When does it make sense not to use a 2N3904/3906?

[amptramp]

One thing to understand is that the resistors at the input to the buffer are in parallel with the source resistors and it is this parallel resistance that sets the noise level.  If you have a guitar with a 10,000 ohm winding, at frequencies below where the inductance takes over, this is in parallel with the biasing resistance and therefore, the resistance used to calculate noise is below this value.  If you have a coupling capacitor, this separates the source and biasing resistance as the frequency gets lower, so there will be a range of frequencies where the noise is still less than that of the buffer on its own.

One the guitarist turns the volume down at the guitar, this inserts resistance from the volume control with resistance above the slider adding to the noise and resistance from slider to ground in parallel with the input, reducing the noise.  If you are happy with the noise performance when you turn the guitar volume control down to equal resistance above and below the slider, then you have the worst case for noise.  If this performance is acceptable, then you don't have a noise problem.

[Rob Strand]

One of the reasons against using a low gain device 2N3904 over say a higher gain transistor is the bias voltages can be poorly defined.

If you have a buffer with a 1M input/bias resistor when the hFE changes say from 100 to 200 you will see large changes in the bias voltages.  If however you used a higher hFE like 400 to 800 the bias voltage would not shift much at all.

Changing the hFE in a circuit can change the performance.    Different noise, different gain, different input impedance.  So you need to be careful about comparing designs.  What does an apples to apples comparison actually mean.

In general you will find higher hFE devices will let you reduce the noise.  Also for a given input impedance you can get a lower output impedance.

For older model transistors the "low noise" types tend to be higher gain, they also tend to produce lower noise with high impedance circuits.    These older models can't be trusted to have low rbb', as rbb' isn't important for high impedance circuits.  For more modern transistors "low noise" can mean transistors with a low rbb' and they will produce low noise in low impedance circuits.  Many will also produce low noise in high impedance circuits, that's because production techniques have improved.  Things like 2n3904 can't be relied upon to have low noise in high impedance circuits (or low impedance circuits).

It is important to include the source impedance in noise calculations and simulations.  For high impedance sources the source impedance sets the minimum noise.  The name of the game is then not to make it worse.

Here's an example of tuning the collector current to get low noise:



This example shows how to tweak a circuit with a low hFE transistor so the noise is close to that of a high hFE transistor.



Notice how the 22k source impedance sets a limit to the noise.

One post isn't going to cover everything but the above covers most of the main points.

[antonis]

It is important to include the source impedance in noise calculations and simulations.  For high impedance sources the source impedance sets the minimum noise.  The name of the game is then not to make it worse.

Exactly..!!

For low frequency applications, optimum Collector current (for lowest noise figure) can be predicted via Rsource = [(0.05*h_FE*r_bb/Ic) + (0.025)²*h_FE/Ic²)]^1/2 formula which, in case of negligible Base spreading resistance can be simplified to Ic = 0.025*(h_FE)^1/2 / Rsource

e.g. for a signal source resistance of 10k and a h_FE of 400, optimum Collector current should be 50μA..

[amptramp]

I designed and built a low-noise amplifier for low impedance (50 ohm) sources back in the 1970's that used a differential pair of PNP transistors feeding an LM318 op amp stage.  The finished amp had a voltage noise of 0.64 nV/SQRT Hz with sensor bias noise included.  The transistor?  The lowly 2N4405 and it was the best choice available then.  This was for a sensor array using HgCdTe photoresistive sensors that respond to the 8 - 14 µM thermal imaging band.

The LM318 did not have a published noise value at the time, so I tested it and it came out to 11 nV/SQRT Hz and later when they finally published a value, it was the same.

[antonis]

The finished amp had a voltage noise of 0.64 nV/SQRT Hz with sensor bias noise included.

Really impressive, Ron..!!

[Rob Strand]

It is important to include the source impedance in noise calculations and simulations.  For high impedance sources the source impedance sets the minimum noise.  The name of the game is then not to make it worse.

Exactly..!!

For low frequency applications, optimum Collector current (for lowast noise figure) can be predicted via Rsource = [(0.05*h_FE*r_bb/Ic) + (0.025)²*h_FE/Ic²)]^1/2 formula which, in case of negligible Base spreading resistance can be simplified to Ic = 0.025*(h_FE)^1/2 / Rsource

e.g. for a signal source resistance of 10k and a h_FE of 400, optimum Collector current should be 50μA..

That formula is always a good starting point.   It works for most things but interestingly it doesn't give the right result for a simple CE amplifier with an unbypassed emitter resistor.

As I recall, for an unbypassed emitter resistor the input noise current is less than with no emitter resistor.  It isn't directly related to reduction in voltage gain.   It related to the factor k = (1/gm) / ((1/gm) + RE); current divider between rpi and (beta + 1)*RE.  The optimum current ends up being *somewhat* higher than that basic formula estimates.   Off hand some it's somewhere between sqrt(1/k) and (1/k)/2 times higher current.

RE and gm are related via emitter bias voltage.  (1/gm) = VT/IC and the emitter bias voltage RE = VE/IC where VT = 26mV.  So k = 1 / (1 + VE/VT).   For a 9V circuit with a gain of 20dB we might end up with VE=400mV then k = 1/16.   So the optimum bias is somewhere around 4 to 8 times higher than with the unbypassed emitter resistor.  With your numbers that's around 50uA*4=200uA to 40uA*8=400uA. 

If we operate at a higher supply voltage we would expect the optimum current to be higher again.  An interesting result.  I really should do a simulation to show the effect.

Another thing that occurs with an unbypassed emitter resistor is the RE can get large as the source resistance Rs and then RE also adds noise.  In that case the optimum current formula needs to use RE+Rs instead of Rs.

To be honest I get a rough idea of the optimum current using the formula you gave then I just use spice to tweak the current.

In some cases the operating current ends up being low and that makes the output impedance so high it is unusable.  Luckily the optimum is very shallow and we can bump up the operating current up quite a bit without affecting noise too much and that reduces the output impedance to something more usable.
I did a quick check 9V vs 50V supply, both 20dB gain with emitter resistors.  Rsource=22k, hFE high-ish (290 to 450)
For the 9V circuit the optimum current was about 143uA with input noise 22.7nV/rtHz.
For the 50V circuit the optimum current was about 445uA with input noise 26.7nV/rtHz; 1.4dB worse than 9V.
The 50V circuit at 143uA produced input noise 29.7nV/rtHz; 2.3dB worse than 9V; in this case RE=16.7k getting near Rs.

The optimum current  for the higher voltage circuit is higher as expected, in this case a factor of 3 18 higher than the formula; 3 times higher than 9V.  It's predicted by the sqrt(1/k) or (1/k)/2 factor but not precisely.  The noise is worse. 

For the HV case:
Optimum IC based on Rs=22k and hFE=444  => IC = 24.9uA
k = 1/93 so we estimate I_opt_hv = 240uA to 1100uA.  445uA is inside that range.

[PRR]

Noise is not *that* important for this particular circuit.

It almost never is. Proper design may rank lower than proper signal level management, a lost art (was it ever found?).

And plagiarize good circuits. The half-dozen broadly useful techniques ran out of patent decades ago.

[antonis]

In some cases the operating current ends up being low and that makes the output impedance so high it is unusable.

Of course..

e.g. Collector resistor of a grounded Emitter CE amp running at 50μA & +9V should be 90k.. It should need about 1M next stage input impedance for retaining stage ordered gain..