Phased Array Decoupling Calculator

In MRI phased arrays, mutual coupling between adjacent loop elements degrades noise correlation and parallel imaging performance. Three decoupling strategies are analysed: geometric overlap (sets mutual inductance to zero), capacitive decoupling (series capacitor between elements), and preamplifier decoupling (low-Z preamp via λ/4 cable).

Equations & Parameters ▸

\(M=\mu_0\sqrt{r_1 r_2}\!\left[\left(\tfrac{2}{k}-k\right)\!K(k)-\tfrac{2}{k}E(k)\right],\quad k^2=\tfrac{4r_1 r_2}{(r_1+r_2)^2+d^2}\)

r	Loop radius (mm). Identical elements assumed.
d	Centre-to-centre distance between adjacent loops (mm).
f	Larmor frequency.
Z₀	Coaxial impedance. Sets λ/4 cable length for preamplifier decoupling.
Z_preamp	Preamplifier input impedance (Ω). Typical: 1–4 Ω. Lower = better decoupling.
Overlap decoupling	Overlap adjacent loops by ~15% of diameter. Mutual inductance cancels.
Capacitive decoupling	Insert a capacitor C_d between element centre conductors.
Preamp decoupling	λ/4 coax transforms low Z_preamp to high impedance in series with loop.

Physical constants used

µ₀	4π×10⁻⁷ H/m
¹H γ/2π	42.577 MHz/T (Larmor frequency per Tesla)
¹H at 1.5 T	63.87 MHz
¹H at 3 T	127.74 MHz
¹H at 7 T	297.7 MHz
σ_muscle @ 128 MHz	≈ 0.77 S/m
ε_muscle @ 128 MHz	≈ 58
IEC SAR limit (WB normal)	2 W/kg (over 6 min)
IEC SAR limit (head)	3.2 W/kg (over 10 min)

Inputs

Loop radius, r

Centre-to-centre distance, d

adjacent elements

Frequency, f

MHz

Larmor frequency

System impedance, Z₀

coax impedance

Preamp input impedance, Z_preamp

lower = better decoupling

Results

Coupling

Mutual inductance, M—

Coupling coefficient, k—

Isolation without decoupling—

Overlap Decoupling

Recommended overlap distance—

Overlap fraction—

Note—

Capacitive Decoupling

Decoupling capacitor, C_d—

Insertion loss (estimated)—

Preamplifier Decoupling

λ/4 cable length—

Z_high (at preamp)—

Estimated decoupling—

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