Generate high frequency and high strength magnetic field is difficult. As the frequency is increase, so is the electromagnet coil impedance. To generate high magnetic field, high current is needed. Because of high impedance, high voltage and high current driver is needed. Such drivers or amplifier are not readily available. For example, to drive 8A into a 500uH magnetic coil at 250kHz, the amplifier driver must be rated for 6280V and 50kW!

Using classic series resonant to generate magnetic field can partially solve the above problem by lowering the impedance and therefore lower the amplifier driver voltage requirement. However the maximum current is limited by the magnetic field generator amplifier driver output current capability. The new resonant circuit discussed below will further increase the coil current by 2X.

Figure 3. Classic resonant circuits (a) series resonant tank. (b) parallel resonant tank.

Figure 2. New resonant circuit doubles the amplifier output current achieving high frequency and high magnetic field.

To generate high-

To generate high magnetic field, a waveform amplifier is needed to drive the resonant circuit as shown in Figure 2. The function generator produces a sinewave. The sinewave is amplifier by a driver amplifier such as the TS200 or the TS250. It can amplify the function generator voltage or current or both. The waveform amplifier is driving a large current into the current-

The series resistance R is optional. It is for better impedance matching. See Maximizing Amplifier Output Current application note for details how to choose the optimal resistance. In general the series resistor can be omitted.

Figure 1 shows the new resonant circuit. It is consisted of two equal value capacitors, labeled C, and a magnetic coil. At resonant the magnetic coil current is twice as much as the input source current from any amplifier. Section 2 below discussed the mathematical theory behind the current amplification.

Figure 4 is showing the new current-

Figure 1. New resonant circuit doubles the magnetic coil current and magnetic field.

The classic series and parallel LC resonant circuit have been used in numerous applications such as oscillators and filters. LC resonant tank can also be used for magnetic field generator. A new resonant circuit is studied in this App Note for the purpose of generating high frequency magnetic field. The most important feature of this new LC resonant tank is it amplifies the magnetic coil current by 2X while generating high-

Figure 3 shows the series and parallel resonant circuits. The series LC resonant tank features low impedance at resonance. The coil impedance is cancelling the capacitor impedance. Thus achieving low impedance enables high current through the LCR circuit. Up to now, the most practical and efficient way to drive high current through magnetic coil is using series resonant circuit. Thus series resonant technique is often used for high frequency magnetic field generator.

The parallel resonant circuit on the other hand, its impedance is maximum at resonance. At resonant the current is resonating between the coil and capacitor. The current passing through the magnetic coil is very high while the source current is very low -

Figure 4. Novel current-

To calculate the resonant frequency, first we need to define the resonant conditions. The requirements for resonant is such that at a given frequency the imaginary (reactive) portion of the input impedance, Z, is equal zero. The impedance is purely resistive at resonance.

In Figure 4 the electromagnetic coil resistance is usually small value and parasitic to the coil. The small resistance has no measurable effect on the tank resonant frequency. To simplify the resonant frequency calculation, the small resistance is excluded. In general magnetic coil with small resistance is better for high strength magnetic field generation. The two capacitors forming the resonant circuit are the same value (CS = CP = C). Looking at ZP only, it is a classic parallel resonant. Using equation A3 from the Appendix section below, the imaginary portion of ZP is given in Equation-

Now substitute Equation-

Next is solving for frequency ω. The result is showing on Equation-

Remember ωo=1/√LC is the classic (series or parallel) resonant frequency of Figure 3. Rearranging Equation-

As mentioned above, the new current-

Figure 5. KVL and KCL are used to calculate the electromagnet coil (inductor) current.

Remember from Equation-

From Equation-

To further rearrange Equation-

In conclusion from Equation-

Figure 6. Visual depiction of the magnetic coil current is two times the source current.

To understand the impedance of the resonant tank circuit, consider the reactive (imaginary part) impedance Z is zero as previously mentioned in Eqation-

Because the L/(2C) term is much bigger than the R2 term, The R2 term is ignored. Equation-

From Equation-

The main topic of this study is the novel resonant circuit’s ability to magnify the input current by a factor of 2 for free. The boosted current is ideal for generating high magnetic field density. From the above equations, the quality factor Q does not impact the current amplification. To complete the new resonant study, the quality factor Q is presented here.

Figure 7. For calculating Q, the current-

Recall the small-

In conclusion the new current-

The current-

In the SPICE simulation, the coil resistance was set to 125mΩThe simulated source voltage was set to 2.5V. The measured source current is 5A. The calculated resonant tank effective resistance is 500mΩ As discussed above the resonant circuit transforms the coil resistance by a factor of 4. Simulation confirms Equation-

When the source generator current vs frequency is plotted in Figure 10, it reveals two resonances: the new resonant and the classic parallel resonant. The current-

Figure 8. Current-

Figure 9. The new resonant frequency is found by the magnetic coil current vs frequency.

Figure 10. The new current-

An experiment was designed to use a real coil (inductor) to confirm the current -

Figure 11. TS250 Waveform Amplifier used to generate high frequency magnetic field.

The first step is to set the function generator and the TS250 amplifier driver to the calculated resonant frequency (112.5kHz) with a 10Vpp sinewave. Next find the resonant frequency by slowly adjust the frequency until the coil reaches maximum current. The resonant frequency was found to be 116.5kHz. Now slowly increase the magnetic coil current by increase the TS250 peak-

Using Equation-

Figure 12. 3App input source current is measured across R2. 1V = 1A.

Figure 13. 6App magnetic coil current is measured across R1. 1V = 1A.

The newly discovered current-

Related App Notes

High-

High-

Waveform Amplifier for Function Generator

PDF Version of this App Note

Figure A. Classic parallel resonant circuit consisted of RLC for calculating impedance and reactance.

As shown in Figure 2, high frequency magnetic field is generated by a waveform amplifier driving the resonant coil. The TS200 Modulated Power Supply or the TS250 series of Waveform Amplifier are ideal for driving high current through magnetic coils. Select an amplifier driver (Table 1) based on the equivalent coil resistance at resonant using Equation-

Waveform Amplifier |
Voltage Range (V) |
Coil Resistance (Ohm) |
Resonant Resistance (Ohm) |
Peak Amplifier Current* (A) |
Peak Coil Current* (A) |

TS250- |
- |
0 to 0.3 |
0 to 1.25 |
- |
- |

TS250- |
- |
0.3 to 1.0 |
1.25 to 4.0 |
- |
- |

TS250- |
- |
1.0 to 2.25 |
4.0 to 9.0 |
- |
- |

TS250- |
- |
2.25 to 8.8 |
9.0 to 35 |
- |
- |

TS200- |
- |
0 to 0.38 |
0 to 1.5 |
- |
- |

TS200- |
- |
0.38 to 1.1 |
1.5 to 4.5 |
- |
- |

TS200- |
- |
1.1 to 4.75 |
4.5 to 19 |
- |
- |