I started with a ship full of max-level veterans, and I'm just a complete noob.

The rain stopped.

At four o'clock in the afternoon, the light bulbs in the confidential cubicle had just been replaced, and the white light was a bit dazzling.

Fang Xudong attached the two alligator clips of the high-frequency quality factor meter to the second bend of the microstrip line on the mixer board. The pointer swung a few times before stabilizing.

"What's the reading?"

Jiang Ming stood opposite the testing platform, holding a notebook in his hand.

"The 3.7 leather method results in a low quality factor, approximately 65."

Fang Xudong noted down the numbers and moved the alligator clip to the next section.

The mixer board is laid flat in the center of the test bench, and the edges and corners are fixed with modeling clay to prevent it from sliding.

The two black germanium diodes were soldered to the center of the board, and the bent metal microstrip lines extended from both ends of the diodes, made three turns on the board, and finally merged into a ring structure.

After Fang Xudong finished measuring the last segment, he turned off the high-frequency quality factor meter and drew a capacitance distribution diagram of each segment of the microstrip line in his notebook.

"The equivalent capacitance of each segment is different; the closer to the ring structure, the smaller the capacitance."

Jiang Ming walked over to look at his record, pointing his finger at the location of the ring structure.

"Mr. Fang, what's the total physical length of the entire microstrip line?"

Fang Xudong turned to a page, which contained the data he had previously measured with calipers.

"25.4 millimeters."

"Divide the waveguide wavelength by four."

Jiang Ming took Fang Xudong's pencil and wrote a line of equations in the blank space of the notebook.

The operating frequency is 2.95 GHz. The dielectric constant of the substrate is estimated based on ceramic and is taken as 9.6. The effective wavelength in the dielectric is approximately equal to the wavelength in free space divided by the square root of the dielectric constant.

The wavelength in free space is 101.7 millimeters, which is shortened to about 32.8 millimeters in a medium.

One-quarter wavelength, 8.2 millimeters.

However, the microstrip lines on the board are folded, and when unfolded, they are 25.4 millimeters long.

"Not a quarter wavelength."

Fang Xudong frowned.

No, look here.

Jiang Ming placed the tip of his pencil on the ring-shaped structure.

What is the circumference of the ring itself?

Fang Xudong looked down and measured.

"Approximately seventy millimeters."

"The circumference of the ring is slightly more than twice the wavelength of the medium, with a difference of less than seven percent."

Jiang Ming drew a circle on the paper and marked the positions of the four ports.

"This is a 3-micron ring directional coupler, with four ports corresponding to input, coupling, isolation, and pass-through, respectively."

"The folded section of the microstrip line is the matching line from the output of the magnetron to the input of the coupler. Its length does not correspond to a quarter of the entire waveguide wavelength, but rather to the impedance transformation section."

Fang Xudong stared at the ring for a few seconds, and suddenly understood.

"The local oscillator signal is injected from another port and mixes with the magnetron signal inside the ring."

"right."

Jiang Ming turned to a new page in his notebook and began drawing an impedance diagram.

The circle diagram was drawn freehand with a pencil. The normalized impedance axis and the isoelectric arc were drawn smoothly without hesitation.

He marked the impedance point of the diode on the circle diagram, then rotated half a circle along the arc of equal conductance and landed at another point.

"The junction capacitance of the diode at 2.95 GHz is approximately 0.3 picofarads, and the reverse recovery charge is estimated based on the germanium tube, taking two to three nanocoulombs."

"The matching point is here."

He drew a small circle on the diagram.

"To achieve the highest mixing efficiency, the local oscillator injection power should not be too high or too low; the optimal point is approximately ten to fifteen milliwatts."

"But more crucial is frequency stability."

Jiang Ming wrote a line of words on the blackboard.

The local oscillator center frequency is 2.9455 GHz, and the phase noise is less than -80 decibels per GHz of carrier frequency.

Fang Xudong walked to the blackboard and stared at the line of numbers for a long time.

"How did you calculate the local oscillator frequency?"

"The intermediate frequency of the mixer output is 4.5 MHz, and the center of the interference signal detected at the front line is this frequency."

"The magnetron operates at a frequency of 2.95 gigahertz. Subtracting the intermediate frequency of 4.5 megahertz gives us 2.9455 gigahertz."

"This is Benzhen."

Fang Xudong nodded; this step of the derivation was correct.

But his gaze never left the impedance diagram on the blackboard.

Jiang Ming draws circles too fast.

From calibrating the reference impedance to performing impedance transformation on the circle graph, there was no pause or table lookup in between; it was as if the fingers themselves remembered where each arc should bend.

This isn't a skill you can develop just by reading textbooks.

Fang Xudong closed his notebook, leaned against the testing table, and crossed his arms over his chest.

"Jiang Gong."

"Um?"

"In which lab in the United States did you perform the calculations for these microwave distribution parameters?"

There was a two-second silence in the cubicle.

Someone walked past on the gravel path outside the window, their footsteps rustling on the wet ground.

Jiang Ming put the chalk back in the blackboard tray and turned around.

"Mr. Fang, I have never been inside a microwave laboratory in the United States."

Fang Xudong didn't respond, waiting for what would follow.

"When Mr. Qian was at Caltech, he taught a course on the wave equations of fluid pipes."

Jiang Ming walked back to the testing table, picked up a germanium diode, flipped it over, and then put it down.

"The propagation equation of electromagnetic waves in a transmission line has the same mathematical structure as the pressure wave equation of fluid in a variable cross-section pipe."

"The impedance circle diagram is essentially a conformal transformation that maps the reflection coefficient onto the complex plane. It can be used for both electromagnetic waves and sound waves, as long as they are waves."

"I studied with Mr. Qian on the ship for three months and worked through many problems on pipe impedance transformation."

"Switching to a microwave transmission line is simply a matter of replacing acoustic impedance with characteristic impedance; the physical quantities are different, but the mathematical methods are exactly the same."

Fang Xudong did not refute.

From a purely mathematical perspective, this explanation is indeed valid.

The equivalence between transmission line equations and fluid pipe equations is known to anyone who has studied partial differential equations.

Knowing something is one thing, but using it so skillfully is another.

He looked down, opened his notebook, and wrote a few words in the blank space on the last page.

Distribution parameter equivalence.

The characters were written very heavily, the pen tip almost tearing the paper.

After he finished writing, he closed the notebook and put it back in his coat pocket.

"Okay, I've heard your explanation."

He walked back to the test bench and reopened the high-frequency quality factor meter.

"The isolation of the ring coupler hasn't been measured yet, continue."

Jiang Ming handed him the alligator clip, and the two of them squatted side by side in front of the testing table.

No one mentioned Leningrad or Caltech again.

The hands swung a few times before settling down.

Fang Xudong read the numbers, and Jiang Ming recorded them, their teamwork so seamless that it was as if nothing had happened.

But Jiang Ming knew that when Fang Xudong wrote those words in the notebook, he had already marked it.

The next time such "interdisciplinary equivalence" occurs, he will not ask again, but he will remember it.

If you memorize enough, one day you'll be able to piece together a complete picture.

As I finished writing the last set of data in my notebook, a muffled thud suddenly came from the direction of the adjacent workshop number one.

Then came Lao Sun's voice. It was hard to hear clearly through the wall, but Jiang Ming recognized the tone.

Fang Xudong's hand was still on the knob of the high-frequency quality factor meter as he looked up at Jiang Ming.

The two of them stood up almost at the same time and walked towards the door of the cubicle.