Silicon and Germanium Transistor Biasing - Part 1
In transistor-based fuzz pedals, particularly vintage germanium-based units, proper operation and sound depends on transistor bias voltage. You may hear that some poor-sounding original units were “mis-biased” or biased poorly. Transistor bias refers to the DC voltage point that the transistor sits at. It is usually the collector terminal voltage that most attention is given to, though the base and emitter voltages also play a role and interact with the collector voltage.
In this article, we’ll look at factors that play into transistor bias without getting into much of the math yet.
A BJT (bipolar junction transistor) transistor has three terminals - collector, base, and emitter.
Figure 1: NPN BJT transistor symbol and NPN BJT transistors in various transistor packages
In an ideal BJT, current can flow from the collector to the emitter and from the base to the emitter. The amount of current going into the base controls the larger amount of current that can flow into the collector. When no current flows through the base, the transistor is entirely “off”, and no current should flow through the collector. As the current into the base increases, so does the current into the collector at roughly
$$I_b*h_{FE}$$In other words, if 10 μA is flowing into the base of a transistor with an ~h_{FE} = 100~, then 1 mA can flow through the collector. A simplified way to view transistor operation is as a current-controlled resistor, where current through a diode (the base-emitter junction) controls the resistance between collector and emitter as seen in Figure 2.
Figure 2: NPN BJT transistor symbol redrawn as a current-controlled resistance
This is a simplified model, but it is helpful for getting an idea of the effects of transistor operation with more easily-understood components. Thinking of the transistor this way, when no current flows from base to emitter, the current-controlled-resistor should have infinite resistance. As more current flows into the base, the resistance decreases down to some non-zero resistance.
Let’s see a transistor in a circuit. Figure 3 shows a common emitter amplifier configuration.
Figure 3: Standard common emitter amplifier with optional emitter bypass capacitor
This is one of the most common transistor configurations you’ll see in audio circuits. It is a very simple amplifying stage. On its own, the above schematic can be used as a simple boost or a gain stage as part of a larger circuit. The EHX LPB-1 boost uses the above circuit but with a 100 kΩ volume potentiometer at the output, and it is very similar to the Dallas Rangemaster treble boost. You may also see this stage without any of ~R_\text{b1}~, ~R_\text{b2}~, ~R_\text{e}~, and ~C_\text{e}~. First, let’s look at the case when ~R_\text{e}~ and ~C_\text{e}~ are left out. We are going to view the circuit with the current-controlled resistor model in place of the BJT:
Figure 4: Common-emitter amp without emitter resistor or emitter bypass capacitor, current-controlled resistor model
In this case, a voltage divider is formed with ~R_\text{c}~ and the effective resistance between collector and emitter. A circuit like this will often be biased so that the collector’s DC voltage is halfway between the power rails, which in this case would be +4.5V. When the AC input signal reaches the base, the effective resistance between collector and emitter will vary in accordance with the input signal, which changes the voltage divider and thus the voltage found on the collector. A small input voltage signal can control a very large output voltage signal, which is how voltage amplification is achieved with a common emitter configuration.
The reason that we want the collector to be biased halfway between the rails is that its voltage can effectively (but not quite) swing from 0V to 9V. If the collector voltage is closer to 0V or 9V, the signal will clip sooner on one half of the cycle, resulting in asymmetrical clipping and clipping with a smaller input signal. Some degree of asymmetrical clipping can be desirable in guitar circuits, but if the bias voltage is too close to either of the rails, it is likely to result in undesirable distortion characteristics.
We’ll now take a closer look at how this bias voltage is determined and how it can be adjusted. Because the bias voltage is a DC voltage, we are only interested in the DC signal. Capacitors effectively have infinite resistance at DC, so for DC analysis we will consider the capacitors to be open circuit and look only at the circuit inside the input and output caps:
Figure 5: Common emitter amplifier DC analysis
In Figure 5, the voltage on the collector depends on the resistance of ~R_\text{c}~ and the effective resistance of the collector-emitter junction. If the effective resistance of the CE junction equals ~R_\text{c}~, the collector will be biased to exactly 4.5V. The resistance of the CE junction depends on the amount of current flowing into the base, which can be adjusted using ~R_\text{b1}~ and ~R_\text{b2}~.
Because there is a diode junction from base to emitter, the voltage on the base needs to be greater than the forward voltage of the diode for current to flow. Note that changing ~R_\text{c}~ will also have an effect on the bias, but ~R_\text{c}~ affects the voltage gain and output impedance of the circuit, so it is often selected based on those requirements while the bias is set with the ~R_\text{b1}~ and ~R_\text{b2}~ resistors.
