
end of the input coil is left open, the fundamental
resonance occurs when the length, l, of the microstrip
is equal to half the wavelength of the RF signal. In
this mode, the microstrip resonator is analogous to a
parallel tuned circuit and, neglecting losses in the
microstrip and the SQUID, one calculates a quality
factor Q ¼pZ
s
/2Z
0
. At the resonant frequency the
current fed into the resonator is amplified by Q, pro-
ducing a magnetic flux that is coupled into the
SQUID via a mutual inductance M
s
¼a(LL
s
)
1/2
,
where L
s
is the microstrip inductance and a the cou-
pling coefficient. One selects the resonant frequency
by appropriate choice of the length of the coil. Q,
which determines the bandwidth of the amplifier, can
be varied by selecting the characteristic impedance of
the microstrip; i.e., by choosing an appropriate width
of the turns of the coil and thickness and dielectric
constant of the insulating layer between the coil and
SQUID. One has to keep in mind, however, that re-
ducing Q will increase the bandwidth and lower the
gain, since the resonant current amplification is pro-
portional to Q.
Since the conventional washer SQUID is an asym-
metric device (the two Josephson junctions are situ-
ated close together rather than on opposite sides of
the SQUID loop), one can either ground the washer
or ground the counter electrode close to the Joseph-
son junctions. Using the washer as ground plane for
the input coil suggests one should ground the washer.
However, it is also possible to ground the counter
electrode and have the washer at output potential. In
this case, depending on the sign of V
F
(which deter-
mines the phase shift between input and output of the
amplifier), one can obtain either a negative or positive
feedback from the output to the input, and using
positive feedback, the gain of such amplifiers can be
enhanced substantially.
Using this configuration, Mu
¨
ck et al. (1998) meas-
ured gains of 20 dB up to a frequency of 1.3 GHz.
Noise temperatures as low as 100 mK (at 400 MHz)
have been measured when the SQUID is cooled to
0.4 K (Andre
´
et al. 1999). This noise temperature is
only about a factor of three above the quantum limit.
The intrinsic noise temperature of the amplifier is typ-
ically 1/4 of the bath temperature, T,and,within
measurement errors, scales with T.
The microstrip amplifier can be tuned by means of
a varactor diode, which is connected to the open end
of the microstrip. Changing the capacitance of the
varactor diode by an applied d.c. voltage enables one
to reduce the resonant frequency of the amplifier by
nearly a factor of two. If gains higher than 20 dB are
desired, two amplifiers can be connected in cascade.
3. Conclusion
For applications requiring extremely low noise tem-
peratures at frequencies of several hundred megahertz
and above, an RF amplifier based on a d.c. SQUID is
a promising alternative to semiconductor amplifiers.
Such applications include intermediate frequency am-
plifiers for superconductor–insulator–superconductor
(SIS) mixers, NMR, or Axion detectors. Gains of
more than 20 dB at frequencies exceeding 1 GHz have
been obtained with such amplifiers and noise temper-
atures as low as 100 mK. An exciting possibility is the
expectation that the quantum limit could be reached
with a d.c. SQUID amplifier cooled to about 100 mK.
A challenge for future work is the extension to higher
frequencies. It should be possible to operate a SQUID
amplifier at frequencies exceeding 10 GHz, probably
by modifying the geometry of the SQUID from the
square washer format to, perhaps, an in-line config-
uration. One may hope that the design and testing of
such SQUID amplifiers will be undertaken in the not-
too-distant future.
See also: SQUIDs: The Instrument
Bibliography
Andre
´
M -O, Mu
¨
ck M, Clarke J, Gail J, Heiden C 1999 Mi-
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ck M, Andre
´
M -O, Clarke J, Gail J, Heiden C 1998 Radio
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M. Mu
¨
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Institut fu
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Universita
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t Giessen, Germany
SQUIDs: Biomedical Applications
A major application of SQUID systems (see
SQUIDs: The Instrument) is in biomagnetism, a dis-
cipline where the faint magnetic fields associated with
electrophysiological functions of the heart, brain,
nerves, or muscles are detected with the ultrahigh
field sensitivity of SQUIDs. Biomedical investigations
1109
SQUIDs: Biomedical Applications