Chapter 30: Chapter 17: The 50Hz Circle
A hoarse voice sounded behind Chen Zhuo.
It was followed by the crisp CLICK of a lighter.
A tuft of orange-red flame flared in the darkness, illuminating a face covered in stubble, with heavy bags under the eyes and hair like a bird’s nest.
Old Zhou.
The head of the physics department at City No.1 Middle School, Zhou Guoping.
An eccentric old man who, in the students’ eyes, always wore an ill-fitting jacket, reeked of smoke, and would go off on tangents about quantum mechanics in the middle of a lecture.
Old Zhou, with a cigarette dangling from his mouth, took a deep drag. The burning tip glowed and faded in the dark laboratory.
He wasn’t angry about catching a student messing around in the lab.
On the contrary, his eyes, usually half-closed, were now watching the oscilloscope screen with great interest.
"The J2459’s signal generator uses an analog circuit. It’s heavily affected by temperature."
Old Zhou blew a smoke ring. The smoke swirled in front of the green fluorescence, adding a hazy filter to the ghostly waveform.
"This piece of junk makes it hard to lock onto higher harmonics. The fact that you could stabilize that three-node Lissajous figure, even for just two seconds, shows you’ve got a good feel for it."
Chen Zhuo turned and got off the round stool.
"Teacher Zhou."
Old Zhou waved his hand dismissively and walked to the lab bench, cigarette between his fingers.
He didn’t turn on the lights either.
The two of them were like a pair of bats accustomed to the dark, facing off in this room filled with the smell of electronics.
"That figure ’8’ from just now, what was the frequency ratio?" Old Zhou asked suddenly.
"1:2," Chen Zhuo replied.
"And the crown?"
"3:4."
Old Zhou raised an eyebrow.
Using the light from the oscilloscope, he looked down at the short kid who only came up to his waist.
’I remember this kid.’
’I remember him all too well.’
The madman who drew a free-body diagram of a wheel on his entrance exam.
The grade-skipper he’d made an exception for and given a spare lab key.
But he hadn’t expected the kid to actually show up.
And to be playing with something so wild on his first visit, no less.
Ordinary middle schoolers who came into the lab either wanted to play with the scales or look through the microscopes.
Only a true weirdo would hide in the dark to play with a beat-up old oscilloscope.
"Can you make a circle?"
Old Zhou suddenly reached out and twisted the oscilloscope’s knobs forcefully.
The waveform, which had at least some semblance of a pattern, was instantly and utterly scrambled, turning into an ugly diagonal line.
"A circle?" Chen Zhuo was taken aback for a moment.
"That’s right, a circle."
Old Zhou pointed at the screen.
"The Lissajous figure. The simplest, but also the hardest to tune: a circle."
"To draw a perfect circle, the frequencies of the two channels must be strictly equal, 1:1. And..."
"The phase difference has to be exactly 90°, or π/2."
"A little more, it’s an ellipse. A little less, it’s also an ellipse. If the frequency is even slightly unstable, the circle will rotate."
"Make me a circle. If you can’t, you can give me that key back."
Old Zhou took a long drag from his cigarette and watched Chen Zhuo quietly.
This was a challenge.
Or rather, it was Old Zhou, in his capacity as the head of the physics department, conducting a true qualification test for this "genius."
Being good at solving problems on paper was nothing.
Physics, in the end, is an experimental science.
If your hands trembled in front of a real instrument, you were, at best, just an armchair general like Zhao Kuo.
Chen Zhuo looked at Old Zhou’s face, barely visible behind the smoke.
He said nothing.
He turned and sat back down on the round stool.
’Making a circle.’
Mathematically, it was just an equation:
x²+y²=r².
But in the world of analog circuits, it was a real thrill.
Chen Zhuo took a deep breath.
His hands rested on the knobs once more.
’First step: frequency synchronization.’
He slowly adjusted the signal generator’s frequency back to 50Hz.
The dot on the screen began to draw a shape, but it wasn’t a circle—it was a mass of tumbling ellipses, constantly tilting left and right.
This meant the frequency wasn’t completely locked.
Chen Zhuo closed his eyes, feeling the stiff meshing of the gears inside the knob.
’Fine-tune left.’
’Fine-tune right.’
’Stop.’
The tumbling stopped.
A stable, slanted ellipse appeared on the screen.
The image now meant the frequency ratio was locked at 1:1.
’Next, the phase.’
The current phase difference was around 45 degrees, hence the slanted ellipse.
