  24 February 2009
Author: Giorgos Lazaridis
BJT Transistor theory

The common emitter connection is a very commonly used connection, mainly due to the high voltage gain that can be achieved. Therefore, we will examine many different common emitter circuits.

Common Emitter with fixed bias

This is the simplest common emitter amplifier and this is the reason why this connection is important to know. We will discuss this connection again when we talk about the transistor as switching devices. In the meanwhile, it's good to know how to design a common emitter amplifier with fixed bias. This type can achieve the maximum voltage amplification possible. Here is the schematic: To design such a circuit, it is very important to know the precise hFE and hfe values (DC and AC current gains), otherwise the calculations will be wrong. This is not simple though, because even two similar transistors from the same batch of the same manufacturer might have different gain, plus this value is sensitive to temperature. So we expect to have some difference between the calculated and the measured values.

One good way to start the design is from the output impedance. The output impedance of the amplifier depends on the circuit impedance that will be connected after the Cout capacitor. If the transistor must provide high current (for a low impedance circuit), then the amplifier must also have low impedance, otherwise we prefer to have high impedance. The amplifier's output impedance is defined by the RC resistor. Therefore, we can begin by selecting an RC value. We can begin with the DC analysis of the DC equivalent: As we know, if no load is connected or if the load's resistance is high enough, we can safely select a VCE value VCE = VCC / 2. We will see later how to calculate VCE if load is connected. In the meanwhile, let's calculate the appropriate RC value to achieve the required VCE. We know that:

VCC = VRC + VCE => VRC = VCC - VCE
VRC = IC x RC => IC = VRC / RC

From the above equation we get an IC value. What we need to do now is set an appropriate IB value to achieve this IC:

IC = hFE x IB => IB = IC / hFE

The IB can be calculated with the ohm's law:

IB = VCC / RB => RB = VCC / IB

Now we can proceed with the AC analysis. As we saw before, we can calculate the internal emitter resistance by the emitter current (which is equal to the collector current):

r'e = 25mV / IC

And from the Î  model we can define the base input resistance:

Zin(base) = hfe x r'e

We proceed with the AC analysis by drawing the AC equivalent: RB is parallel to the Zin(base) of the transistor. So we can calculate the amplifier's input impedance by calculating the total resistance of RB // Zin(base):

Zin = (RB x Zin(base)) / (RB + Zin(base))

Now we can calculate the base AC voltage from the AC input voltage. Rg and Zin are connected as a voltage divider, so the base AC voltage is calculated like this:

uB = ACVp-p x Zin / (Rg + Zin)

Now we can calculate the AC base current:

iB = uB / Zin(base)

The AC collector current depends on the hfe value:

iC = hfe x iB

Finally, we calculate the AC voltage across RC:

uRc = iC x Rc

We have everything we need to determine the amplifier's characteristics. First, we can determine the voltage gain (Av):

Av = uRc / ACVp-p

We can also determine if the amplifier operates as a small signal amplifier. As we've already said, a small signal amplifier has ac peak to peak collector current at least 10 times smaller than the DC collector current. We have already calculated both currents, so we can compare them and determine if the amplifier is a small signal amplifier. This way we can determine if the output will have significant distortion or not.

This methodology may be rather stiff for a beginner, but it is also quite accurate. An experienced designer can calculate such an amplifier within a few minutes by heart.

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