The Imaging of a Magnetic Source - Biological Imaging and Sensing - page 132

Commercially available amplifiers have an input voltage noise of about
0.4 nV/Hz 1 / 2 at best at room temperature, which is normally larger than
the intrinsic noise level of SQUIDs. Therefore, larger ∂V/∂Φ should be re-
quired to reduce the amplifier-attributable noise. Some methods have been
proposed to obtain a large ∂V/∂Φ , which are mentioned later.
The above theory is valid in the white region. On the other hand, 1 /f
noise exists in the low-frequency region below

1.0 Hz. Various mechanisms
of 1 /f noise are predicted, such as the fluctuation of the tunneling probability
in a junction caused by trapped electrons [7-9] and fluctuation of trapped flux
in superconducting films [10]. However, a clear theory is lacking at present.

∼

Readout Methods: Flux-Locked Loop (FLL). The output voltage from
SQUIDs is a nonlinear function with a periodicity of Φ 0 . The linear relati-
onship between the flux and the voltage is achieved with a method called a
“flux-locked loop (FLL)” as a null detector, which provides high resolution,
a large dynamic range, and a high slew rate. Two popular FLL methods are
described in this section.

FLL with Flux Modulation. Figure 3.11 shows a typical circuit of an FLL
with flux modulation. A bias flux Φ b and modulated flux Φ m with a peak-
to-peak amplitude of Φ 0 / 2andafrequencyof f m are applied to the SQUID
loop. A rectangular wave or a sine wave is used as the modulation signal.
With a quasistatic flux in the SQUID of nΦ 0 , the resulting output voltage
V is a rectified signal with 2 f m , as shown in Fig. 3.12a. If this signal is lock-
in detected with reference to f m , with a phase-sensitive detector (PSD), the
output voltage from the lock-in detector V L will be zero. On the other hand, if
the quasistatic flux is ( n +1 / 4) Φ 0 , V is a modulated signal with f m ,asshown
in Fig. 3.12b, and V L will be a maximum. Thus the linearized voltage for a
signal flux can be obtained, as shown in Fig. 3.12c. The lock-in detected signal
is integrated with an integrator and fed back to the SQUID loop through a
feedback coil L f , via a feedback resistor R f . If there is an external flux ΔΦ

Bias Current

Integrator

SQUID

Pre-Amp.

OUTPUT

V L

V

L i

L sq

L p PSD

L f (M f )

Phase
Shifter

OSC.

R f

Fig. 3.11. A schematic diagram of an FLL with flux modulation