To stretch this ellipse out, to plump it into a full, perfect circle, he would have to rely on phase adjustment.
But this old J2459 oscilloscope didn’t have a separate phase adjustment knob.
’What now?’
Old Zhou stood to the side, a mocking smile playing on his lips.
He knew the flaw of this piece-of-junk machine.
Without an external phase shifter, making a perfect circle was nearly impossible.
He was deliberately making things difficult for the kid.
But in the next second, Old Zhou’s smile froze.
Chen Zhuo didn’t touch the knobs.
He stood up and walked around to the back of the instrument.
Chen Zhuo extended two slender fingers and pinched the wire connecting the signal generator.
Then, he began to manipulate it.
He wasn’t using much force, just gently changing the curvature of the wire, almost as if he were using the warmth of his fingers to heat it.
’No, that’s not it.’
Old Zhou narrowed his eyes.
’He’s not pinching the wire.’
’He’s touching a capacitor.’
Chen Zhuo’s fingers were resting on the knob of a variable capacitor at the signal generator’s output. The plastic cap of the knob had fallen off long ago, leaving only a bare, inconspicuous metal rod.
But that was the adjustment for the RC circuit’s time constant.
In other words, the phase adjustment.
Chen Zhuo stared at the screen.
His fingers gently turned the metal rod.
The degree of rotation was so small it was almost imperceptible.
The slanted ellipse on the screen suddenly began to slowly fatten.
It was like a balloon being inflated, starting to swell bit by bit.
Even Chen Zhuo’s breathing seemed to stop.
His eyes saw nothing but that green glow.
’Closer.’
’Even closer.’
At the very instant the ellipse’s major and minor axes became visually, perfectly equal...
Chen Zhuo’s fingers let go.
HUMMM~
On the screen, a faint green line, its ends meeting, curved into a perfect arc.
It floated silently behind the dark glass.
Not flat.
Not pointed.
Not rotating.
Like a green halo floating in the vacuum of space.
A perfect circle.
Phase difference: π/2.
Frequency ratio: 1:1.
It was as if time itself had frozen in that moment.
Old Zhou’s fingers, holding his cigarette, were suspended in mid-air. A long section of ash had formed at the tip, threatening to fall.
He stared at the circle, the mocking look in his eyes gone, replaced by an almost greedy admiration.
You can spot an expert by their touch.
To be able to blindly twist the bare rod of a capacitor on an old relic with bad connections, relying purely on feel to tune such a stable phase...
...this was something that couldn’t be explained away by the word "smart."
This was talent.
It was an absolute intuition for the microsecond-level fluctuations of flowing electrons.
This kid was born to do this.
PAT.
The long ash from Old Zhou’s cigarette finally fell, landing on his leather shoe.
He snapped back to reality, threw the cigarette butt on the ground, and viciously ground it out with his foot.
"Alright."
Old Zhou’s voice was still hoarse, but the condescending air of an examiner had vanished without a trace.
"Turn it off."
Chen Zhuo obediently shut off the power.
The perfect green ring instantly collapsed into a single point, then slowly faded into the darkness.
The lab was plunged into darkness once again.
Old Zhou turned and walked toward the door.
At the doorway, he stopped and glanced back at Chen Zhuo, who was still packing his schoolbag.
"Don’t play with this one anymore."
Old Zhou pointed disdainfully at the J2459 that had just performed so admirably.
"The potentiometers in this thing are almost completely oxidized. It’s useless for anything other than practicing your touch. It’s for those eighth-grade blockheads to look at waveforms with."
With that, he pulled a set of keys from his pants pocket, which jingled loudly.
He took one off the ring. It was clearly much newer than the previous one, with a much more complex cut.
"Catch."
A metal arc flashed through the darkness.
Chen Zhuo raised his hand and caught it securely.
"My office in the physics department just got a Japanese Kikusui dual-trace oscilloscope. 20-megahertz bandwidth. There’s a signal generator too; it can put out triangle and square waves."
Old Zhou pulled the door open, and the dim yellow light from the hallway illuminated his back.
"From now on, if you don’t feel like going to evening self-study, just go play in my office. Don’t sit in here breathing dust."
"Also."
Old Zhou paused, as if he’d remembered something.
"There’s a preliminary round for the National Junior High Applied Physics Competition next April. I left a practice test on your desk. Do it if you have time, don’t worry if you don’t. It’s not like I expect you to win anything. We just need to fill a spot."
With that, Old Zhou waved his hand and left without a backward glance.
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