# The bipolar transistor

0.      Introduction

Over the years, many devices have been developed that can be used as amplifiers. Extensive miniaturization of electronic components, and the development of integrated circuits, has made discrete semiconductor devices less important, but they still play a significant role, especially in low-level measurements and power electronics, and some understanding of basic amplifier circuits seems appropriate. In this lab we will investigate what is still the most common discrete amplifying element, namely the bipolar transistor.

1.      The Ebers-Moll model

In low-frequency circuits, the Ebers-Moll model is often sufficient to describe the bipolar transistor.  This model gives a relation between the collector current, Ic, and the base-emitter voltage, Vbe. Furthermore, it assumes that the collector current is proportional to the base current with a proportionality “constant” b, Ic = bIb. The purpose of the exercises in this section is to determine Ic(Vbe) and b(Ic).

Figure 1 shows a circuit that can be used to determine Ic(Vbe) for collector currents in the range of 0.01 mA to 10 mA. Vbe can be varied between 0 and 1 V using a voltage divider (10 kW fixed resistor plus a 1 kW pot). In the same circuit you can also measure the base current Ib. If you have enough multimeters, you can do a simultaneous measurement of Ib and Ic. Plot Ic versus Vbe and compare with the prediction of the Ebers-Moll model. Also make a graph of b as a function of Ic. You should enter your data in a spreadsheet or graphing program while you are taking data, and immediately look at the graphs!

Notice that Ic is quite sensitive to temperature variations. (Warm the transistor slightly just by touching it.) At higher collector currents, power dissipated in the transistor causes an increase in temperature, which causes an increase in collector current, which heats up the transistor more, etc.  Initially, this will lead to a deviation from the expected behavior. For very large currents you will first burn your finger and than the transistor.  Figure 1.  A possible circuit to measure the relation between Vbe , Ib and Ic. You will have to add voltmeters and ammeters. Vdd stands for +12 V, Vcc for +5V. Note that the collector is directly connected to the power supply, so there is nothing that limits the collector current if you make a mistake in your set-up. It is a good idea to initially limit the current by putting a 200 resistor in the collector line. Also shown is the top view of the NPN transistor ZTX 692B, the object under investigation.

### 2. Transistor drivers

In the previous section you may have noticed that when Vbe exceeded approximately 0.5 Volts, considerable collector current would flow. At smaller values of Vbe there was negligible current. This 'switch-like' behavior of a transitor can be used to drive other elements of a circuit. For example, a typical computer interface, such as the printer port or the serial port cannot directly drive devices that require more than 5V or more than a few mA to operate. This means that to control practically all mechanical devices, motors, solenoid valves, relays etc. one needs an intermediate stage that takes the low-power signal from the computer as input and controls large output voltages and currents. In its simplest form, this can be a transistor with some current limiting resistors.  Figure 2 shows the basic diagram. A signal source can be connected to the base of the transistor. When the input is high, the transistor is driven open, and a significant collector current can flow, in this case through a resistor + LED. To start this experiment, set your function generator to pulse mode, set it up for a 1Hz square wave that alternates between zero and +1V, i.e., only goes positive. You should have the LED flashing once a second. Connect channel 2 of your oscilloscope directly to the output of the signal generator, and trigger on channel 2. (The sync/ext. trigger doesn’t work well for this experiment.) Observe the various signals in your circuit using channel 1. Sketch a timing diagram that includes the signal generator, Vbe, and Vc. Indicate on the timing diagram when the light is on and off. Figure 2. A simple transistor circuit to drive a LED.

Driving resistive loads, such as light bulbs, LEDs, heaters etc., usually does not introduce any complications. Just connect the load and that is it. The situation is more complicated when you try to drive inductive loads, such as solenoids in relays or valves, or motors of all kinds. From some introductory physics course, you may remember that for an inductor with self inductance L you have the relation U = -L dI/dt for the voltage across the inductor. When you switch off the current dI/dt is large and negative, and a large voltage is created across the inductor. To observe this, replace the LED in fig. 2 by a 10 mH inductor (and increase the frequency to 10 – 100 Hz). Again, look at the voltage at various points between the positive supply voltage and the collector. Note the sharp spikes when the current is switched off. On closer examination you will find that the spikes are in fact damped oscillations (decrease your timebase to see the oscillations).  Also note the large difference in switching behavior on switching the current on and off.

