Revisiting the Emitter Resistor
For installment #3 of the series, I am going to answer my original post. Why did Tonmann place a 10K trimmer off the emitter leg of the transistor? Well hopefully I have answered my own question correctly after doing research on various common emitter amplifier topics.
As discussed in the first section above, an Emitter Resistor is added to the Common Emitter Amplifier circuit to accomplish two purposes, reduce distortion and control gain.
The first purpose is to reduce Temperature induced distortion through the Emitter Resistor by Negative Feedback. That is, when Temperature increases, Collector Current (Ic) increases. When Collector Current (Ic) increases, the voltage drop across Re (Ve) increases. Vb, the voltage at the base, remains fixed due to the biasing arrangement, so to compensate the Base-Emitter voltage drop (Vbe) decreases. If Base-Emitter Voltage (Vbe) decreases, Base Current (Ib) decreases. If Base Current (Ib) decreases, then Collector Current (Ic) decreases, bringing it back to towards the original Q point value. The rise in Collector Current (Ic) due to temperature is countered by a fall in Collector Current (Ic) due to the feedback action of the Emitter Resistor (Re). The greater the value of the Emitter Resistor, the better the Temperature stability.
↑Temp = ↑Ic = ↑Ve (as Ic=Ie and V=IR) = ↓Vbe (as No Change in Vb due to bias network) = ↓Ib = ↓Ic
The second purpose is to affect amplifier gain. The value of the Emitter Resistor along with the Emitter Bypass Capacitor acting in tandem can result in an increase in amplifier gain. A good AC voltage gain requires a low value of emitter resistance.
This is where things can get tricky as good AC gain requires a low value of emitter resistance, but the opposite is true for Temperature induced distortion. Good temperature stability requires a high value of emitter resistance. In other words, to reduce distortion related to temperature, the value of the emitter resistance must be increased. In practice, a compromise is often made between these conflicting requirements.
So what is the best way to make a compromise on the value of the Emitter Resistor? Is it possible to get the best of both worlds, good gain and good temperature stability?
Well, the emitter resistance (Re) can be broken up into two parts, which we will call Rea and Reb. That is, you can take the Emitter Resistor value that you had planned to use and split it into two separate resistors in series that add up to the same value of the originally planned resistor value. For example, for an Emitter Resistor (Re) of 5K, you could use a1K and 4K resistors in series that add up to 5K. This is called a Split Emitter Resistor configuration.
If you tap off the Emitter Bypass Capacitor (as above) between the two resistors so that the capacitor is in series with the first resistor (Rea) and in parallel with the second resistor (Reb), you can get the best of both worlds! The resistor in the emitter leg has now been split into two parts: (Rea) and (Reb) forming a voltage divider network within the emitter leg with the by-pass capacitor connected in parallel across the lower resistor.
The upper resistor (Rea) is unbypassed by the capacitor so must be considered when calculating signal parameters. The value of (Rea) is chosen to provide the required compromise between gain and distortion as the AC signal current only sees (Rea). The second resistor (Reb) is connected in parallel with the capacitor and is considered to be Zero ohms as it becomes shorted out at high frequencies. In other words (Reb) the second resitor is bypassed by the capacitor and thus the AC current doesn’t see R2. Because of this, AC Voltage Gain is partially determined by (Rea) and for an AC signal the total value of the emitter resistance is equal to (Rea + Rbe) where Rbe is the Base-Emitter resistance (25/Re). Since Gain comes from Collector Resistance divided by Emitter Resistance or Rc/(Rea + Rbe), the smaller value of Rea, the greater the gain.
Knowing that you want a small value of the upper emitter resistor (Rea) for greater gain, this would result in poor temperature stability and therefore some added distortion. However, the Bypass Capacitor basically blocks (filters out) DC, so DC (bias) is forced to go through the Emitter Resistors placed in series, which is fairly large value. Now you have your temperature stability and mitigate related distortion!
In summary, the DC bias current sees (Rea) and (Reb) in series, which results in good temperature stability, since total Emitter Resistance (Re) is seen by DC bias as a large value. The AC signal current only sees (Rea) since (Reb) is bypassed by Capacitor placed in parallel (AC current doesn’t see R2) and so AC signal gain is related to (Rea) and (Rbe), therefore the amount of gain can be controlled by the size of (Rea).
As you can see, using a potentiometer as a Split Emitter Resistor allows one to adjust the amount of AC Signal Gain if you place the Emitter Bypass Capacitor off of the wiper leg, Lug 2. Adjusting the 10K pot controls the amount of resistance (Rea) that is in series with the bypass cap, so gain can be adjusted. Since in an amplifier, one usually wants a large gain, (Rea) should be kept small.
If you notice in the instructions for the Guitar PCB Pumped Up Rangemaster, that to “adjust the TR2 ‘GRIT’ trimmer properly, turn TR1 all the way up. The further clockwise you turn it, the louder and more of an overdriven sound you will get. Once you have it hooked to your amp, you may want to adjust it back up by 5-15% to suit your tonal preferences.” Turning up the Trimmer apparently means making (Rea) a minimal value for the greatest amount of gain. Backing off the trimmer a bit decreases the gain slightly providing a slightly less “gainy” tone or sound. It should be noted that the early treble boosters were meant to have the gain all the way up (that is to “11”).
Tonmann provided us with a modern design of the old Rangemaster circuit. First, he changed the bias network and added a trimmer at R2, allowing us to fine tune the bias. A large 470K resistor at R1 was changed to 200K possibly for easier parts availability, but in Installment #2 of the series, you can see that Tonmann applied some known standard design concepts to the bias network to conform more with convention. The split emitter resistor is also a great addition providing greater temperature stability to the notorious finicky Germanium transistors that one finds these days along with more flexibility to control overall gain of the pedal (adjustable gain). All Hail to Tonmann (RIP)!