Tech Note: Crafting Your Own V-I Plots at Home

Or, a guide on how to lose money with your friends.

While developing my recent publication, The Secret Life of Circuits, I made a conscious decision to ensure all the artwork was authentic.

My primary grievance with the diagrams found in mainstream electronics tutorials and textbooks is that they are accurate they are mostly fabricated. At their best, they are mere traces of ancient documents; at their worst, they are drawn from memory and are, to put it politely, "inspired by true events."

The Secret Life of Circuits features roughly 290 original illustrations created to avoid these shortcuts. I spent a great deal of time collecting empirical data for various phenomena, including:

• Battery discharge trajectories.
• Quartz crystal frequency responses.
• Vacuum tube characteristics.
• Signal reflections within a 100 ft coax cable draped across my shop.

The Semiconductor Struggle

While most data was easy to acquire, parametric plots—which map the relationship between voltage ($V$) and current ($I$) in semiconductors—proved difficult. I encountered three primary hurdles:

1. The Floor: In certain regions, currents are so minuscule that a standard oscilloscope cannot detect them.
2. The Ceiling: In other regions, current spikes instantaneously.

   "And before you know it, the device lets out the magic smoke."

3. The Drift: Even in the middle, semiconductor junctions are temperature-sensitive. Self-heating occurs at currents as low as $1\text{ mA}$, causing the data point on the screen to drift.

The Initial Workaround

To solve this, I abandoned the oscilloscope for a combination of a benchtop digital multimeter (DMM) and pulsed power from a lab supply.

Automating the Process

Manually logging $V$ and $I$ is tedious and prone to human error. I needed a computer interface. Many professional instruments utilize SCPI (Standard Commands for Programmable Instruments), a text-based protocol.

Depending on the hardware age, you can connect via:

• RS-232
• USB Type B (Printer port)
• Ethernet (TCP connection to port 5025)

To identify a device, you send *IDN?\n, and it returns its make and model. Commands (which return no text) look like this:

• SOUR:VOLT 1.2 $\rightarrow$ Sets voltage to $1.2\text{ V}$.
• OUTP 1 $\rightarrow$ Activates output channel 1.

The Upgrade: The Source Measure Unit (SMU)

Because my power supply lacked remote control, I eventually bought a Source Measure Unit (SMU)—a hybrid power supply and multimeter with rapid response times. While new SMUs are prohibitively expensive, the second-hand market is underserved. I managed to snag a Rohde Schwarz NGU401 for a tiny fraction of its original \9,000$ MSRP.

FastLog Implementation

Standard querying on this unit is slow ($\approx 3\text{ Hz}$). However, it features a "FastLog" mode that allows sampling rates between $100\text{ kHz}$ and $500\text{ kHz}$, delivering $V$-$I$ pairs as binary 4-byte floats.

The Catch: The documentation was unreliable. Specifically, the serial-over-USB interface corrupted the binary data. I eventually resolved this by switching to Ethernet.

My C-based capture logic follows this pattern:

if (current < 0.3_mA) {
    // Keep power ON
    // Average 2,500 points for noise-free microamp readings
} else {
    // Pulse power for 5ms
    // Average the best 20 samples from FastLog buffer
}

Results and Observations

The 1N4148 Diode

I mapped the forward bias of a 1N4148 diode (rated for $300\text{ mA}$), covering a range from a few $\mu\text{A}$ up to nearly $2\text{ A}$.

While the $V$-$I$ relationship is typically called exponential, this only holds at low currents. In a log-current plot, the curve diverges from the idealized model around $10\text{ mA}$ due to the resistive effects of the semiconductor substrate. This proves why real-world data is superior to idealized textbook curves.

The BS170 MOSFET

The same method works for transistors. For a BS170 MOSFET, I plotted the drain-source voltage ($V_{DS}$) against the admitted current ($I_D$).

The results show that the device acts as a constant-current source in its primary operating range; the current limit is determined by the gate-source voltage ($V_{GS}$) and fluctuates by less than $10\%$ as $V_{DS}$ moves from $1\text{ V}$ to $10\text{ V}$.