After the initial bend, the curves approximate a straight line. The slope or gradient of each line represents the output impedance, for a particular input base current. So what has all this got to do with biasing ? Take, for example the middle curve. The collector emitter voltage is displayed up to 20 volts. Let's assume that we have a single stage amplifier, working in common emitter mode, and the supply voltage is 10 volts. The output terminal is the collector, the input is the base, where do you set the bias conditions? The answer is anywhere on the flat part of the graph. However, imagine the bias is set so that the collector voltage is 2 volts. What happens if the output signal is 4 volts peak to peak ? Depending on whether the transistor used is a PNP or NPN, then one half cycle will be amplified cleanly, the other cycle will approach the limits of the power supply and will "clip". This is shown below :
The above diagram shows a 4 volt peak to peak waveform with clipping on the positive half cycle. This is caused by setting the bias at a value other than half the supply voltage.
The lower diagram shows the same amplifier, but here the bias is set so that collector voltage is half the value of the supply voltage. Hence, it is a good idea to set the bias for a single stage amplifier to half the supply voltage, as this allows maximum output voltage swing in both directions of an output waveform.
Input
Characteristic Curves
Before describing
the bias circuits, it is worthwhile looking at a typical input characteristic
curve for a small signal BJT. The following is the input characteristic
for a transistor in common emitter mode, it is a plot of input base
emitter voltage verses base current. It is shown with both x and y axis
slightly zoomed.
The base emitter voltage, Vbe is quoted in most text books as either 0.6 V or 0.7 V Both values are an approximation, and as can be seen from the above graph the value of Vbe varies between this range. For small signal work with base currents of 50uA or below a value for Vbe of 0.6 volts is a reasonable quote. For higher base currents, a Vbe of 0.7 V is a better approximation. In fact, in a large power transistor, the Vbe value can be even higher. The value of Vbe also varies widely with temperature change.
Simple
Bias Circuit
The simplest bias
circuit is shown below. It consists only of a fixed bias resistor and load
resistor. The BJT is operating in common emitter mode. The dc current gain
or beta, hFE is the ratio of dc collector current divided by
dc base current. The BJT is a BC107A. The values of Rb and Rc can be determined
by either mathematical approach or by using the output characteristic
curves for the BC107A.
Quiescent
Point (Q-Point)
The point Vo in
the diagram above is where the output signal would be taken. For simplicity,
the input signal and coupling capacitors have been omitted. For minimum
distortion and clipping it is desirable to bias this point to half the
supply voltage, 10 volts dc in this case. This is also known as the quiescent
point. The ac output signal would then be superimposed on the dc bias voltage.
The Q-point is sometimes indicated on the output characteristics curves
for a transistor amplifier. The quiescent point also refers to the dc conditions
(bias conditions) of a circuit without an input signal.
Q-Point
Value
I have mentioned
that setting the Q-point to half the supply voltage is a good idea. It
gives a circuit the highest margin for overload. However, any amplifier
will clip if the input amplitude exceeds the limit for which the circuit
was designed. However, there are certain cases when it is not necessary
to bias a stage to half the supply voltage. Examples would be an RF amplifier
design where the input signal is in microvolts or millivolts. If the stage
had a gain of 200 then the output (assuming a 2mV peak input) would only
need to swing up and down 400mV about the Q-point. Hence a stage with a
supply voltage of 12 volts could have its Q-point set at 10 volts or even
2 volts without problems. Another example would be a microphone stage where
similar low level input signals are involved.
Output Characteristic Curve for a BC107A
Click
on the graph to zoom in (full screen display)
Bias Design:
The collector voltage
Vc for the simple bias design is 10 volt. The dc current gain, hFE
for the BC107A is obtained from the manufacturers data sheets and varies
between devices. A typical beta is around 290. Taking a base current of
20uA and reading values direct from the output curves, the collector current,
for a collector emitter voltage of 10 volts is around 3.9mA. As hFE=
Ic / Ib then a BC107A must have a beta of at least 3.9mA / 20uA = 195 to
work with this circuit. Also , the base emitter voltage, Vbe is typically
0.6v. Knowing the above data and using ohm's law , values for Rb and Rc
can be determined:
Rb = Vcc - Vbe / Ib = (20-0.6) / 20u = 970k use (1M)
Rc = Vc / Ic = 10 / 3.9m = 2.56K use (2.7K)
Mathematical Approach:
Without using the
output characteristic curve, values for Rb and Rc can still be calculated.
