the sum of collector and base currents, but since the base collector is hFE times smaller, we can approximate it as being insignificant. Voltage at the collector will be RC drop less than VCC, therefore

and the collector-emitter voltage will be

The last Vsat value must be subtracted as well, because we want our transistor to stay in the linear mode of operation, and not approach saturation mode of operation! The resulting VCE due to all possible input values must stay in the linear mode for the circuit to act as a linear amplifier.

The resulting circuit gain is(no CE).

Notice that the gain was the last thing we have calculated. A novice experimenter may want to know how to build a circuit with the largest gain possible, but we have instead built a circuit which is as stable as practical. We did go a little quick thru the calculations, so let us take a step back and see why exactly we need to worry about stability so much.

Notice that the circuit gain is independent of transistor hFE parameter. We have purposefully limited circuit gain to a value which is less than the worst hFE transistor specification. Our circuit is therefore insensitive to individual transistor hFE variations – we can use any transistor in our circuit, and it would still produce a guaranteed gain, set by circuit components and not by device variability.

Quiescent power dissipation is a factor for Class-A amplifiers, because the transistor is always conducting current, especially at Q-point, when it is not actually outputting a signal. Total quiescent power is a combination of dissipated power in each device in the circuit (transistor VCEQ*ICQ, RC, RE, base divider resistors). At small power levels, only transistor PDQ needs to be kept in mind, but if power is increased, then maximum power dissipation must be calculated for each resistor, so that a proper resistor wattage is used. In general, if the circuit is analyzed with advanced circuit analysis methods, theoretical maximum power efficiency of class-A circuit is found to be 25%. At Q-point, of course, the efficiency is 0% (just like a car idling at a stop light has 0mpg).

We are missing some knowledge, which we must learn, before we can finish and build a common-emitter amplifier circuit. Wait just a bit!

5.6 Emitter follower configuration – biasing consideration

The circuit we have covered is called a common-emitter amplifier. It is called that because the input and output both share one terminal: emitter.

Fig 5.21

Common-emitter amplifier has the beneficial aspects of high voltage and current gains. It therefore has power gain as well. Its two limitations are low input resistance and high output resistance. From our discussion of JFET microphone amplifier, we have found out that an amplifier circuit should ideally have very high input resistance, so that it does not at all reduce input source voltage (“load it”). It is also clear that amplifier output ideally would have very low resistance: it should be able to drive a load of low resistance, without having its output voltage loaded by the resistance of the load.

Let us look again at the common-emitter circuit, and examine its behavior without worrying about equations.

What we have is an input bias network, which sets the base at a specific point of voltage and current of the chosen Q-point. Input voltage moves that Q point up and down, producing changes in base current. Transistor emitter follows base voltage with the relationship VB = VE + 0.6V. Emitter current thru the emitter resistor changes up and down according to what the base is doing. Collector current is practically the same as emitter current, therefore it changes just like the emitter does. That change of current thru the collector resistor produces a voltage swing, and a large one, since the value of the collector resistor is larger than emitter resistor value.

So, what we see is that:

Emitter voltage follows base voltage, minus the forward voltage drop

Variations in base current by the input voltage source cause variations in emitter current

Variations in emitter current produce variations in the voltage drop across the emitter resistor

Emitter resistor is much smaller in value than the collector resistor

Can we take the output from the emitter resistor instead?

Fig 5.22

Yes, we can! We will give up voltage gain, since output voltage will be equal to (input voltage – 0.6V), but we will instead receive a much lower output resistance. This configuration is called an “emitter follower” amplifier.

Collector resistor is not even needed for the operation of this circuit, since collector current will be approximately equal to emitter current (it is limited). Also, we do not need to convert a collector current swing into a collector voltage swing in this case. This type of a circuit is used at high power levels, where load resistance is measured in a few ohms. Powerful audio speakers, for example, have 4Ω resistance at AC frequencies (not at DC!). Headphones have a resistance of 32Ω, and so forth.

It is also used as a “resistance converter”. Its input resistance is high, but output resistance is low. It can also, therefore, be used in applications where a large circuit input resistance is required. Let's see how high it is.

Emitter follower biasing circuit example

Let's make an MPS3904 audio amplifier with VCC = 12V, IQ = 35mA. We will aim for ½ VCC Q-point.

Fig 5.23

Note that two base resistors are used, not like in our simplistic Fig 5.22. The reason is the same as for a common-amplifier base divider – stability of Q-point as temperature and hFE change.

Input capacitor Ci is used to block DC but pass the signal frequencies. An electrolytic is commonly used, because it is cheaper and more compact at the capacitance values needed. Notice the polarity: relative to the circuit COM, voltage at the base is a positive value. The input capacitor is therefore oriented with “–” side looking towards the voltage source (which is effectively a resistor to COM). For output capacitor, the “+” side is connected to circuit output, at which point there is a positive quiescent voltage.

Choosing RE. Ω

Choosing the base divider. VB = VE + 0.6V. As a rule of thumb, make the parallel resistance RB1 || RB2 about, or slightly lower (so that it is “stiff enough”). The ratio of two resistances needs to be . At our chosen quiescent current, datasheet lists a hFE of 80. We can simplify our calculation, since resistance of two resistors of equal resistance is half that resistance. Therefore, k, or a 5% standard value of 1.3k. RB2 is therefore a chosen RB1 5% standard value divided by 1.222 (1.1k, a standard value).

We are missing some knowledge, which we must learn, before we can finish and build this emitter follower amplifier circuit. Wait just a bit!

