tomizett
Active Member
Hi All,
Posting in "Maths & Physics" as I reckon that's where the real brains hang out...
I have a question regarding current noise in BJTs. I have found what I believe to be contradictory statements in two textbooks, and I would like your opinions on which - if either - is correct.
The texts agree that the noise current (appearing at the base) of a BJT consists of three contributions:
#1. Shot noise of the DC base current (which is white)
#2. A 1/f component of the above (which rises at low frequency)
#3. Modulation of the base current due to shot noise in the collector current.
It is #3 where my problem lies.
The shot noise in the collector current Ic is sqrt(2.q.Ic). In order for the collector current to vary, the base current must vary in sympathy with it. The amplitude of the base current variation is less than the collector current variation by a factor of hfe (the transistor's AC signal gain). Because the collector current noise remains flat with frequency, but hfe drops as frequency approaches ft, the base current noise due to #3 increases with frequency.
The salient point here is #3 is different from #1 because #3 it is not shot noise of the base current, but is shot noise of the collector current appearing attenuated at the base. By contrast, #1 is the base current's own shot noise.
To me, this means that the base current noise (inoise) should be:
inoise = sqrt(2.q.Ic) / hfe
or (mean-squared)
inoise^2 = 2.q.Ic / hfe^2
The two contradictory texts are The Art of Electronics (Horowitz and Hill) pp 483 equation 8.22 and Design with Operational Amplifiers and Analog ICs (Sergio Franco) pp325 equation 7.19b. I have attached pictures of both.
Horowitz & Hill have approximated hfe as f/ft, whereas Franco represents it as the function beta(j.f).
Despite the differences in form, the Horowitz/Hill expression appears to be basically:
inoise^2 = 2.q.Ic / hfe -- I believe this to be incorrect
where Franco shows:
inoise^2 = 2.q.Ic / hfe^2 -- I believe this to be correct
Can anyone verify that these two books are in contradiction and/or offer an opinion as to which expression they believe to be correct?
Thanks a lot for reading all this folks - your input is, as ever, much appreciated!
Posting in "Maths & Physics" as I reckon that's where the real brains hang out...
I have a question regarding current noise in BJTs. I have found what I believe to be contradictory statements in two textbooks, and I would like your opinions on which - if either - is correct.
The texts agree that the noise current (appearing at the base) of a BJT consists of three contributions:
#1. Shot noise of the DC base current (which is white)
#2. A 1/f component of the above (which rises at low frequency)
#3. Modulation of the base current due to shot noise in the collector current.
It is #3 where my problem lies.
The shot noise in the collector current Ic is sqrt(2.q.Ic). In order for the collector current to vary, the base current must vary in sympathy with it. The amplitude of the base current variation is less than the collector current variation by a factor of hfe (the transistor's AC signal gain). Because the collector current noise remains flat with frequency, but hfe drops as frequency approaches ft, the base current noise due to #3 increases with frequency.
The salient point here is #3 is different from #1 because #3 it is not shot noise of the base current, but is shot noise of the collector current appearing attenuated at the base. By contrast, #1 is the base current's own shot noise.
To me, this means that the base current noise (inoise) should be:
inoise = sqrt(2.q.Ic) / hfe
or (mean-squared)
inoise^2 = 2.q.Ic / hfe^2
The two contradictory texts are The Art of Electronics (Horowitz and Hill) pp 483 equation 8.22 and Design with Operational Amplifiers and Analog ICs (Sergio Franco) pp325 equation 7.19b. I have attached pictures of both.
Horowitz & Hill have approximated hfe as f/ft, whereas Franco represents it as the function beta(j.f).
Despite the differences in form, the Horowitz/Hill expression appears to be basically:
inoise^2 = 2.q.Ic / hfe -- I believe this to be incorrect
where Franco shows:
inoise^2 = 2.q.Ic / hfe^2 -- I believe this to be correct
Can anyone verify that these two books are in contradiction and/or offer an opinion as to which expression they believe to be correct?
Thanks a lot for reading all this folks - your input is, as ever, much appreciated!
