Transistor Biasing - Rule of Thumb not always best

[Rob Strand]

FYI.

The recent Heathkit TA-28 thread and the old Josty 1.5V threads inspired me to do some tinkering,
https://www.diystompboxes.com/smfforum/index.php?topic=128444.0
https://www.diystompboxes.com/smfforum/index.php?topic=126307.0

Those 1.5V pedals can get a little touchy to bias and that got me thinking about transistor biasing.  Many 1.5V pedals, in fact many pedals, in general don't use emitter resistors.  For the 1.5V pedals you don't want large emitter resistors because there isn't a lot of signal swing in the first place.

There is a well known rule of thumb for biasing transistor which say to put 10 times the base current down the
bias divider to reduce variations due to hFE.

After pondering a bit I came the conclusion if you leave off the emitter resistor the rule of thumb for biasing isn't actually that great when you factor in resistor tolerances and the fact the resistors come in discrete values.   In fact you are better off using a simple biasing scheme.   The result isn't just for 1.5V it applies in general.

Here's some examples to convince you,



In each circuit group it shows the ideal case which is biased to VC=4.5V.    Then it shows the worst case when transistor gain varies and one of the base resistors varies.    You can see the collector voltage varies quite a bit from 4.5V.    The circuits marked "BETTER" have less variation on the collector voltage.

The deciding factor is the voltage drop across the emitter resistor VE.

Anyway I just thought I'd put it up for interest.

[m4268588]

It is an interesting result.
Compared Case 1 and Case 3, Case 3 resulted in less variability.


I want to explore myself a little more.

[amptramp]

One of the interesting (but not often used) ideas is to make the collector voltage equal to the base voltage as is done in the LM110 follower.  The idea here is that collector-to-base leakage current has to be zero if the collector and base are at the same voltage.  A cascode connection would make this easy.

The rule of thumb I was taught is to make the voltage drop across the emitter resistor one tenth of the supply voltage.  Everything else is sized to permit that.

I am not a fan of the collector-to-base resistor for biasing as even though it does correct for hfe variations, it reduces the input impedance dramatically.  Using two resistors in series from collector to base with a capacitor to ground at the junction removes the midband feedback so this doesn't happen.

[antonis]

The rule of thumb I was taught is to make the voltage drop across the emitter resistor one tenth of the supply voltage.

+1 ..
(as far as supply voltage is equal to or greater than 10 times V_BE ..)

[Rob Strand]

It is an interesting result.
Compared Case 1 and Case 3, Case 3 resulted in less variability.

These circuits do have something to offer.   For a 1.5V supply it biases to near half supply very reliably.   Without an input resistor the input impedance can be low (as amptramp mentioned) but if the only competition is a stage without a emitter resistor then perhaps it's still on the list.

The rule of thumb I was taught is to make the voltage drop across the emitter resistor one tenth of the supply voltage.  Everything else is sized to permit that.

That one pickups up all the stuff that divider current rule of thumb misses.    Generally the more drop you put across the emitter the better the better for biasing but you lose headroom.  The 1/10 supply rule of thumb is like donating a small amount of voltage for good but not too much.  The emitter resistor reduces the gain (in fact with the 1/10th voltage rule the gain always ends up at 5)  so for max gain you would add an emitter bypass cap - that's the design procedure the old books show.

Even quite small drops across RE can help temperature stabiity.

[Rob Strand]

I wasn't going to do anymore on this but I later realized it was easy to tweak (hack) the RB1 value in my files to do a quick check on the Feedback case.

Here's the basic idea of letting hFE and base resistor RB1 vary.   Sort of an equivalent comparison to the previous results.   I want to stress the IRB2 = 10*Ib rule of thumb produces low value base resistor.  Values which you might not want in practice considering the impedance lowering in the feedback case.     Think of reality being perhaps in between the two cases of IRB2 = 10*Ib and RB2 = infinity.




This one isolates the effect of VBE variations,




And this one shows that in practice the hFE effect is stronger than the VBE effect so we should choose based hFE and the results in the first case (ie. with some sort or RB2).




As for the 1.5V circuit, feedback bias will have a tendency to favour collector bias voltages above VBE.  As you push the collector voltage closer and closer towards VBE you will end-up low value bias resistor which make it useless an AC amplifier.  So in order to bring the collector voltage down we need to return RB2 to +Vcc instead of ground.  That effectively mixes the fixed bias and feedback cases.  You can get some advantages of feedback bias but without stuffing-up the AC aspects as much.

FWIW, the correction factors xA and xB are incorrect.   xA should have no 25.8mV and xB should only be 25.8mV.   I didn't pick up the problem because it's a fine tuning and the nominal voltages were still close to 4.5V - so much for fine tuning  .

[m4268588]

I tried to make a visual plot.


If there is NFB, this phenomenon(?) does not seem to appear.

It is not this thing that I wrote in Reply #1. At that time I did not notice this.

[Rob Strand]

If there is NFB, this phenomenon(?) does not seem to appear.

