Design the circuit
Define electrical behavior, components, pads, and interconnects with familiar engineering logic.
Embroidered Component Models
A clear technical reference linking electrical equations, textile geometry, fabrication constraints, and the SoCl design workflow.
Embroidered Resistor
An embroidered resistor is created by stitching a long conductive-thread path on cloth. The resistance is mainly controlled by the thread linear resistance and total stitched length. A meander shape is useful because it fits a long thread path into a compact textile area.
Meander geometry
Length-controlled R
Conductive thread
Resistance model
For SoCl, the parameter named rho should be interpreted as linear thread resistance, RL, in Ω/m. It is not bulk resistivity. The target resistance is converted into the total stitched length needed for the embroidered path.
Electrical model
R = RLLthread
Lthread = Rtarget / RL
P = I2R = V2/R
Lthread = Rtarget / RL
P = I2R = V2/R
Rtarget Desired resistance in ohms (Ω).
RL Linear resistance of conductive thread in Ω/m.
Lthread Total stitched conductor length in meters.
w / stitch width Affects routing area, current capacity, and fabrication tolerance.
Pad geometry Defines electrical connection area for clips, snaps, traces, or stitched interconnects.
Textile factors Stitch density, tension, washing, bending, humidity, and fabric compression can shift the final measured R.
SoCl code relation:
total_length_mm = (R_target / R_L) * 1000. Enter target resistance or path length in the shared EDA dialog. The meander uses a single circular radius (equal X/Y diameter) and is sized from its centreline length, including leads; terminal fill is excluded from the series-length estimate. The two 1210 connection pads remain 2.50 × 2.50 mm with 4.00 mm centre spacing.
Embroidered Capacitor
An embroidered capacitor can be made as an interdigitated planar structure. Neighboring conductive fingers act as electrodes, and the textile/substrate region between them behaves as the dielectric path.
Interdigitated fingers
pF estimate
Fabric dielectric
Capacitance model
Enter a target capacitance in pF in the EDA tool. SoCl calculates the finger count and length for the same IDC pattern using the existing first-order estimate. Manual finger-count and length entry is also available.
Interdigitated capacitor estimate
weff = 2w + s
C ≈ ε0εr[(weffL)/s](N - 1)
CpF ≈ 0.008854187817 εr[(2w + s)L/s](N - 1)
C ≈ ε0εr[(weffL)/s](N - 1)
CpF ≈ 0.008854187817 εr[(2w + s)L/s](N - 1)
N Number of interdigitated fingers. More fingers create more adjacent electrode pairs.
L Finger length parameter used by the layout estimate, in millimeters.
w Conductive stitch or thread width in millimeters.
s Gap between neighboring fingers in millimeters.
εr Relative permittivity of fabric/substrate region.
ε0 Vacuum permittivity, 8.854×10-12 F/m.
Value-to-geometry mapping:
L = C_target / [0.008854187817 × εr × ((2w + s) / s) × (N − 1)]. SoCl searches integer finger counts while retaining the IDC comb pattern and side terminals, with a minimum 20 mm finger length. Direct entry accepts pF or nF through 1.4 nF (1,400 pF). Larger layouts can expand the drawing area; this does not change the physical machine hoop size. Connection pads stay at 2.50 × 2.50 mm with 4.00 mm centre spacing (1.50 mm edge gap), independent of the capacitance. Defaults: w = 0.40 mm, s = 0.70 mm, εr = 1.5. This is the existing layout estimate, not a calibrated IDC field model; verify the fabricated capacitance by measurement.
Embroidered Inductor
An embroidered inductor is modeled as a planar square spiral. The turn count, average diameter, trace width, and spacing control the magnetic field path and therefore the inductance.
Square spiral
Wheeler model
nH estimate
Inductance model
The square-spiral inductor uses a modified Wheeler-style approximation. The important unit check is that davg must be converted from millimeters to meters before calculating inductance in henries.
Modified Wheeler square-spiral model
L = [2.34μ0N2davg] / [1 + 2.75ρfill]
dout = din + 2[Nw + (N - 1)s]
davg = (dout + din)/2
ρfill = (dout - din)/(dout + din)
dout = din + 2[Nw + (N - 1)s]
davg = (dout + din)/2
ρfill = (dout - din)/(dout + din)
N Number of spiral turns.
w Conductive thread/trace width in millimeters.
s Spacing between neighboring spiral turns in millimeters.
din Inner square opening or inner diameter in millimeters.
davg Average diameter; convert mm to m for the H calculation.
μ0 Free-space permeability, 4π×10-7 H/m.
SoCl calculation check: compute
d_avg_m = d_avg_mm / 1000, calculate L_henries, then display L_nH = L_henries * 1e9. Enter target inductance in nH or specify turns and inner diameter in the shared EDA dialog. The 1210 connection pads remain 2.50 × 2.50 mm with 4.00 mm centre spacing. The centre pad requires an insulated jumper to terminal 2; it is shown as a dashed guide and is not stitched across the spiral.