A value for hFE must be estimated first and a desired collector
current. As hFE varies in each transistor the value chosen should
be the lowest value from the manufacturers data sheets. The equations to
use are:
Rc = Vc / Ic
Ib = Ic / hFE
Rb = Vcc - 0.6 / Ib.
Using the example above with Vcc=20 and hFE =195 yields the same values.
Temperature
Stability
The above circuit
is not good for the following reasons. It relies heavily on a transistor
with a current gain very close to 195. Other samples will give different
results. Variations in the supply voltage produce changes in the quiescent
values, and also a change in temperature will alter the current gain of
the transistor and hence quiescent point. For use as an amplifier this
could mean distortion of the output signal above a certain temperature.
The graph below displays the collector voltage and current for the
simple bias circuit over a temperature range of -50 to +50 degrees Celsius.
As can be seen both Vq and Iq will vary over a wide range. This is the reason that this circuit is seldom used. It is clear that a different circuit arrangement is needed which leads to :
Self
Stabilizing Bias
Coupling capacitors
omitted for clarity, the output is the transistor collector :
This is similar to the self bias circuit with one difference: the base resistor Rb is returned to the transistor collector instead of the supply voltage. The reason for this is simple; if the transistor used had a high current gain, then the collector voltage would fall. As Rb is connected to the collector then the base current would be reduced to counter the effect. If the transistor had a low value of beta, then the collector voltage would rise. This in turn provides more base current for the transistor to conduct harder and stabilize the q-point. The equations to calculate Rc and Rb follow:-
Rc = Vc / Ic
Rb = Vc - Vbe / Ib
as Ib = Ic / hFE then
Rb = (Vc -Vbe) * hFE / Ic
An Example:
A bias circuit is
required to bias a transistor to half the supply voltage. A BC107A transistor
with hfe of 200 is used and supply voltage, Vcc is 20 volts. The
collector current is to be 1mA. The resistor values are:
Rc = Vc / Ic = 10 / 1mA = 10K
Rb = (Vc-Vbe)*hFE / Ic = (10-0.6)*200 /1mA = 1880k a 1.8M resistor is fine here.
Temperature Stability
This method of biasing
is more resilient to changes of temperature as shown in the graph below.
It is unlikely that anything you make will be tested under this extreme
range of temperatures, but the results can be compared to the simple bias
circuit above.
Potential
Divider Bias
This is the most
widely used biasing scheme in general electronics. For a single stage amplifier
this circuit offers the best resilience against changes in temperature
and device characteristics. The disadvantage is that a couple of extra
resistors are required, but this is outweighed by the advantage of excellent
stability. The circuits below:
Here R1 and R2 form a potential divider, which will fix the base potential of the transistor. The current through this bias chain is usually set at 10 times greater than the base current required by the transistor. The base emitter voltage drop of the transistor is approximated as 0.6 volt. There will also be a voltage drop across the emitter resistor, Re, this is generally set to about 10% of the supply voltage. The inclusion of this resistor also helps to stabilize the bias: If the temperature increases, then extra collector current will flow. If Ic increases, then so will Ie as Ie= Ib + Ic. The extra current flow through Re increases the voltage drop across this resistor reducing the effective base emitter voltage and therefore stabilizing the collector current. The equations follow:
Rc = Vc / Ic
Ie = Ib + Ic as Ic >> Ib then Ie ~ Ic
Ve = 10% * Vcc
Re= Ve / Ie
Vb = Ve + 0.6
R2 = Vb / 10 * Ib
R1 = Vcc-Vb / 10 * Ib
An Example:
Using the values
of the previous examples a direct comparison of stability can be demonstrated.
The values are;
Vcc=20V, Vc=10V,
Ic = 1mA, transistor is BC107A with hFE=195
Rc= Vc /Ic = 10 / 1m = 10k
Ve = 10% * 20 = 2V
Re = Ve / Ie= 2 / 1= 2k
Vb = 2+ 0.6 = 2.6V
Ib = Ic / hFE = 1 / 195 =0.005128mA
R2 = Vb / 10* Ib = 2.6 / 0.05128 = 50.7k (use 47K)
R1 = Vcc-Vb / 10 * Ib = (20-2.6) / 0.05128 = 339.3k (use 330K)
Using these values and plotting the change in quiescent conditions for Vc and Ic over a temperature range of -50 to +50 celcius is displayed below:
