RF Engineering: Live Construction of A Coil
“Let’s build an RF human coil.”
Hiroyuki Fujita, Ph.D.1,2,3,4,5
with
Tsinghua Zheng, MSEE1,2
1
Quality Electrodynamics (QED), LLC
2
eQED, LLC
700 Beta Drive, Suite 100, Mayfield Village, Ohio 44143
3
Department of Physics, Case Western Reserve University
Department of Radiology, University Hospitals of Cleveland
10900 Euclid Avenue, Cleveland, Ohio 44106-7079, USA
5
School of Information Technology and Electrical Engineering, The University of
4
Queensland, Brisbane Qld 4072, Australia
Introduction
Last year, we gave our live demonstration entitled “Live construction of coils in
60 minutes: an 8-channel cardiac array coil [1].” This is a continued program in
which we will be constructing another RF human coil. Recent advances of MR
scanner design involve an ever-increasing number of receiver channels (32-128)
for faster scans. While 1.5T and 3T fast MRI clinical applications are now
realized and accepted as everyday routine clinical practices, 7T MRI is also
emerging because of its capability to study neurodegenerative diseases, e.g.,
Alzheimer, and biochemical functional imaging to analyze physico-chemical
parameters used for examining tissue morphology, blood flow, metabolism and
chemistry in vivo. Regardless of the field strengths, the key requirements are
maximum achievable signal-to-noise ratio and multi-detector array coil
optimization within the framework of the parallel imaging scheme to enable more
advanced and faster clinical MR scans. Preamplifiers are also one of the key
components in the detector array coils. In this talk, while appreciating the RF coil
theory, we will construct an RF human coil. To prepare ourselves for the
demonstration, the important and fundamental principles of MRI RF array coils
are reviewed. The reader is also encouraged to review our last year’s
presentation which is available online.
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
Background
The subject on modern RF array coil designs is indeed quite deep and requires a
broad-range knowledge of MR physics and electronics. It is informative for the
reader to know that the number of components/parts used in today’s typical
detector array coils, from, say, an 8-channel head coil to a 32-channel head coil,
ranges from 400 to 1500. If one component is broken or damaged, the coil no
longer functions in its optimized way. This should indicate how complex/delicate
today’s array coils are. In order for the RF coil to function properly, every
component of the RF coil must be integrated, assembled (soldered) and
manufactured right. Provided below is the table listing what we typically need
to build an RF coil. Some commercially available sources are given.
Equipment, Parts
Manufacturer
Website
Network Analyzer
Agilent Technology
http://www.home.agilent.com/agilent/home.jspx
DC Power Supply
MASTECH
http://www.mastechpowersupply.com/
Solder Station
Hakko
http://www.hakko.com/
Solder
Kester
http://www.kester.com/
Digital Multi-meter
Fluke
http://www.fluke.com/
Capacitor
ATC, Voltronics
http://www.atceramics.com/
& Materials
http://www.voltronicscorp.com/nonmag.html
Inductor
CoilCraft
http://www.coilcraft.com/
Pin Diode
MaCom
http://www.macomtech.com/
Signal Diode
Microsemi
http://www.microsemi.com/
Resistor
BREL
http://www.brelintl.com/
ODU, Hypertronics
http://www.odu-usa.com/
(Surface
Mount)
Connectors
(RF,
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
DC)
http://www.hypertronics.com/en/Default.aspx
Trimmer Capacitor
Johanson
http://www.johansonmfg.com/
Coaxial Cable
Coast Wire
http://www.coastwire.com/
RF Coil Theory Review
Hoult provides a detailed overview and discussion on the NMR receiver in his
historic paper [2]. Most of today’s RF receive coil designs are based upon the
phased array coil technology proposed by Roemer et al. in 1990 [3], and its
application to volume imaging was discussed by Hayes et al. in 1991 [4]. The
reader is also encouraged to read a detailed review of array coil theory and
application by Wright and Wald [5]. It is well known that a small surface coil
yields higher SNR at the distances closer to the surfaces of the coil when
compared with that of a volume coil such as the birdcage coil [6]. On the other
hand, a small surface coil B1-sensitive region is much smaller than that of a
volume coil. What is remarkable in the phased array coil approach is that the
high SNR associated with a small surface coil can be achieved and maintained
over an extended FOV, by using a set of RF coils, which may be comparable to
that of a volume coil. This is enabled by the development of various array coil
designs for imaging applications of interest and the techniques to decouple the
mutual inductances and thus the cross talk among the array coil elements.