It is not this thing that I wrote in Reply #1. At that time I did not notice this.

It actually looks OK to me.   When you scan both hFE and RB1 it's scanning from one worst-case extreme to another worst-case, passing through the nominal point on the way.

The fact RB1 is varying is forcing the target collector voltage to change.

If you scan only hFE it will of course be flatter.     Even though there is feedback it won't be *dead flat*  because the forward gain of the amplifier (the transistor) is finite.   However at least it won't have the "deliberate" tilt caused by the RB1 changes.

[PRR]

I tried to make a visual plot.  .....

About 50 years ago, someone else did that.




This author was especially interested in working over a wide supply range. Note that no proposed condition gets "half supply" except by coincidence.

[Rob Strand]

This author was especially interested in working over a wide supply range. Note that no proposed condition gets "half supply" except by coincidence.

There's actually so many aspects which fight against each other you can get overwhelmed.

I did the supply voltage dependency one about 15 years ago.   Ideally you would want something that follows the line Vc = Vcc/2 (or some factor of Vcc/2).    I suspect if you put a diode in series with 10k from base to ground (and reduce its value) the proportionality of Vc to Vcc would improve as Vcc varied.

What's interesting is feedback biasing without an RE tries to keep Vc constant.  If your supply doesn't vary much then that's a good choice.   If the supply does vary then it's the wrong choice, well, unless your hFE variations are worse than the supply variations.

If you are working with a supply that doesn't vary too much,  say from 6V to 10V, you might back-off on how much you care about Vc tracking Vcc and perhaps think about parts variations.   On the other hand if you find parts variations are too much and you put a trimpot to set Vc using a circuit which is tough against part variations is not high on the list.

If you look at commercial products you will often find they use categorized transistor gains (A/B/C or P/Q/R/S).   It free things up to do what you want.   Otherwise you end-up with high supply rails and large emitter resistors to squash all the transistor variations.  Pretty much all the recipes in the old 60's transistor design books.  Most of the old pedals aren't even close to following those recipes which is why everyone is selecting transistor gains.

Another one i looked at was power supply hum rejection.   You might think keeping Vc constant would give a good power supply hum rejection but the presence of the input cap (and also the input resistor) make the AC rejection different to the DC "rejection".  Also  high DC rejection actually goes against have Vc track Vcc!

[PRR]

> feedback biasing without an RE tries to keep Vc constant.

Tends to a semi-constant ratio. Which may be what we want for medium signal handling. Which may be why we see it a lot in 1960s Japanese design.

"2N2222" hacked to give nominal hFE and 1/5th nominal hFE.

Cap on the bias resistor added to reduce objection to low input impedance.

[Rob Strand]

Tends to a semi-constant ratio. Which may be what we want for medium signal handling. Which may be why we see it a lot in 1960s Japanese design.

It's (near) constant ratio when the base resistor to ground RB2 is removed.

When you add RB2 it acts like a VBE multiplier which largely regulates the collector voltage VC.

The more current you allow down RB2 the tighter the regulation.   However, you can't keep making RB2 smaller and smaller.   If RB2 is made too small you will also need a small RB1 to set the collector voltage to the desire voltage.   If RB2 is made too small the divider formed by Rc and RB1 & RB2 will produce an output voltage less than the target VC voltage (say Vcc/2) and the transistor will be permanently off.   If you set the current down RB2 to be say 10 or 20 times the base current Ib the results are reasonable.

(There's a trick to make VC even less dependent on VCC.  It's not used for amplifiers but it may still work.)

[PRR]

The real fix is to note that high-hFE parts hew to simple approximations fine while low-hFE parts don't. Then look at the calendar, and (2019) transistor prices (pennies apiece). Design with direct coupled pairs or triplets. It don't take much to reduce variability from 50% to 5%.

[Rob Strand]

The real fix is to note that high-hFE parts hew to simple approximations fine while low-hFE parts don't. Then look at the calendar, and (2019) transistor prices (pennies apiece). Design with direct coupled pairs or triplets. It don't take much to reduce variability from 50% to 5%.

It certainly helps the cause on many of the circuits.   For the Feedback bias + RB2 you get the same performance with higher RB1 & RB2 resistors - that's a good thing because low RB1 and RB2 resistors stuff things up for the amplifier.    For the circuits which have no RB2 the variations in the collector bias voltage still depends on how much hFE *changes* and not the size of hFE,  Higher hFE => higher RB1 - which still has some advantages.

Changing the structure of the amp affects the behaviour in a pedal.   Even smaller changes can make quite an impact.  I don't think people have milked the options for transistor overdrives.

The reason I started the thread was to show how the small RE case goes against common rule of thumb.   It's a case which has fallen between the cracks but not in a simple way.  If you consider only hFE changes you get stuck on thinking that low base resistors help.  It's not until you factor in practicalities of the base resistor tolerances or steps that the crack appears.    Many times in the past I've noticed large steps in the bias voltage when you change to the next E12 series resistor.  I knew why it occurred but the solution of removing RB2 altogether is not an obvious at all.