# Theory of operation Joulescope simultaneously measures current and voltage, and then computes power and energy. Joulescope combines a voltmeter and a fast auto-range current shunt ammeter.  ## Ammeter The shunt ammeter consists of seven (7) current ranges with six (6) different shunt resistor values ranging from 0.01 Ω to 1111 Ω. Joulescope actively selects the best shunt resistor to keep the maximum voltage across the shunt resistor to 20 mV. This low voltage drop minimizes the impact on the device under test. Other equipment, including standard multimeters, have a much larger burden voltage that can cause the target device to behave unusually. The Joulescope amplifies the voltage across the shunt resistor and then uses an analog-to-digital converter (ADC) to digitize the value. The ADC digitizes the value 2 million times per second to create 2 million samples per second (SPS). The Joulescope instrument sends these ADC values to the host software over USB. Given a known resistor value and the measured voltage, the Joulescope uses Ohm’s Law to compute current. Each Joulescope contains a calibration. The software applies the calibration to convert the ADCs into measured current values. Joulescopes are individually calibrated and tested in the factory to ensure that every Joulescope performs to specification. As the current changes, the ammeter selects the optimal shunt resistor value. Joulescope uses dedicated hardware to quickly select the appropriate shunt resistor to avoid impacting the device under test. The shunt value selection uses the ADC output, dedicated over-range analog hardware, and a unique algorithm that runs in an FPGA. The FPGA selects the active shunt resistors using MOSFETs, which were carefully qualified to meet Joulescope’s demanding performance characteristics. The shunt resistor selection does take some time. How fast does the shunt resistor need to change to have a minimal impact? The linearized equation is: t = C \* ΔV / ΔI Let’s take a typical example. The target device takes 3.3V and can tolerate a temporary 3% (0.03) voltage glitch on a 1 amp change. If the target device has 10 µF of capacitance, the required shunt resistor switching time is approximately: 10 µF \* 3.3 V \* 0.03 / 1 A = 1 µs Joulescope was designed to achieve 1 µs switching speed to meet this demanding case. Most target systems have larger capacitance and less dramatic step current changes. In all cases, the shunt resistor selection is always make-before-break to ensure uninterrupted connectivity to the target device. ## Voltmeter The voltmeter measures the voltage between IN+ and IN-. The voltmeter scales the input voltage, and uses an analog-to-digital converter (ADC) to digitize the value. The Joulescope instrument sends the voltage samples, along with the current samples, to the host computer. The software applies the calibration to convert from ADC values to actual voltage. The voltmeter has two different ranges, and you can manually select the best range for your application. The 5V range provides higher resolution for smaller voltages, while the 15V range allows for larger voltage measurements. ## Host Computer The Joulescope instrument requires a host computer to operate. The Joulescope instrument sends 2 million current and voltage samples per second immediately to the host computer over USB. Unlike traditional oscilloscopes, a Joulescope is always capturing data. The terms “trigger” and “sample buffer” do not fully apply to the Joulescope device, since all sample data arrives at the host computer. The Joulescope User Interface (UI) temporarily stores capture data in a circular buffer. The UI allows you to adjust the buffer size to use your host computer’s RAM. Joulescope can also record to a file, and the capture size is only limited by your computer’s available storage on your hard disk drive or solid-state drive. The Joulescope host software is open-source. The pyjoulescope “driver” communicates with the appropriate operating system USB driver. Joulescopes use Microsoft’s WinUSB on Windows, which is included by default with the Windows operating system. On Linux and macOS, Joulescope uses the popular, open-source libusb driver. The pyjoulescope driver provides an easy-to-use scripting environment. You can also use the driver to build integrated applications, such as the Joulescope UI, that use the Joulescope instrument data. ## Power, Energy, Charge, and Statistics Joulescopes only measure current and voltage. The Joulescope software uses math to compute the power, energy, and charge. Power is the current multiplied by the voltage: **P = V \* I = V² / R = I² \* R** Energy is the integral of power over time. $$ E\ \ = \int_{}^{}{P\ dt} $$ When we talk about energy, we often mean the energy consumed over a specific time interval, which is the definite integral: $$ E\ \ = \ \int_{t = 0}^{T}{P\ dt}\ \ \ \approx \ \ \ \ \sum_{n = 0}^{N}{P_{n}\ \Delta t} $$ The Joulescope host software performs the discrete-time Euler integration shown to the right. The Joulescope software carefully manages the numerical precision to ensure that it computes energy correctly. IEEE double-precision floating-point numbers do not provide sufficient precision. Charge is the integral of current over time. $$ C\ \ = \ \int_{t = 0}^{T}{I\ dt}\ \ \ \approx \ \ \ \ \sum_{n = 0}^{N}{I_{n}\ \Delta t} $$ Charge and energy are mathematically similar. Both voltage and current contribute to energy, but only current contributes to charge. ## High impedance / low leakage Joulescope measures currents at nanoamp resolutions and accuracies. Many contemporary devices have input impedances of 1 MΩ to 10 MΩ, which is not good enough. At 3.3V, a 10 MΩ load draws: 3.3V / 10 MΩ = 330 nA Joulescope features a combined input impedance and leakage current of approximately 1 GΩ. This high input impedance allows Joulescope to make accurate and precise low current measurements. ## Electrical isolation The sensor side of Joulescope is electrically isolated from the host computer. This isolation allows you to insert Joulescope into your test system without worrying about ground issues, including ground loops and ground noise.