5.7 Small-signal behavior (Subtle effects)

Our common-emitter gain equation says that.

Why can't we use RE = 0, making the gain infinite? Or, at least as high as the maximum hFE datasheet specification? If we had a transistor with hFE of several thousand, and we have built a common-emitter amplifier circuit with it, and used RE = 0 we will see that circuit gain will not go over a few hundred. Something is missing from our understanding of BJTs.

rE

So far, we have relied on a BJT following the rules of:

IC = hFE*IB

IC = IE + IB

VBE = 0.6V

A detailed examination of transistor behavior, however, finds that VBE is not constant, and actually varies with IC.

Fig 5.24 For a Fairchild Semiconductor FJL4315

This looks exactly like a diode I-V plot.

Let us revisit a common-emitter amplifier circuit, with RE = 0.

Fig 5.25

Something is limiting the gain of this circuit!

Fig 5.26

That limit can be represented by an emitter resistance rE. A lowercase r here means “resistance derived from AC signal analysis, not DC”. The resistance is just another model of BJT operation, and it is not a real built-in “resistor”. This “resistance” can be seen from the non-vertical slope of the Fig 5.24 plot.

From the slope of the VBE-IC plot, we can approximate that emitter “resistance” as

Ω. Note that IC must be given in mA for this equation.

We can see that rE varies with collector current.

An equation which relates VBE to IC is called the Ebers-Moll equation. A somewhat simplified form of that equation is:

(VT = 25mV at room temperature)

IS is a device and temperature-dependent value. The relationship is therefore exponential, as we can see ourselves from the plot. We will examine this equation for qualitative analysis only.

Before, we have looked at a BJT as a current-controlled current source. We will now look at a BJT as a VBE voltage-controlled current source. The previous model is not wrong, it is just not fine-detailed.

We can extract two rules of thumb from this equation. 1) For a 18mV ΔVBE, IC doubles. 2) For 60mV ΔVBE, IC goes up 10 times.

Since we are looking at subtle effects, we must keep in mind that IC changes VBE just as much as VBE changes IC.

This rE impacts all of BJT circuits we have looked at so far.

Emitter follower:

Fig 5.27

Common emitter:

Fig 5.28

Where the gain is limited by .

A common-emitter circuit with RE = 0 has many more problems besides having limited gain.

Fig 5.29

That rE varies with IC, varying the gain along! Here's a table which clearly illustrates the effect shown in Fig 5.29:

VC

IC

rE

gain

1V

11mA

2.3Ω

-440

½ VCC Q-point

6mA

4.2Ω

-240

11V

1mA

25Ω

-40

That's a huge gain variation! The gain is different for every point of an input waveform – distortion is huge!

Emitter resistor RE

If we use an emitter resistance of a value which is many times that of rE resistance, we can make rE variations have little effect:

Fig 5.30

Our new gain equation is , and our new table results are:

VC

IC

rE+RE, Ω

gain

1V

11mA

2.3+180

-5.49

½ VCC Q-point

6mA

4.2+180

-5.43

11V

1mA

25+180

-4.88

We gave up worthless high gain for stable low gain. We have received little distortion in reward. Notice also that we have made the circuit insensitive to hFE transistor specification – while one transistor may have enough gain to produce the high gain of 440 in the previous table, a another device of the same part number might not. In this case, any MPS3904 is guaranteed to have hFE many times the required 5.49. We can therefore build this circuit in a manufacturing environment, and expect every single of our circuits to have the same gain of 5.49 (more or less due to resistor value spread).

Here we see an example of hFE stabilization. We will see in a bit that the emitter resistor stabilizes the circuit in more ways than one.

Temperature effects

Collector current IC changes exponentially with temperature (and VBE therefore changes as well!). In an emitter follower circuit with RE = 0, it is possible to increase collector current from a quiescent point into saturation just by warming the transistor with the fingers.

At constant VBE, IC grows by about 9%/°C. Per one degree Celsius! If our ICQ is ½ of maximum (saturation) current, then a 10 degree temperature rise will double the current, therefore saturating (turning completely ON) the BJT.

Voltage offset VE due to RE is a temperature stabilization feature. As collector current increases with increasing temperature, voltage drop VE across RE increases as well. Since the VB point of base voltage divider does not change its voltage with increasing temperature, if voltage RE increases then the differential voltage VBE decreases, decreasing collector current, and canceling most of its increase due to the temperature. As a rule of thumb, voltage offset VE should be about 1V at Q-point, which allows us to calculate RE at a chosen quiescent IC.

This is called negative feedback, and is a trick which is universally used in electronics, even more with devices we will study in the next chapter (operational amplifiers).

The reader can now see that the hFE parameter is unpredictable, and varies with temperature and other factors.

Emitter capacitor CE

As a reward for the study, I will introduce the reader to a nice trick – how to increase gain of a common emitter circuit.

Fig 5.31

The circuit looks the same as the common-emitter circuit we have already covered, except for the capacitor CE. What does it do?

If you have studied capacitors behaving at AC, you would know that capacitor "resistance" depends on the frequency of AC current passing thru the capacitor.

A capacitor does not allow DC to flow thru itself, but it will "pass" changing current. At DC Q-point, the capacitor does nothing. An AC signal of high enough frequency, however, sees a path of 0Ω. For signal frequencies there is a path to COM thru CE, bypassing resistor RE. For signals, resistor RE therefore does not exist.

Remember the equation? RE is now 0Ω for signal frequencies. We are only left with rE, so that our new equation is , allowing for high gain, higher than the disappointingly low gain we have calculated for our previous common-emitter amplifier circuit!

