This work will be of interest of those interested in the design of gradient/shim coils for conventional and hybrid MRI scanners. This study aims to present two methods for designing planar gradient coils with emphasis in the simplicity of coil manufacturing and coil performance: $$$\eta^{2}/R$$$ and $$$\eta^{2}/L$$$; where η is the coil sensitivity, L and R are coil inductance and resistance, respectively. The MRI market is broadly dominated by 1.5T whole body scanners. Therefore, in the last decade whole-body gradient coils had all the attention from coil designers to mitigate limitations demanded by the high field strength and fast sequences. However, planar gradient coils have received limited attention despite the extensive use in low field MRI scanners. Designers dedicated to architect planar gradient coils focused their work in variations of the target field method and sometimes the effect of the pole is not considered due to the heavy calculation required for simulating the magnetization effect produced by the gradient field. Moreover, shielding, force balancing and simplicity of construction are not usually considered due to the constrained space (see Figure A) and the limitation of the applied method. The lack of active shielding is justified by the use of a grid of high resistivity material (eddy device) located between the pole face and the gradient coil, leaving the pole ring exposed to the induction of eddy currents. In addition single layer coil create additional difficulty for an appropriate force balancing. In this work convex optimization is used to minimize the coil conductor assuming Euclidian distance¹ and the Manhattan distance, respectively. Different from minimizing ||j||₁¹, in this work the Manhattan (l1-norm) distance of the coil conductor is calculated assuming that the distance between two points is calculated at right angles; which is equivalent to min||J||₁. J and j are the current density vector and magnitude, respectively. Convex optimization was used to minimize the joule loses in gradient and shims coils¹. It was demonstrated that compact circle-shape like winding patterns of reduced conductor length generates higher performance $$$\eta^{2}/R$$$ compared to that produced by coils designed using minimal resistance approach¹. Compact winding minimizes the induction of eddy currents in the pole ring as the coil most external turn is far from the ring (see figure B for reference). However, simplicity of manufacturing where the wires may be placed by hand is highly desirable as one of the ways to reduce cost. Sections of straight wires certainly facilitate the coil manufacturing. This type of current pattern are obtained by minimizing the joule power and applying convex optimization assuming that the coil conductor length is minimized using the Manhattan norm. The optimization problem is stated as $$$min\left\{max\bf ||J_\it{i}||_{\it{2}}\normalsize \sum_i^NA_{i}\bf||J_\it{i}||_{1}\right\}$$$ subject to field, force/torque, shielding and maximal current density Jo constraints. A total of sixteen planar gradient coils were designed using min||J||₁ and min||J||₂. The weighting factor α was used to trade the minimization of the conductor length and resistance. Coil performance and force were evaluated for each strategy and finally two planar gradient coils were designed for each strategy considering the magnetization effect of the iron pole² (the yoke and the permanent magnet were not considered). The maximal current density was constrained to a target value for all designs. The coil diameter was set to 540 mm, the axial position at ±150 mm; a gradient of 40 mT/m and maximal non-linearity of 5% was set as target field within 16.5 mm DSV. Constant wire width of 4 mm was used and Bo magnetic field profile was provided by the magnet vendor (0.35T). Figure C shows a current pattern corresponding to min||J||₁; the pattern shows a typical D-shape like winding while figure D describes a bean-shape resulting from min||J||₂. The pattern showed in D is smooth and that described in figure C has sections of straight wires. Figure E, shows a typical resistance minimization design where the coil covers the whole coil surface domain. Inductive interactions are more likely to occur between this type of configuration and the pole ring due to close proximity between them. However, residual eddy currents for X/Y coils are smaller than 1%; contrary Z coil residual eddy can be as high as 30% but this case is not presented here. Figure F, shows that coils designed using min||J||₂ exhibits better $$$\eta^{2}/R$$$ than that using min||J||₁, mainly due to the shorter conductor length and lower resistance. When α->1 the coil tends to occupy the whole surface hence increasing the wire length and as results the resistance. This effect, however works in favour of $$$\eta^{2}/L$$$ (figure G) and again, in detriment of the force exerted on the coil winding (figure H). Figures I,J and K, describe the planar coils designed considering the iron pole². The iron pole increases the field 1.8 but increases L as much as twice the inductance when no iron is present. Patterns in Figures I and J, show simplicity and compact winding compare to that of figure K. Reverse turns appear in K to compensate the pole effect over the field linearity. The coil performance in I and J are similar but superior to coil pattern in K; the residual eddy in the DSV was 0.05%.