BJT shot noise (AoE3, sec. 8.3)

If you think of the shot noise as being a current source in parallel with r_E, which it is, it makes sense. (I found that discussion a bit mysterious myself. It's all just resistors in series and parallel.)

If the emitter resistor R_E is much larger than r_E, then the shot noise appears mostly as voltage noise on the emitter rather than current noise in the collector.

v_Nshot = i_Nshot * (R_E // r_E)

and

i_NC = (1-1/beta) i_Nshot (r_E/(r_E + R_E))

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

Yeah that's my picture. (Similar to shot noise in a forward biased diode.)

(I found that discussion a bit

That last equation is the shot noise of the collector current? (Which makes some sense to me... in the limit of large (infinite) beta the collector and emitter currents are the same.)

So then why is there shot noise in the emitter follower? (Fig 8.20 B) At least the text implies there is full shot noise there. (I might have to do a measurement :^)

George H.

Yup.

The collector and base split the shot noise by the beta ratio, and so they don't individually have exactly full shot noise. The split makes their noise currents slightly correlated, so you have to add the cross term to make the noise current sums come out right. (A fine point--the noise contribution of the correlation is probably too small to measure easily.)

There's voltage shot noise at the emitter, because I_Nshot is in parallel with r_E. Because R_E is large, this current has no place to go, so it just causes a noise voltage across r_E.

There is.

Always relaxing--BJTs follow their models so nicely. ;)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

Thanks Phil, Just to be clear, in the 1 meg follower case, with 10 uA of current, I should see (a whopping) 1.8 pA/rtHz * 1 Meg = 1.8 uV/rtHz of voltage noise at the emitter? But if I put a few k ohms of resistance in the collector lead.. (let's say 10 k ohm to get above the 2.5k emitter resistance.) (making it a "current source" as in fig 8.20 A) then the noise drops and I only will see the 180 nV/rtHz Johnson noise of the

1 Meg resistor.

Boy, that just seems wrong to me.

George H.

No, because the shot noise is in parallel with r_E, which is only 26 mV/10 uA = 2.6k. That makes the 1-Hz shot noise voltage

v_NE = 1.8 pA * 2.6k = 4.7 nV.

The 1-Hz shot noise appearing in the collector is only 4.7 nV/1 meg =

4.7 fA. The shot noise of the base current will be much larger than this.

There's a reason for that. ;)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

Grin... OK. I'm free to ignore fig 8.20, as more confusing than useful.

Source impedance of transistor is r_E. (~2.5k at 10uA) I can put a big cap across my 1 meg real emitter R and get lots of shot noise. (If that's what I want.)

George H.

Yup.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

Yup.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

One distinguishes between "shot noise" created by the fact that charge comes in electron-sized packets, and Johnson noise created by the fact that these packets are jostling around with energy kT.

Resistors don't show shot noise because the discrete electrons carrying the current interact - an electron in an average resistor is travelling at about walking speed.

Transistors are more interesting. The base-collector region is usually reverse biassed, so charge carriers should go through it as discrete lumps of charge, until you hit the Kirk effect, or "space charge" as the more old-fashioned would call it

spells out transit times, but doesn't put numbers on them.

You and Phil can probably do that in your head.

--
Bill Sloman, Sydney

I'm not sure it's so much the electron-electron interaction that reduces shot noise in resistors, as more the multiple scatterings. (electron-phonon, lattice) Each little scattering event transfers a fraction of an electron charge to the end plates of the resistor. (At least that how R. Landauer explained it.)

You usually just hear about shot noise in the base current... since typically that reflects right back to the input. H&H mumble a little about shot noise in the collector current, but don't say much more....Well at least up to section 8.5. (as far as I've carefully read.) It's not at all clear to me how to think about C-E shot noise. (Is the source impedance 25 mV/Ic as Phil says?)

I've measured the full shot noise of forward biased PN junctions. Comparing that to a diode connected transistor might be interesting. (Perhaps some Friday afternoon.)

George H.

If you take a nearly-ideal transistor (zero emitter impedance, zero noise, finite beta), and in series with the ideal emitter put the parallel combination of i_Nshot and r_E, you get the right answer for most things everything. Most other things can be put in by hand, e.g. Early effect, or come out of Kirchoff, i.e. the three instantaneous noise currents summing to zero.

Base current shot noise is a little bit doubtful, I think--how much should go to the emitter and how much to the collector? One way of thinking about it is that it's the collector current is set by V_BE, so any current coming out the base injects shot noise into the emitter only.

Another way of seeing it is that the carriers emission into the base is a Poisson process, and so has exactly full shot noise. Recombination is a Poisson process too, so the base current will have full shot noise, and so the collector current will have the RMS sum of the emitter and base shot noise, i.e.

i_NshotC ~ sqrt[( 1+2/beta) 2 e I_C) .

So I'm not sure. It's a small fraction of a decibel anyway.

Sounds like fun.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

Ahh OK you are putting all the shot noise in the emitter. I was thinking of two separate sources.

Hmm, I guess I don't know what you mean when you say the base current shot noise is doubtful. I thought it was the base current that gave rise to the input current noise... eq. 8.21 in AoE3 for instance.

If I'm reading you correctly you're suggesting there might be a bit more noise in the collector current, because of the (small) amount of recombination. Hey I could look shot noise in the BE and CE junctions of a transistor, and then diode connect it, and then reverse diode connect it. (B and E shorted) OK barring some fire that has to be put out, I'm making a Friday date for me and a few of my electron friends. :^)

George H.