# Low-Noise Programmable Voltage Source
## 1 Introduction  
Identification and measurement of noise signals are crucial for many electronic devices [1]. This is not only important for device characterization, but also for the study and a deep understanding of microscopic physical phenomena and technologies. For example, noise characterization is needed in order to understand the fundamental causes of the detection limit in spectroscopy [2; 3], data link budgets in free-space optics, etc. In the case of biased devices (such as transistors [4; 5], varistors [6], photodetectors [7; 8; 9; 10; 11; 12; 13] and other materials [14; 15; 16; 17]), the noise introduced by the biasing devices is also very important because it can mask the noise generated by the devices being investigated or limit the performances of the designed instruments. Indeed, in order to perform reliable noise characterization, we need to resort to ultra-low-noise power supply units that introduce negligible noise levels compared to those generated by the device-under-test (DUT). The simplest implementation of such low-noise supplying units consists of resorting to batteries (often lead acid, NiCd or NiMH accumulators) that, under proper conditions, behave like very low-noise voltage sources. However, the fact that we can only use a combination of elementary cells limits the resolution that can be obtained in setting thedesired voltage. Moreover, the voltage changes with time because of discharge. To obtain an adjustable and stable voltage source, it is possible to use a set of batteries and a low-noise linear voltage regulator. This is a simple configuration, but low-noise solid-state regulators, while labeled \"low-noise\", are still characterized by large levels of noise, especially at low frequencies when compared to batteries [18; 19; 20; 21; 22; 23]. The relatively high level of noise is also the reason why commercial voltage sources, while providing a high range of voltage settings, cannot be employed in many cases [24]. Very often, in order to overcome the limitations of commercial programmable sources, dedicated systems need to be designed for obtaining high sensitivity in the case of low-frequency noise measurements. A few of such voltage sources were described in the literature. In [25], a low-noise programmable voltage source is presented with a discrete resistor \(R2R\) ladder network digital-analog converter (DAC) and a cascaded JFET low-noise follower. Low noise is obtained based on a battery being used as a reference and the DAC being based on excess-noise-free discrete resistors. High output current in this source was obtained by resorting to a low-noise power buffer output at the output of the DAC. Its noise voltage spectral density (VSD) is about 10 nV/\(\surd\)Hz at 1 Hz when delivering currents in the hundred mA range. In [26], an \(RC\) filter with 15 mF supercapacitors was used to effectively filter out, down to very low frequencies, the noise generated by a solid-state Digital to Analog Converter (DAC). A compensation circuit was also added in order to compensate for errors in the generated voltage due to the significant supercapacitor leakage current. The output noise of this voltage source was about 4.5 nV/\(\surd\)Hz at 1 Hz and 3.5 nV/\(\surd\)Hz above few Hz. A low-noise voltage reference was also presented in [27]. It is built of a high output current DAC, a lowpass supercapacitor filter, and a voltage follower. Its noise voltage is about 15 nV/\(\surd\)Hz at 1 Hz and 1.2 nV/\(\surd\)Hz at 1 kHz. Another solution proposed in [28] exploits the very low-noise SSM2220 transistors that, when connected as diodes and biased by a solid-state voltage reference (AD586), and provided that strict temperature control is obtained, can behave as a very low-noise, fixed-voltage reference, from which an adjustable low-noise voltage source can be obtained, with noise levels of about 7.7 nV/\(\surd\)Hz and 3.9 nV/\(\surd\)Hz at 1 Hz and 10 Hz, respectively.