## 3 Circuit Performance  
To measure the noise level we use a 12-bit oscilloscope (Teledyne Lecroy, model HDO 4054) to acquire a 10 s long, continuous traces from the monitor output. We also verify the consistency of the noise characterization using a high-accuracy current transducer (IT 400-S Ultrastab, LEM). Both methods appear to be comparable except for currents of the order of 100 mA and less so where the signal-to-noise ratio of the transducer measurements is much worse than that for the monitor output. This is caused by the low sensitivity at low currents of the available transducer, which is optimized for current readouts in the range of several amperes. We characterize the circuit using linear spectral density (LSD), which is derived from the Fourier transform (FFT) of a long-run signal measured with an oscilloscope and the relations LSD\({}^{2}=\mathrm{PSD}\sim\mathrm{\mid FFT\mid}^{2}\), where PSD stands for power spectral density. The measurement is taken with a 2.5 MHz sampling rate, so the cutoff of the Fourier transform, due to the Nyquist theorem, equals 1.25 MHz. The noise floor trace is acquired with the current source (both power supplies) turned off. The LSD noise is measured for several currents and is shown in Figure 2a for the maximum design current of 4 A and for the current corresponding to the value used for stray field compensation along the y-direction. For all investigated currents, the measured noise level is of the order of tens of \(\mathrm{\mu A}/\sqrt{\mathrm{Hz}}\) with 45 ppm of integrated noise at 4 A (the noise integrated over a 1 MHz bandwidth). The bandwidth and the step response depend both on the PID settings and the current value. For the best performance, the resistors and capacitors in the PID loop need to be matched to the inductive and resistive load of the coils. The maximum continuous current of the power amplifiers can reach \(\pm\)8 A, but we deliberately limit it to \(\pm\)4 A, which is sufficient for producing magnetic fields needed for most cold-atom applications with the set of coils we currently use. Even though the setup is fully analog and, in principle, can source any arbitrary current within its operational range, it is controlled with a DAC with limited resolution. Thus, the \(\pm\)4 A limit increases the resolution of the current settings. The DAC we use is an NI PXI-6733 card, which is an integral part of our experiment control system. It has a 16-bit resolution, which corresponds to a control voltage step of 0.3 mV. This translates to 0.54 mA current step or \(\sim\)2.4 mG step for the y-coil. This conversion takes into account the PID and the current source voltage-to-current coefficient of 1.81 A/V, which his determined experimentally by applying a known control voltage to the circuit and measuring the output current with a high-accuracy current transducer. For the maximum current of 4 A, the roll-off frequency of the PID is 1 kHz. It is lower than both the simulated value (\(\sim\)5 kHz) and the value measured on a purely resistive load. This is, however, unsurprising, because the inductive load of the connected coils opposes current changes at both higher frequencies and higher current amplitudes, as it adds another pole to the PID transfer function. As an example of the ability to generate  
Figure 2: (**a**) The linear spectral density for chosen output currents measured at 100 Hz RBW in the range up to 1 MHz. The red line shows the noise level for the \(y\)-axis coils at a current used for compensating the stray field. The blue line corresponds to the maximum current supported by the designed source. The stability measurement is averaged over a period of 1 min; (**b**) The current in the coils is measured indirectly on the monitor output of the current supply. The circuit is driven by a 1 kHz sinusoidal input signal ranging from \(-\)0.5 A to 0.5 A.