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EE338K
HOMEWORK
ASSIGNMENT #9
Random Noise in Amplifiers
Introduction
The accurate sensing of small electrical signals is limited by the presence of noise in the form of random
current and voltage fluctuations in both the resistors and the active devices that makeup an electronic
amplifier circuit. An excellent discussion of the sources of these noises and how they affect the
performance of Op Amp amplifiers is presented in Chapter 12 of the reference book “Op Amps for
Everyone” available online at
http://focus.ti.com/general/docs/litabsmultiplefilelist.tsp?literatureNumber=slod006b
The nomenclature and notations used in this homework assignment for random noise voltages and
currents are as follows:
1. The quantity
( )
f
e
2
( )
[ ]
f
i
2
written with a bar above the square of a lower case letter indicates the
power density spectrum of a noise voltage [current.]
The power density spectrum has the units
V
2
/Hz [A
2
/Hz.] It is generally a function of frequency including the case where it is a constant. When
the power density spectrum is constant with respect to frequency the noise is referred to as white
noise.
2. The quantity
2
E
[ ]
2
I
written as the square of an upper case letter and with overbar refers to the
Mean Square (MS) value of a noise voltage [current] developed in a band of frequencies extending
from
f
1
to
2
. It has the units V
2
[A
2
]. The relationship to the power density spectrum is
( )
( )
]
[
2
2
2
2
2
2
2
2
∫
∫
=
=
f
f
f
f
df
f
i
I
df
f
e
E
(1)
The quantity BW =
2

1
is referred to as the bandwidth of the
MS voltage [current].
3.
The quantity
E
[ ]
I
is the Root Mean Square (RMS) value of the noise voltage [current] and is
simply the square root of the MS value.
4. The quantity
( )
f
e
,
( )
[ ]
f
i
written with a lower case letter and an overbar, designates the spectral
density of a noise voltage [current] and has the units V/Hz
1/2
[A/Hz
1/2
]. The spectral density is
simply the square root of the power density spectrum.
5. The notation for any of the quantities introduced above, whether it is a power density spectrum, MS
or RMS value, or spectral density may have subscripts that provide identification of the component
with which the quantity is associated.
6. The power density spectrum of the open circuit noise voltage,
2
R
e
, generated by a resistor of
R
Ohms is
kTR
e
R
4
2
=
V
2
/Hz
(2)
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Because it is independent of frequency it is white noise. It is referred to as Johnson noise after the first
person that characterized this type of noise experimentally.
7. The noise model of the Op Amp contains three noise sources as shown below.
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 Fall '09
 BOSTICK
 Amplifier, Volt

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