Adjacent coil elements are often partially overlapped to cancel the mutual
inductance between the elements. Next nearest and other coil elements can be
mutually decoupled by the use of a low input impedance (typically less than 5
Ohms) preamplifier decoupling circuit. Other decoupling techniques and
methods are described briefly later in this paper. For detailed discussions of
low noise amplifiers, the reader may refer to [7]. What the low input impedance
preamplifier effectively does in conjunction with a coil matching/decoupling
circuit is to eliminate the current flow in the coil element loop, thereby eliminating
the magnetic fields induced in the neighboring coil elements, as shown later in
this syllabus contribution. In designing array coils, baluns and considerations
pertaining to cable routing are also important design factors to consider. Shown
in Figure 1 is the illustration of how the cables couple with the patient and why
baluns need to be implemented. The details are discussed elsewhere [8].
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
Sample
Figure 1 A side (sagittal) view of MRI scanner showing the electromagnetic
coupling due to the stray capacitances present. Baluns are added to block the
common mode current and allow the differential mode current to flow.
Signal-to-Noise Ratio
SNR is one of the most important parameters to be optimized in MRI
applications, and its detailed discussion is given in [9]. (It is, however, noted
that SNR is destined to be degraded or lowered from the starting point, i.e., the
signal source, to the end point of the receive chain. Thus, the question is how
to minimize the loss of SNR in that process.) Here, it is essential to understand
how SNR relates to the coil-related parameters. The signal is written as
S ∝γ
3
2
xy
0
1
BB
(r )
Eq. (1)
where γ is the nuclear gyromagnetic ratio, B0 the static magnetic field, and B1xy(r)
the RF magnetic field produced by a coil with a unit current 1A. Thus, in
designing a coil, B1xy(r) must be optimized. What this means is that the coil size
over a target FOV and the distance from the FOV both need to be appropriately
chosen to maximize B1xy(r). The size to be chosen also depends upon the
number of available receiver channels, in general.
On the other hand, NMR/MRI noise is thermal noise, and the noise generated
from the coil is given by
N = 4kTΔfR
Eq. (2)
where k is the Boltzmann constant, T the temperature in K, Δf the bandwidth,
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
and R=RC+RS. It is noted that RC is the coil resistance and RS the sample
energy loss (i.e. the equivalent series resistance due to the induced eddy current
losses in the conductive sample). Combining Eqs. (1) and (2), SNR can be
expressed by using the coil-related parameters as
S
∝
N
xy
B (r )
R +R
1
C
Eq. (3)
S
To optimize SNR, B1xy(r) can be maximized by having the coil closer to the
sample, and RS can be minimized by choosing the coil size to match the target
FOV. In fact, Wright and Wald compare an N-element array to a single coil with
respect to the resultant SNR while their overall coil dimension remains
unchanged [5]. For example, they showed that the SNR improvement
disappears at the depth equal to the diameter of the array, when comparing a
single coil with an 8x8 array, a 4x4 array and a 2x2 array. However, for the
distances in-between, the SNR curves vary depending upon the number of
receiver channels. If each coil is made too small, then the coil resistance loss
dominates the sample noise. This implies that an optimization is required for a
given specific application (e.g., target depth and available number of receiver
channels). RC is minimized by making the unloaded coil Q high. It is well known
that at low-B0 field systems ( ≤ 0.3T) the coil resistance is dominant or at least
comparable to the sample noise, but at 1.5T and above, the sample noise
dominates (i.e. RS >> RC). Furthermore, it is useful to be aware that if two coils
yield the same relative sensitivity in free space and if they are each sample noise
dominated, the two coils have the same absolute sensitivity [10]. This
reference discusses the coil unloaded Q, loaded Q, and the sensitivity in detail,
which should be useful to the coil engineer.
Low Noise Preamplifier
As mentioned earlier, a preamplifier is one of the key hardware elements in an
RF coil from a standpoint of SNR performance. Furthermore a preamplifier plays
a critical role in designing a detector array coil. It is noted that the characteristic
parameters of preamplifiers, such as the noise figure, certainly affect SNR.
Below is a brief summary of the function of a preamplifier. The electromotive
force or induced voltage (i.e., signal) in a coil is very small and typically on the
order of a few μV. This small signal is amplified to a few mV by a preamplifier
whose gain is, say, 30dB (i.e., 1000 times greater).
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
One of the parameters to measure the performance of the preamplifier is the
noise figure (NF) discussed in detail elsewhere [2, 11]. Depicted in Figure 2 is a
simple model for preamplifier noise.
Np
V
Ns
r
Figure 2 Depiction of a preamplifier noise model. V, NS, r and NP denote the
signal, the noise generated by the resistance r of the input signal source and the
noise generated inside the preamplifier, respectively.
In Figure 2, V, NS, r and NP denote the signal, the noise generated by the
resistance r of the input signal source and the noise generated inside the
preamplifier, respectively. Using these quantities, NF is defined as
NF = 10 log ( N
2
P
10
+ NS
N
2
2
)
where
N
S
= 4kTΔfr
Eq. (4)
S
The industry standard preamplifier NF is currently less than 0.5 dB. It is also
well-known that the first NF and gain have the most significant impact in the
entire electronics circuit, which is often cascaded, as shown in low noise
amplifier design textbooks such as [7, 11]. Noise is generated in any passive
elements, including cables, in any electronics that dissipates power. This is the
reason that most detector array coils have preamplifier integrated design, which
is to minimize undesirable noise contributions. As seen later in this paper, the
multi-detector array is the key hardware component needed for today’s
advanced MRI applications. These array coils are constructed of many (32-128)
detectors. As emphasized again, a key feature of these detectors is the
preamplifier. These preamplifiers serve many functions beyond the simple
amplification of the signal. One additional critical function, as shown later, is to
aid in the decoupling of the individual detectors from the others, which is critical
for the optimal performance of parallel imaging. An additional feature of modern
preamplifiers is that they must be very small, so that as many detectors as
possible can be tightly packed together to form an optimized array.
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
A Single Coil Model – A Building Block
To understand how the detector array coil works, we start with a schematic
representation of a single coil, a building block, including a simplified preamplifier
decoupling circuit shown in Figure 3. This coil circuit is a building block of an
array coil. L1 and R1 represent the coil inductance and resistance (typically
around 0.5 Ohms in air and approximately 5 Ohms when placed on a phantom),
respectively. C1 and C2 are tuning and matching capacitances, respectively.
L2 is a matching inductor that plays an extremely important role as we will
discuss later; that is, a part of L2 functions to match the coil impedance to 50
Ohms together with C2 when looked at from the side of the preamplifier. At the
same time, L2 achieves a parallel resonant circuit formed with C2, in particular,
when the input impedance of the preamplifier, rpreamp, becomes small (say, 0 to 2
Ohms). What this means is that when looked at from the side of the coil, the
impedance is infinity, thereby, a high-impedance or open circuit. What is
extremely important to note here is that the current cannot then flow in an open
coil, which eliminates the possibility of producing any induced magnetic field
through non-zero mutual inductances present among all the neighboring coil
elements. This is the underlying principle that explains why the cross talk among
all coil elements can be eliminated. This decoupling mechanism is explained in
more detail later in this paper. Note also that the Q of the coil (characterized by
C1, L1 and R1), when the decoupling circuit is in effect, remains unchanged. It is
worth mentioning here that the original signal source is changed from the current
source (without preamplifier decoupling) to the voltage source (with preamplifier
decoupling) that contains all the necessary information without losing the
integrity of the original signal information.
Figure 3 A single coil model with a low-input impedance preamplifier.
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
Preamplifier Decoupling
While other decoupling techniques are available, in this contribution, we mainly
focus on a system of two coupled coils and see how the decoupling between the
two coils is enabled by preamplifier. Shown in Figure 4 is a schematic
representation depicting two coils, Coil 1 and Coil 2, which are coupled through
the mutual inductance, M12. Coil 1(2) is represented by its self-inductance, L1(2),
resistance, R1(2), and capacitance C1(2). The signal induced in Coil 1 is given by
Vsignal, and the output voltage is Vout. When the AC current, I1, flows in Coil 1, the
induced AC current, I2, will flow in Coil 2 through the non-zero mutual coupling
between the two coils.
Figure 4 A system of two coils coupled through the non-zero mutual inductance.
