Chuck D. Bones
Circuit Wizard
Sandy asked me to write an article on BJT gain stages, so here goes. This will be a multi-part article because there is a lot of ground to cover. As a prerequisite to this article, you should read or re-read these articles:
forum.pedalpcb.com
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https://forum.pedalpcb.com/threads/whats-all-this-impedance-stuff-about.4903/
We find BJT gain stages in boost pedals and dirt pedals. So how do they work? What sets the gain?
First, we'll look at something simple: the BMP output stage. This schematic was lifted from the Skreddy P19 (Danube) Fuzz.
R24 is so small that we can ignore it; we'll pretend it is zero Ohms. The voltage gain of this circuit is approximately R21 / R22. 10K / 2.7K = 3.70 or 11dB. I say "approximately" because Q4 does not have unlimited gain. In other words, if we set R21 to 27Ω, we don't get a gain of 3,700. In the 2nd article listed above, I talked about transconductance (gm). The transistor's transconductance (gm) sets an upper bound on how much gain we can achieve with a BJT gain stage. Q4's finite transconductance has the same effect on gain as increasing R22. To make a more accurate gain calculation, we simply increase R22 by 1/gm. To find gm, we have to know the collector current (ic). When we analyze Q4's bias point, we find that ic is around 360μA. As stated in article 2, gm = ic / vt where vt = 26mV at room temp. That means gm = 360μA / 26mV = 13.8mS. If we invert gm, we get the emitter impedance (Ze). Ze = 1 / 13.8mS = 72.5Ω. If we add 72.5Ω to R22, we get 2.77K. There's two more things we need to take into account before we can accurately calculate Q4's gain: Q4's output impedance and the load impedance caused by whatever comes after Q4. We can estimate Q4's output impedance, Zo, by dividing 50V by ic. Why 50V? Suffice it to say that it's a fairly accurate rule of thumb. 50V / 360μA = 139K. This is much larger than R21, so it will only have a minor influence on the gain. The Skreddy P19 has a 100K volume control after Q4, and we'll assume that the next device in the chain has a very high input impedance. Still with me? Q4's total collector load is R21 in parallel with Zo & the 100K volume control. When we parallel all three impedances, we get 8.53K. So now let's run the gain calc one more time. 8.53K / 2.77K = 3.08 or 9.8dB. Our initial gain calculation was only off by about 1dB, which is plenty close for pedal applications. If R21 was a lot larger, or R22 was a lot smaller, the error from using the simplified formula at the top of this article would be much greater. Which leads me to another rule of thumb: for gains <10, the simplified formula is usually good enough. For gains > 10, we should go the extra mile and take transconductance and collector loading into account. Or can take the easy way out and use a simulation tool like LTSpice.
Let's try one more thing and then call it a day. Circuits like the Rangemaster add a capacitor in parallel with the emitter resistor to increase the gain. Let's look at the same circuit as above, only with 100uF in parallel with R22. At 82Hz (guitar's low E), the impedance of 100uF is 19Ω. Electrolytic caps have an ESR (equivalent series resistance) of a couple of Ω, so we'll call the capacitor's impedance 21Ω. When we put 21Ω in parallel with 2.7K, we get close to 21Ω. Recall, we calculated Q4's emitter impedance to be 72.5Ω. Add on the 21Ω and we get 93.5Ω. The collector load is still 8.53K, so the gain is 8.53K / 93.5Ω = 91.2 or 39.2dB. This is about as much gain as we can hope to get from a single BJT stage running on 9V. We could increase the transconductance by increasing the collector current, but then we'd have to reduce R21 to maintain the same collector voltage. Otherwise, we give up some headroom. It's a zero-sum game. However much we change the collector current, we have to change the collector resistor the same precentage, but in the opposite direction. A Darlington transistor won't help because it has the same transconductance as a single transistor. A Sziklai pair could provide more gain, but that's cheating because then we're using two transistors. Don't get me wrong, we can build a great gain stage with a Sziklai pair, but that's a topic for another day.
Next time we'll look at the BMP input stage.
What's All This hFE Stuff About?
