Daniel Højrup Johansen^{1}, Juan D. Sanchez-Heredia^{1}, Vitaliy Zhurbenko^{1}, and Jan H. Ardenkjær-Larsen^{1,2}

This work presents the method of achieving ideal decoupling between elements in a receive coil array. Generally, preamplifier decoupling is limited by nonidealities of the implemented components. It is shown analytically and numerically, that for the ideal (lossless) matching circuits the input resistance of the preamplifier should be zero, while for the realistic lossy case a small negative resistance can be used to achieve ideal decoupling. Here we use a negative input resistance preamplifier (NIRP) to compensate for the loss of the circuit. The analysis is verified experimentally showing a decoupling of -62 dB when a NIRP with an input resistance of -0.023 Ω is used.

The coupling between elements in a receive coil array is primarily determined by the amount of current one coil can induce in another. Hence, increasing the impedance seen by the coils, while being noise matched to the preamplifier, ensures decoupling between elements.

The
principle of decoupling achieved by the matching circuits, described by Roemer
et al. ^{1} and Reykowski et al. ^{2}, is that a parallel resonance is created with
an inductor such that a high impedance is presented to the coil. Hence impeding
the current on the coil. An example of the parallel matching circuit is shown
in Figure 1, where decoupling is achieved when C1 resonates with the equivalent
impedance of C2, C3, Lp and Rp thus forming a parallel resonance. In the
lossless case, this parallel resonance exhibits an infinite Q-factor when the
preamplifier has a zero input resistance. Given that the resistance of the
preamplifier is increased the Q-factor of the parallel resonance is lowered,
the equivalent impedance is also lowered, more current is able to flow in the
coil and thus a worse decoupling entails. In the case of a lossy matching
circuit a zero resistance preamplifier does not yield an infinite Q-factor of
the parallel resonance. To achieve the ideal decoupling the loss of the
matching circuit can be compensated. The loss compensation is realized by an
NIRP with a specific negative resistance such that the impedance seen by the
coil is, theoretically, infinite.

The
decoupling is measured using a system of two small loop coils of 1 cm diameter
separated by a distance of 4 cm connected to a vector network analyzer as seen
in Figure 2. A parallel matching circuit, including active transmitter
detuning, is used as presented by Sanchez-Heredia et al. ^{3}. The coil is an 8 cm loop coil with an
unloaded Q-factor of approximately 350 at 32.13 MHz, corresponding to the
frequency of ^{13}C at 3T. The NIRP is a custom design (based on the
design presented by Johansen et al. ^{4}) where the input impedance can be tuned while
the noise figure remains constant at approximately 0.5 dB.

1. Roemer, P. B., Edelstein, W. A. & Hayes, C. E. The NMR Phased Array. Magn. Reson. Med. 225, 192–225 (1990).

2. Reykowski, A., Wright, S. M. & Porter, J. R. Design of Matching Networks for Low Noise Preamplifiers. Magn. Reson. Med. 33, 848–852 (1995).

3. Sánchez-Heredia, J. D., Hansen, E. S. S., Laustsen, C., Zhurbenko, V. & Ardenkjaer-Larsen, J. H. Decoupling Scheme for a Cryogenic Rx-Only RF Coil for 13C Imaging at 3T. Proc. Intl. Soc. Mag. Reson. Med. 3639 (2016).

4. Johansen, D. H., Sanchez-heredia, J. D., Zhurbenko, V. & Ardenkjær-larsen, J. H. Practical Aspects of Preamplifier Designs for 13C Imaging. in Proc. Intl. Soc. Mag. Reson. Med. (2017).