Thus, the output voltage is expressed, assuming the harmonic time dependence
(i.e., e-iωt), as
⎛
⎛
1 ⎞ ⎞⎟
⎟ I 1 + iωM 12 I 2
Vout = Vsignal + ⎜⎜ R1 + i⎜⎜ ωL1 −
ωC1 ⎟⎠ ⎟⎠
⎝
⎝
Eq. (5)
This equation is essential to understand why the coil needs to be resonated at
the target Larmor frequency and how the preamplifier decoupling works. First,
the second term in the right hand side in Eq. (5) associated with I1 may be
realized as the noise related to Coil 1, and the third term associated with I2 is
recognized as the noise due to the coupling between Coil 1 and Coil 2. The
noise related to Coil 1 can be minimized by tuning and matching Coil 1 for its
resonance, i.e., the imaginary part of the term associated with I1 vanishes, and
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
we are left with the intrinsic real resistance R1. For decoupling, it is required that
the third term, i.e., the noise through the mutual coupling, in the right hand side
in Eq. (5), iωM12I2, be zero. For this condition to be satisfied, we can arrive at two
cases: either M12=0 or I2=0. M12=0 corresponds to the case where the two coils,
Coil 1 and Coil 2, are overlapped to null the mutual inductance between the two
coils. Capacitive decoupling may be employed here to cancel the mutual
inductance [12]. The principle behind the capacitive decoupling is that the
non-zero mutual impedance is modeled as an inductance and the inductance is
canceled by the addition of capacitance (i.e., the two coils are connected by a
capacitor). I2=0 corresponds to the case of so-called preamplifier decoupling.
Figure 5 A system of two coils coupled through the non-zero mutual inductance.
A low-input impedance preamplifier is added to Coil 2 for preamplifier
decoupling.
Now Coil 2 is integrated with a preamplifier decoupling and matching circuit as
shown in Figure 5. Here, L2 is a matching inductor, and the input impedance of
the preamplifier is shown as rpreamp. It is recognized that as rpreamp becomes 0, the
inductor L2 and the capacitor C2 can be chosen to form a parallel resonant circuit
at the target MR frequency, which yields a high impedance (i.e., infinity,
theoretically speaking). Coil 2 then becomes an open circuit, and there is no
current flow, i.e., I2=0. At this stage, even if the mutual coupling between the two
coils is not zero, Coil 1 and Coil 2 are decoupled via the use of a low-input
impedance preamplifier. This is the art of preamplifier decoupling. Furthermore,
it is emphasized that the matching inductor, L2, now denoted as L2A and L2B in
Figure 6, indeed plays several crucial functions, which may not be too obvious,
as illustrated in Figure 6. First, L2A functions to match the coil impedance to 50
Ohms together with CM when looked at from the side of the preamplifier (III Æ II).
At the same time, L2A (and L2B and C2 which are adjusted to be “short,” i.e., the
series resonance) achieves a parallel resonant circuit formed with CM, in
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
particular, when the input impedance of the preamplifier, rpreamp (approximately
RL2B+RC2), becomes small (say, 0 to 2 Ohms). What this means is that when
looked at from the side of the coil (I Æ II), the impedance is infinity, thereby, a
high-impedance or open circuit. In other words, the decoupling circuit
considered here and shown in Figure 6 (sandwiched by two dashed lines) is
equivalently a mismatched
λ
4
(quarter wavelength cable) circuit; one end open
and the other end short. It is furthermore instructive and meaningful to view the
circuit (regions denoted as II and III) that each region may be represented as a
corresponding
λ
4
circuit with its characteristic impedance Z0. For a
transmission line that is an odd multiple of quarter wavelengths long terminated
in an impedance ZLoad at the far end presents an input impedance
2
Z in =
Z0
where Z0 = the characteristic impedance. This equation in turn reads
Z Load
Z 0 = Z in Z Load . In other words, a quarter-wave section can be used to match
any two impedances by choosing the characteristic impedance of the matching
section appropriately. This is what is happening in sections II and III of Figure 6.
As each region has its associated and appropriate characteristic impedance, the
impedance transformations from I to II to III and in the reverse directions are
executed in a correct and consistent manner. With this quarter-wave matching
section mechanism, we turn to the preamplifier side.
A preamplifier is noise matched.