CE resistance at AC frequency (to be more proper, reactance) must be significantly less than rE resistance for our new gain equation to be correct.

Actually, we have the surprising problem of having too much gain, which is either more than the worst transistors we will encounter (of the same part number), or is more gain that is needed.

We actually need to limit the gain, and we can use either of the two methods:

Fig 5.32

In the first case, RE1+RE2 is equal to the old RE value. However, the resistance RE1 is unbypassed, and is used in the gain equation.

On the right side, we have a resistor in series with the capacitor. RE4 is equal to the old RE value. In this case, RE3 resistor can be either a fixed value, or a trimpot, allowing resistance to be adjusted as needed.

Early effect

Remember the effect we noticed when we looked at the BJT I-V plot?

Fig 5.33

The fact that those plots are not horizontal? The fact that collector current IC depends on VCE, making the BJT a poor controlled current source. What we see is somewhat like a resistance of high value connected from collector to emitter.

Fig 5.34 Early BJT model

The new symbol, a small circle with an arrow inside, is a constant current source, in this case controlled by either IB (Rough large-signal model) or VBE (Ebers-Moll).

At an arbitrary point VBE, “Early Effect” causes a variation in IC – with increasing VCE, it decreases the value voltage drop VBE, increasing collector current. Remember that VBE sets the collector current. When that required VBE to set the same amount of current becomes a lesser value, then more collector current will flow if VBE was tied to a non-changing voltage point in the circuit (of the base voltage divider).

Compensating for Early effect is similar to compensating for temperature – an emitter resistor RE will oppose collector current increases, by lowering voltage drop VE value.

Transistor frequency response

Now, remember my threat that BJTs were hard to understand, and that a lot of knowledge was required to create practical circuits? This section was the “hard to understand” part! Look back: you now have the knowledge to grasp the operation of many different semiconductor devices. Congratulations on making it this far! From now on, I will make the circuits easy and fun at the same time!

5.8 Practical common-emitter amplifier circuit

Now that we have a better picture of BJT operation, we can finish our common-emitter and emitter follower amplifier circuits.

Fig 5.35

For simplicity and to avoid repetition, we are going to reuse the same formulas and calculations as for our emitter follower circuit. We are not going to repeat base dividers and RE calculations here. Do keep in mind that RE for a common-emitter amplifier is only 1V, and base resistors must provide 1.6V. Since our MPS3904 common-emitter amplifier will not drive a low-resistance load, we are going to decrease quiescent current to 5mA.

Setting DC biasing:

Choose RC.

Choose RE. Ω

Choose the base divider. VB = VE + 0.6V. The parallel resistance RB1 || RB2 will be. The ratio of two resistances needs to be . At this current of 5mA, datasheet lists hFE of 80, . RB2 is therefore 10k (a 5% standard).

Circuit response to AC signal

Calculate rE. I have purposefully added a "phantom" rE resistor in the circuit, so that the reader always sees it as a mental image when looking at common-emitter circuits. I have also made it a variable resistor, since rE value depends on the current. At Q-point, its value is

Choose maximum circuit gain. Since we want this circuit to work with any device which might be lying in our drawer, we will set the maximum gain at 50, and we will leave an ability to lower that gain as needed, with the trimpot RG. This will make the circuit universal for the reader's needs!

We can solve for RG with a suitable calculator: RG=21Ω. So, we can either put in a fixed value resistor to set the gain, or use a trimpot, probably 1k value, to make the gain variable. Why 1k? Because if RG is set to 1k, then the capacitor is effectively not increasing the gain, the minimum value of which will be . At a low pot setting of 21 Ω, the gain will be increase to 50. Decreasing the resistance even further may increase gain, if the hFE is large enough, but distortion and device variability will be the tradeoff.

Choose CE. Resistance seen by the capacitor is rE+RG, therefore,

(with a little margin). Note: this is a physically large electrolytic capacitor! However, its voltage rating may be as little as (1.5 margin * Vinmax (of 6V)) = 9V.

Choosing Cin. We want this capacitor to block DC, but pass frequencies as low as 20Hz (for audio applications). Its value is calculated from the high-pass filter equation (not covered in this book). Resistance needed for that equation is AC input resistance, in our case:

Rin(AC) = RB1 || RB2 || (hFE*(rE+RG)) = 830Ω

Note that resistances rE and RG are also part of the equation, making input resistance the resistance of four resistors in parallel. As a rule of thumb, a capacitance 3x-5x the value calculated should be used, for safe margin. That gives us

μF (a 3x margin).

Choosing Co. Loads attached to this amplifier circuit must have resistances higher than 1.2k, the higher the better (less loading). However, the load attached might have a resistance as low as 1.2k, so we must use for our capacitance calculation. That gives us 47μF, 16V (with margin).

Power ratings for the components must also be calculated. Quiescent point is the point of largest power dissipation, since at points above and below Q-point either the voltage drop or the current is less. PDRE=1/4W. Two 1/4W resistors should be used in parallel for the emitter resistor, for 1/2W rating (and cooler operation). PDT is 0.25W. Tasks for the reader: to what temperature will transistor case climb with this much dissipated power? Will any datasheet parameters change due to this temperature? Will those parameter changes impact our transistor circuit operation?

Let us look at input and output resistances again. Rin== 830Ω. Rout = RC = 1.2k. We see that common-emitter circuit input resistance is less than output resistance, which is not a very desirable condition. Also, the circuit will operate OK as long as input source has an output resistance at least several times less than 800Ω, and as long as an attached load has a resistance several times that of 1.2k. If these conditions are not met, then circuit components will be “loaded”, and circuit operation and characteristics will change.