When there is no emitter resistor, the DC current through the base-emitter junction is determined by the effective resistance of the base-emitter junction. This effective resistance tends to be very small, and component tolerances can cause the resulting bias to vary substantially. The effective resistance is also dependent on other factors such as collector current and temperature (moreso in the case of germanium). In this configuration, small changes to temperature or component values can have a large effect on the bias voltage, which is undesirable.
This is where the emitter resistor comes in:
Figure 6: Common emitter amplifier DC signal analysis with emitter resistor
With the ~R_\text{e}~ resistor in place, the current flowing into the base is determined by the effective resistance of the BE junction in series with the emitter resistance. The emitter resistance is usually selected to be larger than the BE resistance. The emitter resistor is less sensitive to temperature and current changes, so the bias voltage becomes more stabilized and less affected by fluctuations in temperature and component tolerances. Note that the base voltage will need to be higher if an emitter resistor is used, as both the emitter resistor and the base-emitter diode drop contribute to a voltage drop rather than just the BE diode. This can be achieved by decreasing ~R_\text{b1}~ or increasing ~R_\text{b2}~.
~R_\text{e}~ also has the effect of reducing the gain of the amplifier due to the fact that ~R_\text{e}~ provides local negative feedback to the input. ~R_\text{e}~ also drops enough voltage that the headroom on the collector will be lower. To get around this, an emitter bypass capacitor can be used. Figure 7 shows the full circuit with the emitter bypass capacitor included.
Figure 7: Common emitter amplifier with Re and emitter bypass capacitor
Note that for DC analysis (capacitors become open circuit), nothing has changed. The DC bias point is still going to be stabilized with the ~R_\text{e}~ resistor, and the base voltage will need to be larger to overcome the higher voltage drop. However, for AC analysis, capacitors become closed circuit.
Figure 8: Common emitter amplifier AC signal analysis
Since the path through ~C_\text{e}~ can be viewed as a short circuit to ground for AC signals, ~R_\text{e}~ is effectively removed from the circuit. In this case, the short-circuit path through ~C_\text{e}~ bypasses the emitter resistor entirely, allowing for audio signals to still achieve full gain and headroom, while gaining the benefits of more stable DC bias. Note that normally, the emitter resistor also provides more linearity to the amp. Swings in collector current can have an effect on the gain provided by the transistor. Since the collector voltage depends on the input signal, the input signal is partially responsible for this change in gain, resulting in a less linear output. By including ~R_\text{e}~, a change in collector current has a smaller effect on gain since the stable resistance of ~R_\text{e}~ also contributes to the amount of gain.
However, when bypassing ~R_\text{e}~ with an emitter bypass capacitor, the benefits of the stable bias remain (because bias is a DC signal), but the linearity benefits of ~R_\text{e}~ are lost, as the linearity issues are caused by the AC signal which bypasses ~R_\text{e}~.
In practice, ~C_\text{e}~ also forms a high pass filter. For higher frequency signals, full amplification is achieved. For lower frequency signals, the effective impedance of the capacitor becomes non-zero, reducing the effective gain of the transistor for lower frequency signals. ~C_\text{e}~ can be selected to allow the full signal to pass through, or intentionally selected to trim some low end.
Remember that some amount of base voltage is required for current to flow into the base and turn the transistor on. Increasing the base voltage increases current going into the base, which increases current flowing into the collector. The more current that flows through the collector, the more voltage dropped by ~R_\text{c}~, lowering the voltage on the collector. With this in mind, we can look at how the bias is affected by tweaking various components:
- ~R_\text{b1}~: Part of the voltage divider that sets the base voltage. If this resistance is increased with no other changes, the base voltage will drop, reducing current into the base and current into the collector, reducing the voltage drop across ~R_\text{c}~ to raise the voltage on the collector. If this resistance is decreased, the opposite happens.
- ~R_\text{b2}~: Being the other part of the voltage divider, an increase in resistance here results in the base voltage increasing, increasing current into the base and current into the collector, and thus increasing the voltage drop across ~R_\text{c}~ and lowering the voltage on the collector. If the resistance is decreased, the opposite happens.
- ~R_\text{c}~: also known as the “load” resistor. It has an effect on gain and output drive capabilities, but its value will also contribute to the bias voltage. Because the current through this resistor is set by the transistor, current through this resistor effectively remains the same when the value is changed. Because of this, large resistance values will result in a large voltage drop across the resistor (lower collector voltages), while smaller resistances will result in a small voltage drop (higher collector voltages).
