Download Noise in BJT

Noise in BJT
The objective is to determine Eni , En and I n for a bipolar transistor.
The hybrid-  model that includes the noise sources is shown below
Fig 5-3
The feedback elements
. This is OK for frequency
C and r are removed
fT
<
. At frequencies
above that value the noise mechanisms are
 01 / 2
partially correlated.
Eniis caused by the thermal noise of the base-spreading resistance. the
noise current generator
is Ithe
shot noise of the total base current, and
nb
I nc
is the shot noise of the collector current.
2
E x2  4kTrx , I nb
 2qI B , I nc2  2qI C
The 1/f noise contribution is represented by a single noise current
generator which flows through the entire base resistance. The spectral
density of 1/f noise is given by
I 2f 
KI B
f
• The exponent  ranges between 1 and 2. The experimental value of K
varies over a wide range of values. An alternative expression for 1/f noise
2qf L I B
2
is
I 
f
f
• where fL varies from 3.7MHz to 7 MHz.
An expression for the 1/f noise
 '2
2qf L I B rx
voltage generator is
E 2f 
f
• where rx'  rx / 2. 1/f noise results from trapping and detrapping of carriers
in surface and bulk defect states. Transistors with high at very low
collector currents seem to have little 1/f noise as these traps are also
recombination centers.
Equivalent Input Noise
• To derive the equivalent input noise Eni we first calculate the total
noise at the transistor output, the gain from the source to output, and
then divide the output noise by the gain.
• The output is shorted then the output noise current is
2
I no
 I nc2  ( g m E ) 2 or
2
 ( E x2  Es2 ) Z2
( I nb
 I 2f ) Z2 (rx  Rs ) 2 
I I g 


2
(rx  Rs  Z ) 2
 (rx  Rs  Z )

2
no
2
nc
2
m
g VZ
• For an input signal Vs, the output short-circuit current is I o  g mV  m s 
rx  Rs  Z
I
g
Z
m 
• The transfer gain is K  o 
t
rx  Rs  Z
Vs
• The equivalent input noise is therefore
2
I no
E  2
Kt
2
ni
I nc2 (rx  Rs  Z )
 E  E  ( I  I )( rx  Rs ) 
g m2 Z2
2
x
2
s
2
nb
2
f
2
• For a zero source resistance case

2qI C r 2qf I r
2 f 
 
En2  4kTrx  2qI B rx2 


2
qI
r
C x 
2
0
f
 fT 
2
'2
L B x
2
Noise in Field Effect Transistors
• Three main types of noise are found in FETs -- Shot noise, flicker
noise and thermal noise
• The small-signal noise equivalent circuit for an FET is shown below
• Fig 6-1
• There are three principle sources of noise in a MOSFET identified as
2
I ng
 2qI dc
2
I nd

I 2f 
•
•
•
•
•
8kTgm
3
AF
K f I DQ
f Cox L2eff
where KF is the flicker noise coefficient
IDQ is the quiescent drain current, AF is a constant, f is the frequency.
The total noise current at the output drain-current channel is
2
2
I no
 I nd
 I 2f
We reflect this noise current to the gate as an equivalent input noise
voltage using the Ktr reflection coefficient defined as
K tr 
id ( signal)
v gs ( signal)
 gm
2
I 2f
I nd
E  2  2  En2
gm gm
2
ni

8kT
KF

3 g m 2 K p fCoxWLeff
• The first term of the above equation is equivalent to a single resistor of
value
2
Rn 
3g m