Building the circuit

Time to build this circuit! You can either use a breadboard or a proto-PCB. I recommend a small PCB, so that you can save the circuit, either for reuse or as a proof of your study. If you build the circuit on a breadboard, and you reuse capacitors taken off other boards, keep in mind that their leads have been clipped short. They are usually bent as well and won't reach deep breadboard contacts. Ensure that all components make electrical contact with breadboard connector strips. Before powering the circuit, inspect it for any wiring mistakes. Then, insert an ammeter in series with the power supply. Turn on the circuit for a moment and note the current. A large current will indicate a short, and something with the circuit being drastically wrong. Turn off the power supply. Now move the ammeter to collector resistor. Turn on the circuit and measure quiescent collector current. It should be close to what you have chosen, or calculated. If it is off by a lot, then there's a problem somewhere.

Perhaps the easiest input source for a hobbyist is the “line in/out” present in consumer electronics. Set a music player to low volume, and connect it to any speaker amplifier and note that it does not sound very loud. Now insert your circuit between the player at the same volume, and the speaker amplifier, and see if there is audible amplification of the volume!

5.9 Practical Emitter Follower Amplifier Circuit

Fig 5.36

Notice that we have made calculations for an emitter follower without using rE in our calculations. Since emitter follower RE resistance is a large value due to the large (quiescent) voltage drop, rE in comparison is usually insignificant. As a reminder, our old calculations have showed an RE of 171Ω, and RB1 = 1.368k, RB2 = 1.1k.

I will leave it as a task for the reader to redo all emitter follower calculations using RE = REold + rE, and see if there is a significant change in resistor values or circuit operation.

However, rE does play a role when input and output impedances have to be calculated. Its value at Q-point is

Zin = RB2 || RB1 || hFE*RE = 1.368k || 1.1k || (80*171) = 584Ω.

Zout

= 7.84Ω

where Ris is input source resistance. We would have to assume it can be as low as 600Ω. Zout in our case becomes 7.84Ω, but notice that it will change with changing emitter current. We have discovered something interesting: this output impedance is less than the impedance of headphones (32Ω). We have therefore designed a circuit which can act as one of the channels of a stereo headphone amplifier circuit!

Choosing Cin. Resistance needed for that equation is RB1 || RB2 || (hFE*RE || RL) = 7.5Ω. Note that load resistance RL is also part of the equation, making input resistance the resistance of four resistors in parallel. Since we don't know the load resistance for our example, we can use 8Ω as the worst load resistance. The equation is

That gives us Cin=1054μF. This is a very big capacitance, especially as a capacitor size. It is up to the reader to decide whether to restrict the circuit to a minimum load resistance of, say, 32Ω, and recalculate capacitance for that, or whether to keep the large capacitance, and make the circuit universal down to RL = 8Ω.

Choosing Co. Loads attached to this amplifier circuit must have resistances higher than 7.8Ω, the higher the better (less loading). However, the load attached might have a resistance as low as 8Ω, so we must use

for our capacitance calculation. That gives us 2000μF. This is a very big capacitance, especially as a capacitor size. It is up to the reader to decide whether to restrict the circuit to a minimum load resistance of, say, 32Ω, and recalculate capacitance for that, or whether to keep the large capacitance, and make the circuit universal down to RL = 8Ω.

Power ratings for the components must also be calculated. Quiescent point is the point of largest power dissipation, since at points above and below Q-point either the voltage drop or the current is less. Emitter resistor PDRE=1/4W. Two 1/4W resistors should be used in parallel for the emitter resistor, for 1/2W rating (and cooler operation). Transistor case PDT is 0.25W. Tasks for the reader: to what temperature will transistor case climb with this much dissipated power? Will any datasheet parameters change due to this temperature? Will those parameter changes impact our transistor circuit operation?

Notice that the input resistance of this circuit is 75x the output resistance. This is the beneficial aspect of an emitter follower circuit. The input resistance of a common-emitter circuit is the opposite, lower, than output resistance. For this beneficial relatively high input resistance, the tradeoff is a voltage gain of less than 1. An emitter-follower amplifier does have current gain, however. This is why emitter follower circuits are used either on the input of a multi-stage circuit, for high input resistance, or at the very output, where it is driven by a common-emitter circuit which produces the necessary base voltage drive.

5.10 BJT as a switch revisited – five warnings

1. With all this talk of the effect of temperature on BJT behavior, we have forgotten to explore whether it applies to switch circuits as well. It does, and very much so.

The reason we have built a BJT switch circuit without having a complete picture of temperature and rE effects is the fact that the BJT switch is ideally only operated at two points: cut-off and saturation, and a large current is applied thru the base to ensure saturation with a big load.

However, increasing temperature will affect a switch circuit as well. Increasing temperature will increase hFE. Leakage current ICBO will increase. This will seem to make the transistor “easier to turn on” at a high temperature, since less base current will be needed to have a specific amount of collector current to flow.

A bigger problem comes when the transistor needs to be turned off. Reducing base current to a small, but non-zero value into a warm transistor will fail to completely cease the collector current. As the transistor does not turn completely off, it will continue to conduct some collector current. The resulting VCE voltage drop will warm up, or keep warming up, the transistor.

Effectively, base current must cease completely for a warm transistor to turn off, because there is a huge decrease in required base current at higher temperatures.

The problem is due more to the simplistic design of pass-transistor circuits than it is to the behavior of the BJT. A more proper design of pass-transistor circuits will either use adequate heatsinking to prevent the transistor from ever greatly increasing its case temperature, or use of temperature-dependent circuit components to compensate for the temperature increase.

