﻿ High-Frequency Electromagnetic Coil Resonant              # High-Frequency Electromagnet Using Resonant Technique   Electromagnetic coils such as relays, solenoids, inductors, Helmholtz coils, electromagnets, and electric motors often time required high-current and high-frequency operation.  At low frequency it is straightforward to drive high current through the coil using a waveform amplifier such as the TS250 and the TS200. The coil’s inductance is low enough it can be driven by the amplifier directly as shown in Figure 1. The coil can be modeled (simple model) as a parasitic resistor in series with an ideal inductor. The parasitic resistor resistance is generally small.

Figure 2. Waveform amplifier drives high current through the coil at resonance.

At high frequency on the other hand, the impedance of a coil or inductor increases with frequency. Z = jL. At high frequency the coil impedance is very high such that high voltage is needed to drive high current through the solenoid coil. For example, at 200kHz the impedance of a 2mH electromagnet will be 2512 ohm. If you drive the electromagnetic coil with 40V for example, you would get about 16mA (40V/2512 ohm = 16mA). For most applications, this is not enough current to produce enough magnetic field. For high magnetic field applications, higher current through the coil is desired. To drive a 1A high-current through the coil, 2512V is needed! It is difficult to generate 2kV at 200kHz.

Figure 3. At resonance the inductor and capacitor impedance cancel each other and act like a short circuit.

To operate the coil in resonance mode, a series capacitor is added as shown in Figure 2. The series capacitor impedance has an opposite polarity than the inductance. Thus the capacitor is acting as an impedance cancellation device. It reduces the total impedance. At resonance the capacitor reactance (imaginary portion of the impedance) is completely cancels the inductor reactance. That is the inductor and capacitor reactance are equal magnitude but opposite polarity. Only the inductor’s parasitic resistance remained. With only resistance remained, the waveform amplifier can drive high-current through the circuit (LCR) even at high frequency. This method enables the high-current amplifier driver to drive large current through the high-frequency coil, but it can only operate at a very narrow frequency range near resonance. The disadvantage of resonant technique is that you need to change the capacitance when you change the frequency.

To further understand impedance cancellation at resonance, consider Figure 3 using 2mH solenoid and 200kHz. At resonance the voltage across the capacitor is -2.5kV and the voltage across the coil is +2.5kV. So the net voltage is 0V across the capacitor and inductor in series. Thus the LC is acting as a short circuit at resonance. The lab amplifier (TS250) will only “see” inductor’s parasitic resistor as a load. Since the parasitic resistance is generally small, the waveform amplifier can drive high-current through solenoid coil even at high frequency. Note the sum of voltages in a closed loop is zero as required by Kirchoff’s Voltage Law. Figure 1. Waveform amplifier directly drives an inductor coil with a parasitic resistor.

## Resonant Technique

To achieve high-current and high-frequency electromagnetic field in coils such as relays and Helmholtz coils, resonant technique is used in this application note.  ## Capacitor Selection

Choose the series capacitor with capacitance such that the capacitor reactance is the same as coil reactance at a given resonant frequency.

Using the above example for 2mH Helmholtz coils and 200kHz operation, the series capacitance is calculated 317pF. The capacitor should be high-Q (low ESR) and low ESL (electrostatic inductance). The capacitor must be rated for high voltage. The voltage rating is calculated by the following:

I is the peak current.

Using the above example, the voltage rating must be at least 2.5kV (V = 1A * 2512ohm = 2512V). Add additional voltage rating margin in case higher current is used.

The total resistance is the coil’s AC resistance and the capacitor electric static resistance (ESR) combined. At high frequency the capacitor ESR can be large, sometimes even larger than the coil resistance. Use only low ESR capacitor for resonant technique.

## Coil Selection

If you have the ability to choose your own relay coil or design your own coil, consider the follow criteria.

- The coil must be rated for the current and power (heating) handling capability

o Low resistance to reduce heating and allows higher current

o Consider resistance increases at high frequency due to skin-effect

- Make sure the coil self-resonant frequency is much higher than the operating frequency

- Design the coil to handle high voltage (avoid voltage arc)

Caution

High-current electromagnetic coil discussed above can store enough energy to become an electrical shock hazard. Make sure all electrical connections are insulated with high-voltage insulators. Wires must be rated for voltages rating discussed above. Always disable the waveform amplifier output before connecting or disconnecting the coil and capacitor.

### Table 1. Waveform Amplifier Selection Guide       Visit TS200 Page    ### Related Technical Information

TS250 Price List

50mm diameter 100kHz Helmholtz coil set

207mm diameter (109mm inner) 20mT Helmholtz coil pair

## We offer custom-made coils to meet our client’s specifications. We design and optimize coils and solenoids to produce the maximum magnetic field and operating at the highest possible frequencies. These coils include solenoids and Helmholtz coils for many scientific and research experiments. High frequency magnetic coils are more difficult to design, because of increase in AC resistance and inductance. We consider the coil size, magnetic field, needed driving current, and required frequency. We have a number of coil drivers available such as the TS250 and TS200. Custom-made high current driver is also available. Furthermore we offer complete custom-made solution that include the coil, matching resonant capacitor, and driver. Request a Quote for Custom-Made Coil  ## Matching resonant capacitor, driver, and harness are available. 175mm diameter 80mT 10kHz Helmholtz coil set Six TS250-2 drivers connected in parallel using a custom-made harness to obtain 32A (peak-to-peak) current. 