## 2 Circuit Design
Within the range of unity gain of the transfer function, the current flowing through the coils can be expressed as  
\[I=U_{\text{control}}\frac{R_{\text{f}}}{R_{\text{in}}R_{\text{sense}}} \tag{1}\]  
where resistances \(R_{\text{f}}\), \(R_{\text{in}}\) and \(R_{\text{sense}}\) 470 pF refer to the feedback resistor, the input resistor, and the sense resistor, respectively (see Figure 1). A bidirectional current shunt monitor (INA170, Texas Instruments) is used to measure the current flowing through the sense resistor. We choose this particular part for its high common mode rejection, high voltage input, and low output noise density of 20 pA/\(\sqrt{\text{Hz}}\). This serves both as a process variable input for the PID feedback loop and as an output for current monitoring. The current monitor output is chosen to be within the 0-2.5 V range (symmetric around 1.25 V reference voltage) such that it can be easily measured with a microcontroller referenced to 2.5 V.  
To reach the stability of the current of the order of tens of ppm, we control the current source section with a PID controller. In the controller's design, we use OP07C and OPA227 amplifiers by Texas Instruments with 0.6 MHz and 8 MHz bandwidths, respectively. The measured PID transfer function rolls off at 1 kHz. Although the OPA549 amplifiers can operate at higher frequencies, the stability requirements and high output current range put constraints on the transfer function of the system. For this reason, the total roll off frequency is lower than for individual elements. The user-defined set point is fed into the circuit via a differential amplifier (AD8421, Analog Devices) to ensure isolation between the board and the environment. The resistors and capacitors in the PID feedback loop are placed in DIP sockets to allow easy modification of the parameters of the PID. For the integral part, mainly responsible for the response time, the capacitors can be changed with a piano DIP-switch located in the easily accessible front part of the board. All PID parts are built around one operational amplifier. This solution intertwines the dependence of the PID settings on electronic components, but it makes the circuit more compact and less prone to interference with other parts of the circuit due to a minimized number of electronic elements and traces. Due to the linearity of functional sections of the PID, the one-amplifier solution operates in the same manner as separate amplifiers for individual PID sections. An additional amplifier is added to provide variable gain of the total control signal, which is fed into the current source section. We account for potential dark or parasitic currents by including a potentiometer to set an offset level to the control signal. The device is powered from external, linear power supplies available in most laboratories. The push-pull configuration uses operational amplifiers that can be single supplied. The direction of the current flowing through the system depends on the relative levels of voltages at the outputs of the amplifiers; thus, there is no change in the voltage polarization when the current polarization changes. The amplifiers only switch between the sink and source modes. The PID, current sense, and logical parts require a 24 V power supply. The current source part uses a separate 18 V supply to minimize unnecessary heating due to voltage drops on the internal output transistors. When used at lower currents or with external cooling, the setup may be powered from one source.