If you look carefully, you will observe that these oscillations are present even at the connection to the power supply line. In more elaborate circuits, this is a major problem. Switching in one part of the circuit couples via the supply lines to other parts. You can fix this problem very effectively by placing a capacitor between the supply line and ground close to that part of your circuit that causes the problem. This is called the “decoupling” of the supply lines. Figure 3. The transistor driver with protective diode and supply line decoupling capacitor.

The voltage induced across the inductive load will (Kirchhoff’s law) also appear across your transistor, and possibly other parts of your circuit. The induced voltages can be large and are potentially destructive. The most convenient way of eliminating them is to place a diode in parallel with the load. Figure 3 shows the “improved” circuit.

Because drivers of this kind are so useful, you can buy them pre-packaged. A typical example is the ULN2003. It contains 7 driver stages, each with some input circuitry to make interfacing with different sources easy, and with protection diodes connected to the collectors. To get familiar with this type of devices

a) Replace the driver in figure 3 by one of the stages of a ULN2003, and convince yourself that the switching spikes are adequately suppressed. Towards the end of the spec sheet for the ULN2003 there are examples of such circuits. Note that the inputs for these drivers require voltages between 1.5 and 2 Volts in order to be activated, i.e., turned 'on'.

b) Design and build a circuit that, using a ULN2003, flashes on and off two LEDs such that when one of the LEDs is off, the other is on. (Your signal generator still provides the low-power input signal that determines the rate at which the LEDs flash.)

### 3. A simple amplifier

On the basis of the results of section 1, you can now design a simple transistor amplifier stage.  First you have to decide what you want the amplifier to do, especially what the gain and bandwidth should be. Also important are the input and output impedance of the amplifier. Let us for the purpose of this exercise try to realize something with the following specifications:

Voltage Gain: 10

Bandwidth (3 dB): 100 Hz – 100kHz. Frequencies outside this range are attentuated.

Input impedance > 50 kW

Output impedance < 10 kW Fig. 4: A common emitter amplifier stage. Component values are determined by the user's design specifications.

Here are the steps one would follow to design the amplifier having the specs listed above.

·         The output impedance is approximately equal to Rc, so we take Rc = 10 kW.

·         The gain is approximately equal to Rc/Re, so Re = 1 kW.

·         To get a large dynamic range the voltage drop across Rc should be about ½ of the supply voltage, let us say 5 V.  The collector current is then 5V/10kW or 0.5 mA. This gives a voltage drop across Re of 0.5 V.

·         We now have to determine the appropriate values for R1 and R2. The base voltage is Vbe + 0.5 V = 1.1 V (You can improve upon this estimate using the results obtained in section 1.) So R1 has to be approximately 10xR2. The current in R1 and R2 should be at least 10 time the base current. We estimate the base current as Ic/b. With b > 500 this gives Ib < 1 mA, so reasonable values for R1 and R2 are 1 MW and 100 kW.

·         Let us check if we have met the requirement for the input impedance. The input impedance is equal to R1//R2//bRe. This turns out to be somewhat larger than 50 kW.

·         The last step in the design is to determine the appropriate values for C1 and C2. For C1 we want 2p ´100Hz´Rin´C1 > 1, and for C2: 2p ´100Hz´Rout´C2 > 1.

A)     Build this circuit and verify that it meets all specifications. You may find that it doesn’t meet the bandwidth spec. Check for distortion with a 100 kHz square wave.

B)      Add the capacitor Ce (1 mF) to increase the gain, and investigate what effect this has on the bandwidth, and the input and output impedances. Recall that input and output impedances can be determined by connecting a variable load resistor and adjusting the value until the voltage drops by 50%. For input impedances, connect the variable resistor in series with the input to the amp; for the output impedance connect the variable resistor in parallel with the output of the amp.

C)      To drastically lower the output impedance, add an emitter follower stage as shown in the Fig. 5. Again determine the specs of the amplifier. Figure. 5. A common emitter amplifier with emitter follower stage.