While low-power and simple pass/switch circuits are often made with BJTs, I do not recommend BJTs for high-power pass/switch applications.

2. If load current increases beyond IB*hFE, a saturated transistor will get out of saturation, VCE will increase, and heat dissipation will rise. This is why over-driving of a switch transistor is always implemented.

3. VBE has a low voltage limit, and it is easy to exceed. So does the maximum base current IB. Question: since a diode or the base-emitter junction will only have a forward voltage drop of 0.7V, then how can a typical VBEmax of 5V be exceeded? Answer: connecting the base to a constant-voltage source of a high supply current capability, or transient voltage spikes on the base terminal can easily exceed base voltage and/or current maximum ratings.

4. Constant-voltage base drive must never be used, but it crops up in unexpected places. Let me illustrate with my own experience:

Fig. 5.37

Pay no attention to the elephant in the room: that the emitter arrow points towards the base. We will find out what that means in the next section. The purpose of this circuit is to sense current across a low-resistance “shunt” (look it up) resistor (0.03Ω), and to turn on the relay CR1 if the current exceeds a certain value, disconnecting supply to the output thru the NC (normally closed) relay contacts, and latching itself into this condition until the reset switch X is pressed.

Task for the reader: think about how this circuit operates. I'll provide my own explanation in the next section.

5.11 PNP BJTs and NPN-PNP stages

Fig 5.38

There is an opposite polarity of a BJT available: a PNP BJT, where an emitter-base arrow (pointing to the base) indicates proper PNP current flow direction. All voltage polarities are are reversed compared to the NPN we have studied so far. For example, emitter is kept more positive than collector. A long time ago, circuit COM connected to the “+” of the power supply were more widespread than the other way around, but now a “negative voltage” COM is the standard.

By “opposite polarity”, we just mean that in a standard-COM circuit, a PNP will usually be “upside down”, with emitter on top and collector on the bottom. In order to apply analysis techniques we have already covered to a PNP, all that is needed is to flip the circuit, and analyze it as a normal NPN circuit.

In general, PNP transistors perform a little worse than NPN transistors, and less of them are sold, leading to lesser purchasing choices.

The most important applications of PNPs are NPN-PNP circuit combinations and “complementary” operation. “Complementary” means that the two transistor types are matched in their parameters as closely as possible, so that the output of each mirrors the other. Datasheets often list suggested “complementary” device part number. I have also compiled a list of them for RadioShack devices at my website. There are also “transistor arrays” sold, which have two or more transistors in one package or IC. Matching between the two types of devices in that case is excellent, compared to separate devices combinations.

Analysis of improper overload switch circuit

We can now return to Fig 5.37 and analyze how the circuit works and why it was not properly designed.

Fig. 5.39

What we see is a shunt resistance of 0.03Ω. What we mean by “shunt” is something which allows current flow thru itself, minus a very tiny portion which is just enough for a measurement or a control purpose. Your DMM 10A range current measurement works the same way, for example.

The purpose of this circuit is to activate the relay if current thru the shunt increases above a certain value, and to disconnect the input from the output using the relay contacts. To turn ON, the transistor at the very least requires a VBE voltage of 0.65V. Should the current thru the shunt increase to 20A, a voltage drop of 0.6V will develop across the shunt. Notice that emitter voltage is more positive (differentially) than base voltage, which is a proper setup for a PNP transistor. However, this circuit has a critical flaw.

I have built this circuit in my high school years, and had it work most of the time. What I saw on frequent occasions was that the circuit would activate, but would not release after the reset button was pressed. After further troubleshooting, I have discovered that I was destroying transistors.

Using the head on my shoulders, I found out the cause of the problem. The circuit designer's assumption was that during a short circuit, a current of 20A will flow, which will activate the circuit. This is not true. There is a huge capacitor sitting inside a power supply feeding this circuit. During a short circuit condition, before the transistor was fast enough to respond, a current not of 20A was flowing, but one of many times that! For example, if a current of 100A for a very brief time flowed when the capacitor was discharged by a short circuit condition, then the voltage across the shunt will be 3V.

Notice that two BJT drive conditions are being violated. First one is the fact that the BJT is being driven by a voltage level, not a limited base current. Second condition is the excessive amount of voltage across B-E junction. Either of the two effects can destroy the B-E junction of the transistors.

I have then placed a Zener diode to limit voltage to less than the 5V VBE limit. Failures stopped. This tells me that very large currents, well above 100A, were flowing as the capacitor discharged, as they were high enough to exceed 5V VBE limit for the BJT I used.

As an alternative, two fast diodes in series to limit VBE to 1.2V can be also used to protect this circuit. Inserting a resistor in series with the base to limit base current will also ensure that BJT operating conditions were not being violated.

Nevertheless, I have seen this circuit used (shunt connected to a BJT VBE junction) in many, many places. Those circuit designers do not have practical experience with failure modes of this circuit, like I did by actually building and using it.

Darlington configuration

A Darlington transistor will be the first device combination we will explore.

Connected like this, the overall hFE is the gain of Q1 times the gain of Q2. Current gain of several thousand is typical for a Darlington device. RadioShack sells a TIP120. The reader should explore its datasheet.

Fig 5.39

Darlington transistors make switching circuits easier – required base current is no longer as large as for a discrete BJT. They can also be used in a circuit which must present a very high input resistance.

