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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Magn Reson Med. Author manuscript; available in PMC 2010 May 13.
Published in final edited form as:
PMCID: PMC2869245

Noise Figure Limits for Circular Loop MR Coils


Loop coils are the fundamental building blocks of phased arrays. With the advent of parallel imaging using large numbers of loop elements [1] along with high-field MR, the geometric size of the loops is critical in determining detection and/or transmission efficiency. As loop size decreases, the coil noise becomes dominant and adversely affects the realizable signal-to-noise ratio (SNR) by increasing the noise figure (NF) of the detector system. Consequently there are real limits to the gains in SNR that can be achieved as the number of array elements are increased and the size of elements is reduced. These limits depend on coil design and size, field-strength, and array size. The purpose of this study is to determine these relationships in order to optimize array design and to investigate possible limits to the number of channels that can reasonably benefit an MR system.

We use a combination of analytic formulae, numerical EM analysis and experimental measurements to quantify the effect of loop radius, coil design, and number of array elements to determine the practical limits to coil NF over the frequency range 64–400 MHz.


The NF of a resonant coil in dB is NF = 10log [(QU/QL)÷(QU/QL−1)] where QL and Qu are the loaded and unloaded Q. This NF measures the reduction in SNR due to the losses in the loop coil only [2]. NF = 1.77 dB , for example, corresponds to a 50% coil noise contribution. This NF adds directly to the system NF. Losses in the coil stem from: (i) conductor surface resistance; (ii) effective series resistance (ESR) of capacitors; and (iii) solder joint resistance. Conductor loss is calculated from the standard skin depth conduction formula. Solder joint losses are measured by introducing solder joints and observing the effect on coil Q.

Coils are made of 4 mm wide copper (Cu) tape or 1/8” Cu tubing. Coils are loaded with a physiological-equivalent NaCl based agar gel phantom. Theoretical Q is calculated with analytical inductance formulae, with conductor and sample losses determined using full-wave numerical method-of-moments (MoM) EM analysis (FEKO, South Africa). Coil sensitivity ([proportional, variant] B1) was also calculated using FEKO.


Fig.1 shows the NF for a single coil as a function of frequency, coil radius and number of capacitors. The MoM calculations are confirmed by measurements at 64,130, and 400 MHz for 0.5 dB NF, and at 64,130, and 200 MHz for 1.77 dB NF, using loops tuned with 4 capacitors (Δ’s). Results show loops tuned with 2 capacitors actually perform better with smaller radii at 1.77 dB NF, as compared to those tuned with 4 capacitors (Fig. 1; dashed line). This is validated by measurements at 64, 130, and 200 MHz (Fig. 1; Xs). The 1.77dB NF coil (with 50% noise) has radius ~23 mm at 64 MHz decreasing to <10 mm at 400MHz.

Fig. 1
Loop radius vs MR frequency for single tape coils.

Figure 2 compares arrays made with wire loops to arrays made with tape loops [1]. Fig.2(b) shows the NF at 128 MHz determined from Q measurements of the configurations in Fig.2(a). The wire loops behave significantly (0.1–0.4 dB) better.

Fig. 2
(a) Array geometries (i–v) for wire loops and flat tape loops. (b) Effect of array geometry, (i–v), on NF for wire loops (D =46mm) at 128 MHz, and flat tape loops (outer diameter, 44mm; inner diameter, 36mm) at 128 MHz.


We have determined NF values for circular MR coils as a function of radius, frequency and number of tuning capacitors. Increasing the number of capacitors to reduce E-field losses, actually increases NF of loops with small radii (r < 20mm) due to capacitor ESR. For arrays, loops made of Cu wire or tubing have reduced eddy currents and perform better than tape loops. As static field increases, the radii of coils that contribute a NF ≤1 dB, decrease.


Supported by NIH grant RO1 EB007829.


1. Wiggins GC. Proc ISMRM. 2007:243.
2. Edelstein WA. ISMRM 2006, RF Sys Eng Ed. Sess; 2