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Using high frequency Helmholtz coils

03 Feb 2016  | KC Yang

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A pair of high frequency coils can be model as shown in figure 2. Each coil can be modelled as a parasitic resistor in series with an ideal inductor. The parasitic resistor resistance is generally small. For most high frequency Helmholtz coils application where the testing frequency is well below the self-resonant frequency, this model is sufficient.

If the Helmholtz coil operating frequency is close enough to its self-resonant frequency, the circuit model must also include its parasitic capacitances (CP1 and CP2). The parasitic capacitors are parallel to each inductor and resistor in series as shown in figure 3.

Figure 3: High-frequency Helmholtz coils are modelled as two LCR circuits connected in series.

The parasitic capacitance and inductance formed a self-resonant frequency. Although the coils are designed to be as closely match as possible, but some small variations between them are expected. Each coil has its own series resistance and parasitic capacitance. The parasitic capacitance and the coil inductance formed a self-resonant frequency.

High Frequency Helmholtz Coils Connections
High frequency Helmholtz coils may be connected in series (figure 2) or in parallel as shown in figure 4. Series connection allows the same electrical current flow through the two magnetic coils. Generally series connection enables the highest current and thus highest magnetic field. However, because two coils are in series, the total impedance is also double. Higher impedance may require higher driver amplifier voltage. If used resonant techniques described below, the impedance is reduced.

Figure 4: Helmholtz coils are connected in parallel.

The advantage of parallel Helmholtz coil connection is lower impedance. In fact the impedance is cut in half, but the current is also cut in half (current is split into two). Thus lower the magnetic field. Parallel connection is acceptable if the required magnetic field density is achieved at half the current and low impedance is required such as the case of low-voltage amplifier driver. More details on Helmholtz coil impedance below in the Direct Drive Method section.

Driving High Frequency Helmholtz Coils
There are three ways to produce high frequency AC magnetic field. The first method is direct drive method. This method is the simplest way to produce magnetic field for testing. It is very easy to vary the frequency and magnetic field under test. The second method is series-resonant method. This method is a powerful way to produce high magnetic field and very high frequency in the order hundredskHz or even MHz. The third way is using a new current-amplified resonant method. This method generates the highest magnetic field density. The below sections will describe each method.

Direct Drive Method
If the experiment is low frequency or the coils are low inductance or both, the Helmholtz coils may be driven directly using a waveform amplifier driver such as the TS250 Waveform Amplifier [insert hyperlink] from Accel Instruments [insert hyperlink]. Because of low frequency or low inductance, the coil's impedance is low enough it can be driven by an amplifier directly as shown in figure 5 and figure 6.

Figure 5: TS250 Waveform Amplifier drives a pair of Helmholtz coils.

Figure 6: Circuit representation of a Waveform Amplifier directly drives a pair of Helmholtz coils connected in series.

Use the Equation-1 to calculate the coil current for a desired magnetic field. Then use Equation-2 to calculate the maximum voltage is needed. Note the small parasitic resistance is ignored. The maximum voltage is when the current and frequency are both at maximum. The next step is to drive the Helmholtz coils with a high-current and high-frequency amplifier driver such as the TS250 function generator amplifier.

Series Resonant Method
If the generated magnetic field is high frequency, Helmholtz coils impedance increases with frequency (Z = jwL). At high frequency the coil impedance is very high such that high voltage is needed to drive high current through the coil. For example, at 200kHz the impedance of a 2mH coil will be 2512Ω. If you drive the coil with a 40V for example, you would get about 16mA (40V/2512Ω = 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 2A high-current through the coil, 5024V is needed! It is difficult to generate 5kV at 200kHz.

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