Darlington transistors do have disadvantages, however:

Overall VBE is the sum of the two transistors (1.3V typical)

Increased saturation voltage, equal to saturation of one transistor plus VBE of the other. (1.2V typical)

Slow switching speed (10kHz limit is typical)

High leakage (ICBO=0.5mA typical)

If the load can tolerate the high saturation voltage, then Darlington transistors are recommended where digital logic or a microcontroller drives large loads.

Push-pull complementary

Now we will take care of the very poor quiescent-point circuit energy efficiency and very poor output power.

Fig 5.40

What we have in Fig 5.40 are two types of a transistor, both connected as emitter followers (make sure you see this!). When a sine wave input is applied, positive voltages control Q1, while Q2 remains off. Negative input voltages control Q2. No current flows with Vin = 0V. Transistors are only open when energy must be supplied to the load. This circuit is very energy efficient, has a very low output resistance, and can be very powerful. Note that two power supply rails are used in this circuit. There is also no output capacitor, since there is no DC current flow to block. This amplifier therefore has no low frequency limit imposed by a blocking capacitor.

We will later build an amplifier like that. For now, I will only note that there are many ways to build circuits utilizing both NPN and PNP transistor types. We will just see if we catch a circuit like that, instead of trying to predict all the possible ways to interconnect the two transistor types.

5.12 Multiple stages

We have so far covered a number of standalone transistor amplifier circuits. As the reader has seen, each has its advantages and limitations. But it's easy to predict that the different types of circuits can be interconnected together to build a more usable circuit. Let's review the different types of amplifier stages we have covered so far:

Input resistance

Output resistance

Gain

Polarity

Advantages

Disadvantages

Common emitter

Low

High

High

Inverts

Gain

High output resistance

Emitter follower

High

Low

GV=1

Non-inverting

Low output resistance, high power

No voltage gain

JFET common source

Very high

High

Low

Inverts

Very high input resistance, low noise

Low voltage gain

Fig 5.41

How do we build a circuit which, for example, amplifies a microphone input to an audio speaker output level? A typical input from a microphone is 1mV, and its output resistance is high. A speaker might perhaps require 10W into 4Ω, which equals 6.3Vrms (9V peak-to-peak) at 1.6Arms. That would mean a requirement of a high input resistance, very low output resistance, a voltage gain of more than 6 thousand (due to volume control), and significant current gain.

Schematically,

Fig 5.42

Which just represents our requirements for a volume control, a voltage amplifier (V), and a power amplifier (P).

When several amplifying stages are interconnected together, their individual gains are multiplied to arrive at the overall gain. For example, two common-emitter amplifiers each with a voltage gain of 50 have a total gain of 2500. We just need to add a high-input-resistance circuit (since common emitter amplifiers have poor input resistances), and a high-power output circuit (since common emitter amplifiers have high output resistance and low current capability).

We also see blocking capacitors between the stages. We don't want biasing conditions of one stage to impact the other stage! Something to watch out with multiple blocking capacitors is their f3dB filtering property. The reader should look up capacitor impedance and AC behavior, as well as “bode plots”. Here, I will only mention that those blocking capacitors should each have very low f3dB frequency. Otherwise, overall circuit gain at low frequencies will be very low. For an audio circuit, for example, with a range of input frequencies of 20Hz-20kHz (audible range), f3dB frequency for each capacitor should be set to 10Hz, and capacitance result of the calculation multiplied 3x...5x for a good margin of safety.

Power Supply Filtering (decoupling) capacitors

Fig 5.43

Let's see what happens if a circuit has several amplifier circuits working at the same time. Amplifier B has an output resistor RO2, which sees a changing current, and which therefore produces a changing voltage drop across itself. However, that changing current is seen by every other device attached to that output resistor. Amplifier A has an input resistor RI1 connected to VCC. It also sees a “signal” on VCC line. If this circuit was fed from a powerful power supply, that power supply will try to deliver more current when the circuit requests it, to prevent voltage drops or sags on the VCC line. Those voltage drops, after all, is what carries the noise. However, if this was a battery-powered circuit, then a battery cell has a limited ability to respond to load current changes. What would happen is that each amplifier would introduce noise to the other one's input.

However, if capacitors C1 and C2 are installed, then the current fluctuations take a different path. The current sees a path of least resistance thru the capacitors, and takes it. These capacitors are therefore filtering capacitors.

Notice that two capacitors are used, one polarized, one not. Why? Because they have slightly different roles. The polarized capacitor is usually an electrolytic, a type which is easily obtained with high capacitance in a small package. This capacitor also does a double duty as “energy storage”. If the circuit required a sudden burst of current to the load, then the capacitor will supply the energy. The battery cell has an undesirable “internal resistance”, which would create a large sagging of battery voltage output when a lot of current is requested. The energy storage electrolytic is usually selected to have a low ESR – equivalent series resistance – which means that it can supply a large amount of current on short notice.

Capacitor C2 is a much smaller capacitance, usually around 0.1μF, and is usually a ceramic. The second task of this capacitor is to catch high frequency part of the noise. Remember the “path of least resistance” adage. For high frequency current, the large electrolytic is not a path of least resistance. That path is thru the small capacitance, which at high frequencies is an effective short to COM (for noise).

For simple circuits, two capacitors are sufficient. For large circuits, integrated circuits, and digital logic, the pair of such components must be placed next to each chip, as closely as physically possible on the PCB.

