Biomedical Engineering Reference
In-Depth Information
In this calculation, no noise is taken into account. Therefore, theoreti-
cally, the
I
-
V
curve intersects with
I
-axis at
V
= 0 with zero slope. The
corresponding
Φ
-
V
curve has infinite slope near
V
=0for
I
b
<
2
I
c0
.Butin
practical SQUIDs, the
I
-
V
curve and the
Φ
-
V
curve are rounded by noises,
which consist of the thermal fluctuation of the critical current and some other
noises. The noise attributed to the thermal fluctuation at a finite temperature
T
is characterized in terms of the noise parameter
Γ
, defined as the ratio of
the thermal energy
k
B
T
and the coupling energy of the junction
I
c0
Φ
0
/
2
π
,
where
Γ
is
Γ
=
2
πk
B
T
I
c0
Φ
0
.
(3.37)
It is necessary for stable operation of a SQUID that the coupling energy is
much larger than the thermal energy, or
Γ
1. According to the study by
Tesche and Clarke [6],
Γ
should be smaller than 0.05, from which a SQUID
requires a minimum critical current larger than 3.5
A at 4.2 K.
μ
Noise in dc SQUIDs.
In practical SQUIDs, noise should be discussed in
order to evaluate the field sensitivity. After thermal fluctuation of the critical
current, the main source of noise is the Johnson noise generated in the shunt
resistors. In this section, noise estimation of dc SQUIDs is outlined, including
the attribution of preamplifier noise for practical use [4-6].
A dc SQUID provides the maximum voltage modulation,
ΔV
max
,ifthe
bias current
I
b
is equal to the maximum critical current of the SQUID, 2
I
c0
.
From (3.36),
ΔV
max
is given by
I
cm
=
R
s
I
c0
1
2
(2
I
c0
)
2
ΔV
max
=
R
s
(
I
cm
−
−
2
I
c0
)
2
,
(3.38)
where 2
I
cm
is the minimum critical current of the SQUID obtained with the
flux of (
n
+1
/
2)
Φ
0
. The difference of 2
I
c0
and 2
I
cm
is called the modulation
depth
ΔI
c
, which is approximately given by
2
I
c0
−
I
cm
2
I
c0
ΔI
c
2
I
c0
1
1+
β
L
.
=
=
(3.39)
From (3.38) and (3.39),
ΔV
max
is written as
1+
β
L
1+2
β
L
.
R
s
I
c0
ΔV
max
=
(3.40)
A SQUID has the maximum sensitivity if it is operated at the steepest
slope on the
Φ
-
V
curve, which provides the largest differential coecient
∂V/∂Φ
.
∂V/∂Φ
is called the “flux-to-voltage transfer coecient”, or simply
“transfer coecient”, with the units of [
V/Φ
0
] normalized by
Φ
0
. Using (3.40),