- ~R_\text{e}~: As discussed previously, ~R_\text{e}~ has an effect on the bias point and bias point stabilization, and if not bypassed with a capacitor, also provides additional linearity at the cost of reduced gain. By increasing ~R_\text{e}~, the effective voltage drop from the base to GND increases, requiring a larger voltage on the base for the same current through the collector. With no other changes, an increase in ~R_\text{e}~ will cause less current to flow through the base and thus collector, reducing the voltage drop across ~R_\text{c}~ and increasing the collector voltage. If the resistance is decreased, the opposite happens.
| Resistor | Increase resistance | Decrese resistance |
|---|---|---|
| ~R_\text{b1}~ | Voltage increase | Voltage decrease |
| ~R_\text{b2}~ | Voltage decrease | Voltage increase |
| ~R_\text{c}~ | Voltage decrease | Voltage increase |
| ~R_\text{e}~ | Voltage increase | Voltage decrease |
Note that changing ~R_\text{b1}~ and/or ~R_\text{b2}~ has fewer secondary effects on the circuit, so it is usually better to tweak one or both of those values to adjust bias. However, sometimes you will come across a circuit that is missing either ~R_\text{b1}~ or ~R_\text{b2}~.
Figure 9: Input gain stage of the Tonebender Mk2, drawn as a negative ground NPN circuit
Figure 9 shows the input gain stage of the Tonebender Mk2. It has been redrawn as a negative ground NPN circuit for simpler analysis, but the original is a PNP positive ground circuit. The analysis is the same, only for the PNP version the voltages are negative and current flows in the opposite direction.
This amplifying stage does not have an ~R_\text{e}~. Including one would allow for more stable bias, but more critically, it is missing ~R_\text{b1}~. Remember that the base voltage needs to overcome a diode drop for current to flow and the transistor to operate. For a silicon transistor, this diode drop is around 0.7V. For a germanium transistor, this diode drop is around 0.3V. The Tonebender Mk2 used a germanium transistor here, so the base voltage does not need to be very high. However, as it is drawn, it looks like this amplifying stage should not work. Although the base only needs a fraction of a volt for current to flow, the base should sit at 0V. Both ~R_\text{b2}~ and the base-emitter junction will pull base to GND (0V), and no current should flow into the base and the transistor should be in a permanent off state.
If the transistors in the Tonebender Mk2 were silicon, this would be true. Attempting to use silicon transistors in a Tonebender Mk2 with no other changes will result in a non-functioning pedal. The reason this circuit works is due to the normally undesirable characteristic of leakage current. There is some amount of leakage current in all transistors, but in silicon transistors it tends to be small enough to be considered negligible.
In germanium transistors, leakage varied. Some transistors have very low leakage, which is often desirable, but ~Q1~ in a Tonebender Mk2 cannot be low leakage. Leakage current is current that flows through the transistor at all times. For an ideal transistor, current flowing into the base controls the amount of current flowing into the collector, and the collector current should be controllable all the way down to zero. For a leaky transistor, current flowing into the base still controls the amount of current flowing into the collector, but the transistor cannot be turned entirely “off”, and some amount of current will flow through the transistor at all times. Leakage current is somewhat analogous to a high value resistor connected from the transistor collector to base.
Figure 10: NPN Tonebender Mk2 input stage redrawn with a leakage-simulating resistor
With the leakage drawn as a “leakage-simulating resistor” in Figure 10, it is easy to see that current will flow from collector to base through ~R_\text{leak}~. Some of that current then flows into the base, turning the transistor on. ~R_\text{leak}~ and ~R_\text{b2}~ effectively form a voltage divider like ~R_\text{b1}~ and ~R_\text{b2}~ in Figure 5, which will result in a positive voltage on the base. Though Figure 10 is just an approximation of how leakage functions, wiring an actual “leakage” resistor like this will simulate the functionality of leakage to make a silicon transistor work here. A smaller resistor is analogous to higher leakage.
This method of transistor biasing is known as collector feedback biasing. It biases the transistor by feeding some of the current from the collector into the base, but it also introduces negative feedback, which improves linearity of the amp but decreases gain. The smaller the ~R_\text{leak}~ resistor, the more feedback.
Note that although ~R_\text{b1}~ is missing, like our previous examples, ~R_\text{b2}~ can still be adjusted to modify bias, with a higher ~R_\text{b2}~ resistance resulting in a lower voltage on the collector and vice-versa.
Also note that more transistor leakage (analogous to a smaller ~R_\text{leak}~) decreases the collector voltage, so a lower ~R_\text{b2}~ can be used to compensate. You can even see this in the Mk2 circuit. The Mk2 used both OC75s and OC81Ds (and less commonly, Impex S3-1Ts). OC75s tend to be leakier than OC81Ds, and the OC75 circuit used a 10kΩ resistor for ~R_\text{b2}~ instead of the 100kΩ resistor used in the OC81D variant (and in the above drawings), which will somewhat counteract the higher leakage of the OC75s.
