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The development board and the circuit board with the potentiometer from the Raspberry Pi Pico Experimenting Kit from Elektor are excellent for such a small project, as I found out. Only a few additional circuits are needed on small PCBs, as I will show.

After I had dealt in detail with the program examples in the instruction book, where the display is used on the above-mentioned Develop Board, I first built the electronic circuits required for a characteristic curve representation on breadboards and designed the first version of a program suitable for my project in Micropython for the Raspberry Pi Pico. This makes the Pico a simple characteristic curve recorder for diodes, LEDs, npn and also pnp transistors, field-effect transistors and mosfets.
The characteristic curves are shown in color on the small display of the Development Board.
For the sake of clarity, circuit details of the Development boards and those of the PCB with the potentiometer from the Raspberry Pi Pico Experimenting Kit from Elektor not shown in Figure 2. They can be found on the Makerfabs website. The program in Micropython generates a continuously changing PWM signal at Pico-GP0 starting from 0 V. This is pending at X14, is smoothed and passed to the non-inverting input of OP1 in IC1 (pin 1,2 and 3). With the help of R11 and R12, the DC voltage created in this way is doubled from 0 V to a maximum of approx. 3.3 V to approx. 6.6 V and OP2 is transferred to IC1 (pins 5, 6 and 7), which serves as a voltage follower.
OP1(pins1,2 and 3) of IC2 serves as a voltage follower. The output voltage (Pin1) is connected to the ADC2 pin of the Pico (GP28). Its input voltage may not exceed 3.3 V. For this reason, a voltage divider consisting of R13 and R14, consisting of two resistors of 1 megaohm each, is connected to the non-inverting input of OP1. The measurement of the current during the characteristic curve recording of diodes, transistors, etc. is done here by the respective pin of the semiconductor to be examined not directly connected to GND, but to X9 GND*. The low current in R8 is measured indirectly using OP1 (pins 1,2 and 3) in IC3 by offering the small voltage drop at R8 to the non-inverting input and increasing it to a hundredfold using R1, R2 and R4 in OP1. The output of OP1 is connected to OP2 in IC3, which serves as a voltage follower.
1 milliampere in R8 becomes 0.1 V, or 10 milliamperes become 1 V in OP1 of IC3. For the exact setting, connect a resistor of 1k between X13 and GND* and use a digital multimeter to measure the voltage applied to it at the end of the program when running the program in Micropython. According to Ohm's law, the voltage value corresponds to the current value in milliamperes. The voltage gauge between the output of OP2 in IC3 and GND is connected to it and the voltage is set there with the help of the trim potentiometer R2 according to the current previously measured indirectly at the resistance of 1k, for example at 3 milliamperes the voltage at pins 6 and 7 of IC3 is 0.3 V. These pins are connected to ADC1, Pico-GP27. The measurement of the current in the component to be examined, in this case a resistance, is measured indirectly with the help of ADC1 of the microcontroller.
The circuit around IC4 is similar to that around IC1. The Micropython program measures the voltage at the potentiometer at ADC0(Pico-GP26) and generates a PWM signal at Pico-GP1 accordingly. This is fed to a PC817 optocoupler. Its output signal is smoothed and offered to the non-inverting input of OP1 in IC4 (pins1,2 and 3), which serves as a voltage follower. At the output of OP1 (Pin1, X2), an adjustable DC voltage is available using the potentiometer from the Raspberry Pi Pico Experimenting Kit. IC4 is supplied with its own voltage source, so that the circuits presented here can also be used to calculate current-voltage characteristics of pnp transistors, field-effect transistors, etc. can be recorded and displayed.
On the third small circuit board there is a micro button, which serves as a reset button for the microcontroller, another Micro button connected to Pico-PG9, as well as a red light-emitting diode with a resistor, which are connected to Pico-PG8. With this micro sensor, another button is available for the project for a selection of another, here the red color of the current-voltage characteristic curve to be displayed, which is indicated during recording with the help of the red light-emitting diode.
Figure 2 also shows how to connect a diode, an LED or a resistor to be tested for characteristic curve recording. If an npn transistor is connected for examination, its base must be connected to X2 in the case of a current control via a series resistor of 100 k. In a voltage control, the base of the npn type is directly connected to X2. The collector of the transistor is connected to X12 and its emitter to GND*. GND is also connected to GND_extern. Because of the extremely low base current, instead of the collector current, the emitter current = collector current + base current is indirectly measured. The base current is measured indirectly with the help of a digital multimeter parallel to the 100k resistor during the characteristic curve recording when the transistor is currently controlled.
The setting of the same is done in the Micropython program by reading the voltage at the grinder of the potentiometer and then converting it into a corresponding value of the PWM signal at pin Pico-GP1 and using the circuits around IC4 into a corresponding adjustable DC voltage. In order to record the characteristics of a pnp transistor such as a BC557B in current control, its base is connected to X10(GND_extern) via a resistor of 100k. The emitter of the pnp type is connected to X12 and to X2 (output from OP1 to IC4). The collector of the transistor must be connected to GND*. With such a transistor, the collector current is measured indirectly. The base current is measured indirectly in a current control as in an npn type using the voltage drop at the 100k resistor.
When recording the output characteristics of the pnp transistor in voltage control, X10 must be connected directly to the base of the transistor, whereby a digital multimeter measures the currently set base-emitter voltage. 
The display area of the small display on the Develop Board is 128x128 pixels. For this reason, two 9V batteries or rechargeable batteries with the same output voltage are sufficient as sources of operation for the circuits presented above. For this reason, the display range of the voltage is limited to 6V. The current display range is a maximum of 10 milliamps.

Summary, outlook: On the display of the Raspberry Pi Pico Experimenting Kit, after adding only three small printed circuit boards with a few components, current-voltage characteristic curves of semiconductors can be displayed as colored lines with the help of a program in Micropython. Due to the small display in the Raspberry Pi Pico Experimenting Kit of 128x128 pixels, two 9V batteries or two rechargeable batteries with the same output voltage serve as power supplies in the project. When displaying current-voltage characteristics, their display range is limited to a maximum of 6 V and a maximum of 10 milliamperes. This should be enough for the hobby sector. 

The use of a color display, for example with 240x320 pixels, would allow for a larger representation of the grid on the display with horizontal and vertical lines.
With a voltage source of 12 V, the display range for the voltage values could be increased to 10 V and that for the current to 20 or 40 mA. In addition, more current and voltage values could be displayed in color in the free area of the display for the relevant current-voltage characteristic curves.