We see lots of discussion here and on other forums regarding hFE, but I get the feeling that many of us don't really know what it means or why it's important. First, a little background. Bipolar transistors are current-mode devices. We have to supply base current to get collector current...
forum.pedalpcb.com
Another Way to Measure Transistor Gain
We've talked about hfe, which represents current gain, but there is another way to measure gain in a transistor. Some devices, like vacuum tubes or FETS, don't draw any input current, so the concept of current gain makes no sense. For those devices, engineers use the term "tranconductance,"...
forum.pedalpcb.com
Biasing BJTs - part 1
There's a lot to cover, so I'll break this up into parts. This discussion will focus on the DC operating point of the transistor. First, some basics. Many of you will already know this stuff. Vbe is the base-emitter junction voltage. It's around 0.6V with silicon and around 0.15V with...
forum.pedalpcb.com
https://forum.pedalpcb.com/threads/whats-all-this-impedance-stuff-about.4903/
We find BJT gain stages in boost pedals and dirt pedals. So how do they work? What sets the gain?
First, we'll look at something simple: the BMP output stage. This schematic was lifted from the Skreddy P19 (Danube) Fuzz.
R24 is so small that we can ignore it; we'll pretend it is zero Ohms. The voltage gain of this circuit is approximately R21 / R22. 10K / 2.7K = 3.70 or 11dB. I say "approximately" because Q4 does not have unlimited gain. In other words, if we set R21 to 27Ω, we don't get a gain of 3,700. In the 2nd article listed above, I talked about transconductance (gm). The transistor's transconductance (gm) sets an upper bound on how much gain we can achieve with a BJT gain stage. Q4's finite transconductance has the same effect on gain as increasing R22. To make a more accurate gain calculation, we simply increase R22 by 1/gm. To find gm, we have to know the collector current (ic). When we analyze Q4's bias point, we find that ic is around 360μA. As stated in article 2, gm = ic / vt where vt = 26mV at room temp. That means gm = 360μA / 26mV = 13.8mS. If we invert gm, we get the emitter impedance (Ze). Ze = 1 / 13.8mS = 72.5Ω. If we add 72.5Ω to R22, we get 2.77K. There's two more things we need to take into account before we can accurately calculate Q4's gain: Q4's output impedance and the load impedance caused by whatever comes after Q4. We can estimate Q4's output impedance, Zo, by dividing 50V by ic. Why 50V? Suffice it to say that it's a fairly accurate rule of thumb. 50V / 360μA = 139K. This is much larger than R21, so it will only have a minor influence on the gain. The Skreddy P19 has a 100K volume control after Q4, and we'll assume that the next device in the chain has a very high input impedance. Still with me? Q4's total collector load is R21 in parallel with Zo & the 100K volume control. When we parallel all three impedances, we get 8.53K. So now let's run the gain calc one more time. 8.53K / 2.77K = 3.08 or 9.8dB. Our initial gain calculation was only off by about 1dB, which is plenty close for pedal applications. If R21 was a lot larger, or R22 was a lot smaller, the error from using the simplified formula at the top of this article would be much greater. Which leads me to another rule of thumb: for gains <10, the simplified formula is usually good enough. For gains > 10, we should go the extra mile and take transconductance and collector loading into account. Or can take the easy way out and use a simulation tool like LTSpice.
Let's try one more thing and then call it a day. Circuits like the Rangemaster add a capacitor in parallel with the emitter resistor to increase the gain. Let's look at the same circuit as above, only with 100uF in parallel with R22. At 82Hz (guitar's low E), the impedance of 100uF is 19Ω. Electrolytic caps have an ESR (equivalent series resistance) of a couple of Ω, so we'll call the capacitor's impedance 21Ω. When we put 21Ω in parallel with 2.7K, we get close to 21Ω. Recall, we calculated Q4's emitter impedance to be 72.5Ω. Add on the 21Ω and we get 93.5Ω. The collector load is still 8.53K, so the gain is 8.53K / 93.5Ω = 91.2 or 39.2dB. This is about as much gain as we can hope to get from a single BJT stage running on 9V. We could increase the transconductance by increasing the collector current, but then we'd have to reduce R21 to maintain the same collector voltage. Otherwise, we give up some headroom. It's a zero-sum game. However much we change the collector current, we have to change the collector resistor the same precentage, but in the opposite direction. A Darlington transistor won't help because it has the same transconductance as a single transistor. A Sziklai pair could provide more gain, but that's cheating because then we're using two transistors. Don't get me wrong, we can build a great gain stage with a Sziklai pair, but that's a topic for another day.
Next time we'll look at the BMP input stage.
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