An example of a pedal that biases its transistors with a resistor from base to collector (like the ~R_\text{leak}~ resistor in Figure 10) is the Mosrite Fuzzrite. The input gain stage of the silicon Fuzzrite can be seen in Figure 11.
Figure 11: Silicon Fuzzrite input gain stage
Note that the output is split, but that has no effect on the biasing. The Fuzzrite uses a base-collector resistor in both the germanium and silicon versions. The silicon version is seen in Figure 11, but the germanium version uses the same arrangement with different component values. The germanium versions could operate without the base-collector resistor if the transistors have the right amount of leakage, but the silicon version will not work without that resistor.
Note that actual transistor leakage is very temperature sensitive. Relying on leakage to bias a circuit will make it more susceptible to temperature fluctuations. Using a leakage-simulating resistor with a silicon transistor or low leakage germanium transistor would be substantially less temperature-sensitive than relying only on leakage and leaving ~R_\text{leak}~ (or ~R_\text{b1}~) out.
Note also that connecting a resistor from base to collector, even with a silicon transistor, will result in less predictable biasing compared to using ~R_\text{b1}~ connected to 9V as was done in Figure 2. Because the collector voltage is dependent on various factors - temperature, component tolerance, supply voltage - it can fluctuate more than the 9V supply. With the configuration seen in Figure 9, fluctuations in collector voltage will result in fluctuations in base voltage, which will change the bias point.
A more reliable way to re-work the first stage of the Tonebender Mk2 for silicon is to simply add an ~R_\text{b1}~ resistor connecting from base to 9V. This can be seen in Figure 12.
Figure 12: Input gain stage of a Tonebender Mk2 reworked for silicon
The ideal resistance value for ~R_\text{b1}~ will depend somewhat on the transistor type, but the voltage on the base should be a lot lower than 9V, so it’s best to start with large ~R_\text{b1}~ values (>1M) and decrease as necessary.
Note that a transistor stage can also leave out the resistor ~R_\text{b2}~ in either silicon or germanium circuits. This was the case in the Fuzzrite seen in Figure 11. Figure 13 shows the similar input gain stage of the Sam Ash Fuzzz Boxx. It has a collector resistor and a base-collector resistor, but no ~R_\text{b2}~ and no emitter resistor.
Figure 13: First gain stage of the Sam Ash Fuzzz Boxx
Like our simulated leakage circuit in Figure 10, current flows through ~R_\text{leak}~ to base. In Figure 10, some of this current went through ~R_\text{b2}~ to GND, whereas in Figure 13, all of the current that flows through ~R_\text{leak}~ will flow through the base-emitter junction to turn the transistor on.
Note that leaving out ~R_\text{b2}~ is the same as giving it an infinite resistance, and increased ~R_\text{b2}~ resistance results in a decrease in collector voltage. On the other hand, a large ~R_\text{leak}~ results in an increase in collector voltage. By leaving out ~R_\text{b2}~, the necessary ~R_\text{leak}~ value will be relatively high.
The Fuzzz Boxx uses silicon transistors, but note that leaving out ~R_\text{b2}~ in a germanium circuit will result in a bias voltage that is even more sensitive to temperature fluctuations, as in that case the base voltage becomes more dependent on the fluctuating effective resistance of the base-emitter junction, and the current flowing into the base is entirely dependent on the leakage current which is also very temperature sensitive.
Note also that the effects of changing the existing resistors remains the same even when some of the resistors are left out. For example, if a common-emitter amp does not have an ~R_\text{e}~ or an ~R_\text{b2}~, increasing the resistance of ~R_\text{b1}~ will still increase the voltage on the collector. The below table holds true for any single-stage common emitter amp:
| Resistor | Increase resistance | Decrese resistance |
|---|---|---|
| ~R_\text{b1}~ | Voltage increase | Voltage decrease |
| ~R_\text{b2}~ | Voltage decrease | Voltage increase |
| ~R_\text{c}~ | Voltage decrease | Voltage increase |
| ~R_\text{e}~ | Voltage increase | Voltage decrease |
| ~R_\text{leak}~ | Voltage increase | Voltage decrease |
The above table makes it easy to know which changes can be made to tweak the bias point of any single common-emitter stage, which is helpful for re-biasing existing circuits to allow for a wider range of acceptable component and transistor specifications. In part 2 of the Silicon and Germanium Transistor Biasing series, we will get deeper into the math that can be used to calculate transistor bias point and select the necessary biasing resistors, and also take a look at the more complex biasing arrangement of two common emitter stages with feedback, as seen in the Fuzz Face, Tonebender Mk1.5 and Mk2, etc.