5.13 Class-AB power amplifier

Large-signal amplifiers

Class AB operation

We have already seen a method to use two output transistors to create an energy efficient and powerful amplifier:

Fig 5.44

This arrangement is known as "push-pull". It is also called a "complementary class-B amplifier"

Class-B

Class-B refers to the transistor mode of operation. Class-A amplifiers conduct throughout input signal positive and negative polarities (full cycle of the sine wave, 360°). Class-B gets rid of the quiescent point idea, and only has the transistor conducting with one polarity of the input signal (half the sine wave cycle, 180°).

Class B distortion

There is a big problem with the shown arrangement, operating in class-B. Between input voltages of ±VBE = 0.65V, neither of the two transistors is responding to input. The resulting distortion looks like

Fig 5.45 Step distortion

The way to solve this distortion is to have the base of each transistor sit at 0.65V with no input signal, and for both transistors to conduct a little current, so that they can respond to the smallest input signal amplitude. This takes us back to class-A ideas of quiescent points and quiescent power dissipation. We therefore operate somewhere between-class A and class-B, and we call this "class-AB" operation.

We now need to find out how to properly bias and stabilize this arrangement. For temperature stabilization, we will reuse the tried-and-true emitter resistor, and we will use one for each of the transistors.

Push-pull class-AB biasing

Fig 5.45

One trick commonly used to bias this configuration is shown here.

Notice the three diodes, which, when current-limited in a forward bias direction by RB1 and RB2, develop a voltage of 0.65V*3 across the three diodes. Resistors RB1 and RB2 provide enough current to both make the diodes start conducting in the forward direction, and also to supply some bias current for the transistors to establish some quiescent emitter current in each of the transistors.

Notice also that this simple network simultaneously provides two proper biasing voltages for the two transistors, negative for one and positive for the other (in relation to each other and to the centered COM).

Since those diodes are already conducting at some current, the reader must not think that the input voltage level will be affected by the diodes. That input source will be able to wiggle (change) the current thru the diodes, but its voltage will not be “reduced” by the “diode forward voltage”.

What is the purpose of the third diode? It turns the transistors on and establishes quiescent voltage flow thru the emitter resistors. Note that the emitter voltage drop in this case is very low – ½ the single diode forward voltage drop, for each of the emitter resistances. That means a low emitter resistance, low temperature stabilization and low quiescent current flow (at currents of powerful class-AB amplifiers, 0.3V at a large current is a lot of quiescent power wasted in emitter resistances). In return, we get low RE resistances and good energy efficiency.

Improvements on the class-AB complementary push-pull amplifier

A lot of improvements can be made to the circuit:

1. As the output stage transistors get hot, their VBE changes. If biasing diodes are not in good thermal contact with the transistors, their VF change does not track transistor changes due to temperature. This leads to poor temperature stability. A possible solution is to mount those diodes at the same heatsink on which transistors are mounted to. However, such an amplifier is only somewhat temperature stable. Another solution would be diodes integrated into the same package as the transistors. The only transistors with internal diodes that I am aware of are ON Semiconductor NJL4281D / NJL4302D. Negative feedback can be used to get rid of the remaining distortion and non-linearity.

2. The third temperature-stabilization diode can be replaced with an adjustable resistor or a transistor-based current source.

3. Like I have mentioned before, there are no exact PNP equivalents of NPN transistors. Parameters of PNP transistors are somewhat worse. There are methods to only use NPN transistors for the output transistors, for example:

Fig 5.46

4. BTL (Bridge-tied load). As shown, the circuit requires two voltage rails. At any point of the input signals, only one of the power rails is being used to supply power to the load.

For example, if the reader does the calculation, it will not be clear how car audio system amplifier can produce the claimed 120W of power at a single voltage supply of 12V. (Task for the reader: do a calculation for power rails voltage needed at Prms=120W, Rspeaker=8Ω).

The solution is a bridge-tied-load configuration;

Fig 5.47

Only one voltage rail is needed. Also, a bridge-tied-load configuration, similar to an H-bridge, effectively “doubles” the power supply voltage. Notice that a controller is needed for a circuit like this to prevent undesirable bridge conduction conditions such as shoot-through.

Regarding the task given to the reader: Required voltages would be ±?. The conundrum is solved by using a BTL configuration, low speaker impedances (4 Ω and less), and using four or more amplifiers for as many speakers. At even higher power of professional car audio amplifiers, those amplifiers use on-board DC-DC step-up voltage conversion.

5. Negative feedback, which will reduce distortion and non-linearity even further.

If the reader wishes to build a class-AB push-pull amplifier, complete with a dedicated power supply, I have a complete write-up with additional information and explanations on the website for this book.

5.14 Additional notes and further reading

Common-base circuit. A BJT is a three-terminal device, and it can be connected in three different ways by having one of the terminals common to both input and output. The connection we have left out is the common-base configuration. It is only used in RF (radio-frequency) applications.

ESD. A BJT is not as sensitive to ESD as a MOSFET gate is, but care should be taken to limit ESD at all times when working with electronics.

Phototransistor. A phototransistor is a light-sensitive device, much like a photodiode. It is usually a two-terminal device, with no base terminal. A light source controls the transistor collector instead of the base terminal of a regular BJT. The resulting collector current, due to hFE multiplication, is many times larger that of a photodiode, therefore a phototransistor is very easy to use in a circuit.. Compared to a photodiode, the device is more sensitive and can control more current (compared to tiny leakage light-controlled current of a photodiode). Practical note: it is hard to tell apart a photodiode from a phototransistor from its looks. Do not mix them! Phototransistor analysis should be simple for the reader with everything we have already learned. Just look at a phototransistor I-V plot from its datasheet.