What this means is that for a given field-effect
transistor (FET) there exists a signal-source impedance that optimizes or
minimizes the noise figure. Thus, the optimum noise figure can be achieved
when the impedance of the receive coil matches the source impedance of the
FET. The FET impedance is relatively high (>>50 Ohms), and thus there exists
an impedance transformer consisting of L2B and C2 together forming a λ/4 circuit
in section III of Figure 6 that transforms 50 Ohms to the high input impedance of
the FET for the lowest noise figure. An optimal impedance for the lowest noise
figure of typical FET is on the order of a few-hundred Ω. Thus, L2B and C2
transform the coil’s 50 Ohms to the high impedance of FET for the lowest noise
figure. As an additional note, the input impedance of the preamplifier in Figure 6
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
is approximated as the sum of resistances associated with L2B and C2. However,
since the Q of the capacitor is typically much higher than that of the inductor, the
input impedance is dominated by the contribution of the resistance associated
with the inductor.
λ
λ
4
4
Figure 6 The matching inductor L2 (L2A+L2B) plays several critical functions in
preamplifier decoupling. Each quarter-λ circuit has its characteristic impedance
for necessary impedance matching.
With this preamplifier decoupling method in mind, it is straightforward to extend
the array concept to 8-channel, 16-channel, and even larger numbers of
channels. Figure 7 shows an 8-channel array coil to illustrate the concept.
Each coil has its own B1 sensitivity profile as shown in Figure 8. Because the
coil is a surface coil, which yields a high SNR only over a small region, high SNR
can be generated over a larger field of view or region of interest, i.e., FOV or ROI,
if each channel SNR is combined by a sum-of-squares method [3], for example.
This achieves an overall high SNR over the target FOV, illustrated in Figure 8.
The number of the coil channels is determined by the number of available
receiver channels and the target FOV or ROI while considering the appropriate
size of each coil with SNR optimization in mind, as already discussed earlier.
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
There are many references that discuss different array coil designs and their
principles for various imaging applications at different field strengths [13]. No
matter what RF coil design we choose, we need to construct it correctly, and it is
the topic of today’s demonstration.
Coil 1
Coil 2
Coil 3
Preamp
Preamp
Receiver
Coil 4
Receiver
Reconstruction
Reconstruction
Preamp
Receiver
Receiver
Coil 8
Coil 7
Preamp
Preamp
Receiver
Reconstruction
Receiver
Receiver
Reconstruction
Reconstruction
Reconstruction
Coil 6
Preamp
Preamp
Preamp
Receiver
Coil 5
Reconstruction
Reconstruction
Digital MUX
Figure 7 Schematic representation of a detector array coil (8-channel).
Figure 8 Depiction of B1 sensitivity profile in an array coil.
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
References
[1] Fujita H, Zheng T. Live construction of coils; let’s build an RF human coil, In:
ISMRM 19th Scientific Meeting Weekend Syllabus 2011.
[2] Hoult DI. The NMR receiver: a description and analysis of design. Progress in
NMR spectroscopy 1978; 12:41-77.
[3] Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR
phased array. Magn Reson in Med 1990; 16:192-225.
[4] Hayes CE, Hattes N, Roemer PB. Volume imaging with MR phased arrays.
Magn Reson in Med 1991; 18:309-319.
[5] Wright SM and Wald LL. Theory and application of array coils in MR
spectroscopy. NMR in Biomed 1997; 10:402.
[6] Hayes CE, Edelstein WA, Schenck JF, Mueller OM, Eash M. An efficient,
highly homogeneous radiofrequency coil for whole-body NMR imaging at 1.5T.
Journ of Magn Reson 1985; 63:622-628.
[7] Kucera J, Lott U. Low noise amplifier design, In: Golio M. The RF and
microwave handbook. CRC Press, 2001; 548-571.
[8] Yang X, Zheng T, Fujita H. T/R switches, baluns, and detuning elements in
MRI RF coils, In: ISMRM 14th Scientific Meeting Weekend Syllabus 2006.
[9] Hoult DI, Richards RE. The signal to noise ratio of the nuclear magnetic
resonance. Journ of Magn Reson 1976; 24:71-85.
[10] Froncisz W, Jesmanowicz, Kneeland JB, Hyde JS. Counter rotating current
local coils for high-resolution magnetic resonance imaging. Magn Reson in Med
1986; 3:590-603.
[11] Horowitz P, Hill W. In: Chapter 7 The art of electronics 2nd edition.
Cambridge University Press, 1989; 434-435.
[12] Li BK. The design and analysis of high frequency phased array coils for MRI.
Ph.D. Thesis. The University of Queensland, 2006; 84-89.
[13] Fujita H. New Horizons in MR Technology: RF Coil Designs and Trends.
Magnetic Resonance in Medical Sciences, Vol. 6, No. 1, 2007; 29-42.
Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)