﻿ Magnetic Field Calculator                   Figure 1. Cross-section view of the magnetic coil showing diameter, coil length and width. Support both solid and Litz wire, calculates AC resistance over frequency and temperature, support resonance technique calculation, and much more.

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-related calculations, this is the DC current. For AC-related calculations, this is the current amplitude which is defined as zero-to-peak. For example, 5A means the current is a sinewave from -5A to +5A.

Distance From Plastic Surface: If you need to calculate the magnetic field outside of the coil, enter the distance from the bobbin surface.

Distance from the center of the inside of the coil: If you need to calculate the magnetic field intside of the coil, enter the distance from middle of the coil. Figure 2.

Frequency: Enter the solenoid/coil operation frequency (sinewave). For DC, just leave the default 1kHz and use the DC parameters calculated below.

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.

Capacitor Dissipation Factor: Enter resonance capacitor dissipation factor or loss tangent. For example, Polypropylene film capacitor have a dissipation factor of 5x10^-4.

Plastic Thickness: Bobbin side thickness. You may enter 0 if you want to exclude bobbin in the calculation.

Winding Porosity-Factor: This factor is used for calculating the proximity effect for AC resistance. Typical value is 0.85.

Core Relative Permeability: Enter the core relative permeability constant, k. Enter 1 for air core.

Winding Compact-Factor: Enter the coil winding density compact factor. If the coil is wound such that the distance between two copper layers is equal to the diameter (Figure 3), the compact factor is equal 1.0.  However, practical wounding is shown in Figure 4. This is the most tightly wound with no space wasted. The ideal compact factor is 0.866. A practical compact factor range is 0.88 to 1.0. Typical compact factor is 0.9.

Outputs:

Magnetic Field From Plastic Surface: The calculated magnetic field outside the coil using the distance entered above. Valid for air core (permeability = 1) coil only. For coil with a core (permeability > 1), the magnetic field outside the core cannot be calculated accurately.

Magnetic Field From Center: The calculated magnetic field inside the coil using the distance entered above. Magnetic field vs distance is valid for air core (permeability = 1) coil only. For coil with a core (permeability > 1), the magnetic field inside the core is approximately constant. To calculate the magnetic field inside the core, enter 0 for “Distance from the center of the inside of the coil”.

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-to-DC Resistance Ratio: Information only.  This is the ratio of AC resistance to DC resistance.

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 -9.8V to + 9.8V (or 19.6Vpp).

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-Henry (uH). Tip: For high frequency coils, keep the inductance as small as possible. It is better to reduce the number of turns, but increase the current by the same proposition.

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 5). 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-1 dielectric (i.e C0G/NPO) has lower loss than class-2 (i.e X7R).

Resonance Capacitor Voltage Rating: For resonance technique (Figure 5), this is the minimum capacitance voltage rating. This is the sinewave zero-to-peak amplitude voltage across the capacitor. This is also the voltage across the coil. Tip: capacitor voltage rating is degrades at higher frequencies, Figure 6. When design high frequency coil, this is the highest priority. Maximum practical voltage is about 15kV.

Capacitor ESR: Capacitor resistance at the frequency entered above. Tip: Use Polypropylene file capacitor. NPO/C0G ceramic capacitor maybe okay as long as the ESR is low enough and the capacitor can handle power dissipation.

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-Effect (Litz) Resistance: Information only. Ignore.

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-Layer Max Voltage: This is the voltage between two adjacent copper layer. Make sure the voltage is less than the dielectric breakdown of the wire coating. Typical breakdown is 500-1000V at DC. Breakdown derates at higher frequency.

 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 3. Coil winding spacing factor of one. Figure 4. Ideal compact factor. The distance between two layers is 0.866 of diameter.

Figure 2. Calculated magnetic field at distance x from the center. Figure 5. High-current Waveform Amplifier drives coil and resonance capacitor.  Figure 6. Dielectric strength reduction over frequency (kHz). Source: UL.

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### Coil Input Parameters

Coil Inner Diameter (mm):
Coil Length (mm):
Number of Turns:
Coil Current (A):
Distance From Plastic Surface (mm):
Distance from the center of the inside of the coil (mm):
Frequency (kHz):
Wire Outer Diameter with Insulation(mm):
Strand Diameter (without Insulation):(mm):
Number of Strands:
Capacitor Dissipation Factor:
Copper Temperature (C):
Plastic Thickness(mm):
Winding Porosity-Factor:
Core Relative Permeability, k:
Winding Compac-Factor:

Magnetic Field From Plastic Surface(mT):
Magnetic Field From Center (mT):
Coil Outer Diameter(mm):
Copper Wire Lenghth (ft):
DC Calculated Output Parameters
DC Resistance(Ohm):
Minimum DC Driver Voltage Required (V):
Coil DC Power Dissipation (W):
AC Calculated Output Parameters
Coil AC Resistance (Ohm):
Coil AC-to-DC Resistance Ratio:
Minimum Coil+Cap AC Driver Voltage Required (V):
Minimum Coil Only AC Driver Voltge Required (V):
Coil AC Power Dissipation (Wrms):

Inductance (uH):
Resonance Capacitor Capacitance (nF):
Resonance Capacitor Voltage Rating (kV):
Capacitor ESR (Ohm):
Capacitor Power Dissipation (Wrms):

Penetration Ratio:
Skin Depth (mm):
Skin-Effect (Litz) Resistance (Ohm):
Total Impedance (Ohm):
Number of Layers:
Coil Layer Height(mm):
Average Inter-Layer Max Voltage:
Copper Wire Lenghth (meter):

## High-Voltage Safety

- Caution: High voltage. Both the capacitor and the coil are high voltage at resonance.

- High voltage and high frequency can couple the electric field to your fingers and hand even without physically touching the coil or the capacitor.

- It is strongly recommended you use a plastic safety cage to enclose the capacitor and coil. At moderate high voltage and frequency (5kV and 10kHz), human hands must be least 6 inches away from any part of the coil and capacitor. At higher voltage and frequency (10kV and 100kHz), at least 12 inches.

- To start with, you may use a plastic container, flip it over and cover the capacitor and coil.

- It is recommended that you put the coil and capacitor on a plastic tray or platform and raise it above the table by at least 6 inches. This will prevent the electric field from coupling to the table frame which is made of metal.

- Use high-voltage wire for the high-voltage portion of the connection, namely the wire connecting the capacitor and the coil.

- Keep the ground return wire (or any low-voltage wires) at least 1 inch from any part of the coil and capacitor. If the low-voltage wire and the high-voltage wire are too close, dielectric breakdown may occur. For example, we used 40kV wire for a 15kV and 250kHz capacitor. When the ground return wire got close to the high-voltage wire, the strong electric field burned the 40kV wire insulation. At 250kHz, the dielectric strength have severely degraded to well less than 15kV.

- Avoid sharp or pointed metal such as solder joints or tiny wire sticking out. Sharp point will amplify the electric field and may cause corona or arc. Use a file to polish any sharp metal and make it round. You may use “Super Corona Dope” from MG Chemicals # 4226 to coat any high-voltage metal to avoid corona or arc.

## Coil Design Tips

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-layer max voltage”. This voltage must be within the dielectric breakdown strength of the copper wire enamel. Furthermore, the dielectric strength is degraded by high frequency AC electric field. The inter-layer max voltage should in the range of 500V.

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-Key. Its voltage needs to be high enough at resonance frequency. Polypropylene Film capacitor voltage rating derates a lot at high frequency. Below figure 7 is an example of capacitor voltage de-rating.

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. 