On 02/12/2013 12:59 PM, Phil Hobbs wrote:
> On 02/12/2013 12:44 PM, Mark wrote:
>>
>>>
>>> IIRC the best noise match impedance of a bipolar transistor amplifier
>>> does not change when you go from common-emitter to common base. The
>>> power match does, but not the noise match.
>>>
>>>
>> speaking of noise figure...
>> something thats troubled me...
>>
>> it seems to me the any LNA ***that provides a good input match****
>> (talking about RF amplifiers in a 50 Ohm system) and is physically at
>> room temperature cannot also have a noise figure better then 3 dB.
>>
>> To look at it another way, can you create an active (or otherwise)
>> 50 Ohm load that creates less noise than a 50 Ohm resistor creates?
>>
>> Mark
>>
>
> Grab yourself a cold beer from the fridge, and think about how it could
> be at 40F in a 70F ambient. Same basic answer.
>
Well, I suppose _maybe_ I could be a bit less of a smartass about it. ;)
The small-signal emitter resistance of a bipolar transistor is
r_E = kT/(eI_C),
i.e. about 26 mV/I_C at room temperature. If you multiply that by the
shot noise of the emitter current, which is
i_N = sqrt(2*e*I_C),
and do two lines of algebra, you get
v_N = sqrt(2*k*T*r_E).
Comparing this with the usual Johnson noise formula, you find that the
noise temperature of a forward-biased emitter is T/2, i.e. 150K at room
temperature.
(At thermal equilibrium, you can't have a bias voltage or a net emitter
current, so the forward and reverse diffusion currents are equal. They
each contribute half of the fluctuations, so the factor of 2 is
restored. You need the full Ebers-Moll expression to show this, but I'm
too lazy to type it out.)
The beta of a BJT is the really low noise thing in electronics. The
intrinsic base (i.e. neglecting the actual resistance of the silicon)
has an impedance r_B = beta * r_E, but has exactly the same noise as the
emitter. (It has to, because there are only two wires involved.)
Thus the noise temperature of the input resistance of an ideal BJT CE
amplifier ought to be right around T_J/(2*beta).
It's never quite that good, of course, because the base current has shot
noise and there are real physical resistances that have noise of their own.