Instruments For Testing Your Innovations
Figure 1. Cross
This calculator uses advance techniques to calculate magnetic field Helmholtz coils. It is the most comprehensive and accurate calculator available. In addition to magnetic field, it also calculates AC resistance, inductance, power dissipation, resonance capacitance, and much more. It support both solid and Litz wire.
Coil Inner Diameter: Coil copper inner diameter, excluding plastic bobbin. Note the copper inner diameter is not same as the bobbin inner diameter. Copper inner diameter must be larger than bobbin inner diameter. See Figure 1 for details.
Coil Length: Enter the length of the solenoid or coil. See Figure 1 for details.
Number of Turns: Enter the number of turns in the coil or solenoid.
Coil Current: Enter the coil current. For DC
Plastic
Window Calculating Field Variation: This is the distance along the z
Wire Outer Diameter with Insulation: Enter the overall wire diameter, include insulation.
Strand Diameter: For solid wire, enter copper wire diameter WITHOUT coated insulation. For Litz wire enter the single strand diameter WITHOUT coated insulation. This is the bare copper diameter. This diameter is used to calculate the resistance more accurately.
Number of Strands: For solid wire enter 1. For Litz wire enter the number of strands.
Frequency: Enter the operation frequency (sinewave). For DC, just leave the default 1kHz and use the DC parameters calculated below.
Plastic Thickness: Bobbin side thickness. You may enter 0 if you want to exclude bobbin in the calculation.
Capacitor Dissipation Factor: Enter resonance capacitor dissipation factor or loss tangent. For example, Polypropylene film capacitor have a dissipation factor of 5x10^
Mutual Inductance Factor: Enter the mutual coupling factor for the two coils. Most Helmholtz coil coupling factor is 11%. Enter 1.11. The total inductance is calculated by the sum of each coil coil inductance and then multiply by 1.11.
Winding Porosity
Winding Compact
Core Relative Permeability: Enter the core relative permeability constant, k. Enter 1 for air core.
Outputs:
Magnetic Field at Center: The calculated magnetic field at the center between two coils.
Minimum DC Driver Voltage Required: This is the voltage needed for DC magnetic field.
Coil DC Power Dissipation: This is how much power is dissipated for DC magnetic field.
Coil AC Resistance: This is the resistance at the frequency entered above. AC resistance is dominated by proximity effect and increase exponentially with frequency and winding layer. Reduce the number of winding layers, or reduce the wire diameter, or use Litz wire to reduce the resistance.
Coil AC
Minimum Coil+Cap AC Driver Voltage Required: This is the minimum voltage amplitude need to drive the coil using resonance technique. For example, 9.8V means you need a coil driver that can output sinewave from 
Minimum Coil Only AC Driver Voltage Required : Information only. Ignore it.
Coil AC Power Dissipation: This is the AC coil power dissipation at the current entered above.
Inductance: Coil inductance in micro
Resonance Capacitor Capacitance: This is the capacitance needed to form an LC resonant tank. The coil impedance is reduced or canceled using this series resonant capacitor (Figure 4). Click here for more information about series resonant magnetic coil. It is calculated using the coil inductance and the user input frequency. Tip: Generally use Polypropylene film capacitor, especially at higher frequencies. Ceramic capacitor is acceptable if the ESR is low enough and can handle the power dissipation. Class
Resonance Capacitor Voltage Rating: For resonance technique (Figure 4), this is the minimum capacitance voltage rating. This is the sinewave zero
Capacitor ESR: Capacitor resistance at the frequency entered above. Tip: Use Polypropylene film capacitor which has the lowest loss tangent. NPO/C0G (Class
Capacitor Power Dissipation: This is how much power (heat) will be dissipated by the resonance capacitor. Make sure the capacitor can handle the power.
Penetration Ratio: Information only. Proximity effect penetration ratio. Generally keep the ratio less than 0.5.
Skin Depth: Information only. Ignore.
Skin
Total Impedance: This the magnitude of the coil impedance. It includes both the reactive and resistive components.
Number of Layers: Total number of layers of winding.
Coil Layer Height: Total number of layers adding up to the height or thickness.
Average Inter
Gauge 
Diameter 
10 
2.67716 
11 
2.39268 
12 
2.13868 
13 
1.91516 
14 
1.7145 
15 
1.53162 
16 
1.36652 
18 
1.09474 
20 
0.87884 
Gauge 
Diameter 
10 
2.58826 
11 
2.30378 
12 
2.05232 
13 
1.8288 
14 
1.628 
15 
1.45034 
16 
1.29032 
18 
1.02362 
20 
0.8128 
Table 1. Wire gauge diameter with insulation in mm.
Table 2. Gauge diameter without insulation (bare copper) in mm.
Figure 2. Coil winding spacing factor of one.
Figure 3. Ideal compact factor. The distance between two layers is 0.866 of diameter.
Figure 4. High
Figure 5. Dielectric strength reduction over frequency (kHz). Source: UL.








Generally speaking, first priority is to reduce the resonance voltage. That means reduce the inductance. Keep the coil diameter as small possible. The inductance is proportional to the number of turns square. Reduce the number of turns by half will reduce the inductance by a factor of 4. Then increase the current by 2. The magnetic field remains about the same, but the resonance voltage is reduced by 2x.
AC resistance is dominated by proximity effect. Copper wire diameter either too large or too small will increase the resistance. Using the calculator to experiment with the different wire diameter for the lowest resistance. If the resistance is still too high, either use Litz wire or reduce the number of winding layers.
Pay attention to the “inter
Often time and at high frequency and high current, the coil design can only be one layer. More than one layer is not possible due to too high voltage between two layers. You also need to look at the voltage between two loops. This voltage should not be higher than 500V. The voltage between loops is the resonance voltage divided by the number of loops.
You may use “Super Corona Dope” from MG Chemicals # 4226 to enhance the dielectric strength.
As a reminder, you need to use Polypropylene Film capacitor in most cases. The KEM R74 and R76 series capacitors are available from Digi
Here are the steps for choosing capacitors:
1) Us our online calculator to calculate the resonance voltage and capacitor.
2) Choose capacitor with high AC voltage. For example 700VAC, which is the RMS voltage. So the peak voltage is 989V.
3) Choose capacitance that does not derate at your maximum test frequency.
4) Connect capacitors in series to meet the resonance voltage. For example, if the resonance voltage is 5000V, you need to connect 6 capacitors in series. This is one string of capacitors.
5) Connect as many strings of capacitors as need to meet the required resonance capacitance.
Making the capacitor bank:
1) Use a breakable plastic tray, place the capacitors in the tray with the electrical leads (pins) point upward in an array. i.e. 6 x 5, 6 caps in series and 5 strings.
a. Recommended to use 3D printer to print a thin plastic tray.
2) Use the "Super Corona Dope" from MG Chemicals # 4226 to glue all of the capacitor together.
3) Wait for the glue to dry.
4) Gently bent the adjacent (series) leads (pin) toward each other.
5) Use soldering iron to solder the adjacent leads
6) Use a 18 AWG tinted copper wire to solder the input and output of the capacitor network.
Figure 7. Capacitor voltage derating over frequency.