Unfortunately, I cannot recommend RadioShack IR phototransistor and photo-detector devices (276-142, 276-145, 276-640). These devices have no datasheets and no exhaustive specifications. Worse, there are reports from online feedback which say that photodiodes are placed into some packages instead of photo-transistors.

I recommend for a novice reader to either choose a transistor from an online parts distributor such as Digi-Key, or use a “logic output” photodiode module, which are many times easier to use.

DC negative feedback

Fig 5.48

The reader may encounter a circuit like this, with base bias resistor connected to collector instead of VCC. This is a form of DC negative feedback. This configuration has less gain, but a somewhat worse performance. The reader can read about this further, elsewhere.

IC (integrated circuit) BJT schematics. A novice electronics designer would not gain anything by trying to look at IC schematics. IC circuits have the following requirements, which usually do not apply to discrete (made from separate electronic components) circuits:

An IC must operate over a wide range of supply voltages and temperatures.

It is not possible to create a capacitor inside an IC. Therefore, IC circuits cannot use internal DC blocking capacitors. Circuits are built which can use direct DC coupling between the stages.

It is relatively hard to make a humble resistor inside an IC. An IC resistor equivalent is usually a MOSFET operating in ohmic mode. IC circuits therefore are designed to use as few resistors as possible.

There is little difference in cost for an IC to use 10 or 30 transistors inside. Therefore, what to a discrete circuit designer looks like a mind-numbing complex circuit is actually simple stuff for an IC designer.

Discrete electronic circuits, on the other hand, are designed to use as many resistors as possible. Looking at a populated PCB, we see that resistors outnumber other components 5+ to one.

Fig 5.49

It is also easy to see esoteric BJT drawings such as a line thru the base or multiple emitters;

The drawing on the left is just a connection between the two bases. The drawing on the right is a BJT which actually has several emitters. Things such as these are a piece of cake in IC realm.

Variable power supply voltage. In this chapter, we have assumed that our power supply was a stable and reliable voltage level and had a large current supply ability. But how are battery-operated circuits made? How can ICs specify a very large power supply operating range?

In case of ICs, in addition to what has been discussed in the previous section, current sinks, sources, and mirrors are used to keep biasing conditions stable with arbitrary power supply voltage levels.

Variable power supply voltage affects BJT bias and operation conditions. A proper solution is, just like with ICs, current mirrors and current sources use in biasing. A cheap solution is a high enough voltage so that battery voltage drop (as it discharges and loses its energy) is little compared to circuit limits such as VBE, VE, VQ, etc. Say hello to the 9V battery! A while ago, it actually was called a “transistor battery”. This battery is actually the most expensive, the least powerful, and the shortest lasting battery-based source of power. Inside, a 9V battery is actually a stack of what looks like watch “cell” type batteries, stacked six high. The battery is considered dead at 7.2V (1.2V is dead for any non-rechargeable battery cell), which is a manageable voltage drop (from 9V) for a circuit. The battery can supply little current. More involved analysis of transistor circuits over a changing power supply voltage and low-power battery-based design is outside the scope of this book.

Working with an unknown BJT

1. Find device part number. This has been covered in chapter 1.

2. Identify type of transistor. If you are working with an unknown component, it may be something other than a BJT. Identification is done either by locating the part number and the datasheet, or by exploratory testing with a DMM.

3. Identify leads and test a BJT with DMM.

For testing purposes, a BJT can be represented by:

Fig 5.50

Don't think that a BJT is made of two discrete diodes!

There are three terminals, and two DMM leads. There are six ways to connect those DMM leads to the transistor. A digital multimeter with a diode check function, and a grounded ESD strap must be used to test a BJT. The collector-emitter connection should show an “open” in diode check mode, or high resistance in resistance check mode, in both ways. It is easy to find out which of the leads is the base. It's a little harder, but possible, to identify a collector from an emitter. Use resistance check function. Compare the forward bias resistance of the “diodes”. The one with slightly lower resistance (or voltage drop) is the base-collector junction.

Identification of BJT leads is also possible with a DMM which has an hFE or a transistor check function. The connector usually looks like

Fig 5.51

The two emitters for each BJT type are connected to each other. This is done for testing convenience, so that BJT pins do not have to be bent in order to be able to insert a transistor in any lead configuration. It is easy to just stick a BJT into the connections at random and see which connection shows a gain measurement on the display.

4. Find gain. The easiest way to find gain is with a DMM as outlined before. Finding gain is useful for pass/reject testing of new devices for a circuit, or for verifying gain and operation of old or reused transistors.

Further reading. A BJT can fundamentally do three things: amplify, switch, or oscillate. We will cover oscillation a bit, later, but the reader should read about it at length, elsewhere.

We are limited in this book by not having spent time with mathematical circuit analysis. The job of covering circuit analysis is done very well by other textbooks; it is intuitive and clear explanation of semiconductors that they are not very good at.

I highly recommend for the reader to pick up a used college textbook on the subject. Many are available, such as “Basic Engineering Circuit Analysis” by J. David Irwin. There is absolutely no need to buy the expensive hard-cover, latest edition. Used, previous editions, soft-cover, and “international” versions are always cheaper.

Alternately, the reader can take a course at a local community college.

The circuit analysis skills to learn are: Kirchhoff's Laws, Node and Loop analysis, Thevenin equivalent, and so on.

After that, one of the other textbooks, such as any recent edition of “Electronic Devices and Circuit Theory” by Robert L. Boylestad should be studied. If the reader is patient and shows commitment, then such involved concepts as the list below can be understood:

Oscillators

Small-signal modeling, small-signal BJT equivalent circuit and analysis

Fast switching

RF circuits

Frequency response

Bode plot