Chapter 109: Postmark and Tolerance

Chalk dust had fallen onto his cuff like a thin layer of frost. Lin Chen stopped writing and rubbed his stiff knuckles. The derivation of the Laplace transform on the blackboard had reached the third step; the quadratic coefficient in the denominator was still short one constant. He glanced at the wall clock: 3:20 in the afternoon.

The EMS from Provincial Institute of Technology should have arrived.

He gathered his scratch paper and slid the brass key back into the lock. As he turned it, the rough bite of metal on metal traveled up through his fingertips. He went downstairs and crossed the athletic field. The numbness in his left foot had already spread to his ankle; with every step, the friction between sole and ground felt as though it were separated by a thick layer of rubber. He adjusted his center of gravity, shifting the weight onto his right leg and the outer edge of his left foot. Shorter stride, same cadence. Breathing steady.

The iron door of the gatehouse was half closed. Old Zhao sat in a rattan chair reading the newspaper. Hearing footsteps, he looked up and pointed at the kraft-paper envelope on the windowsill. “Express from the provincial capital. Sign for it.”

Lin Chen handed over his student ID. Old Zhao did not ask for a pen; he only had him press a thumbprint. The envelope was thick, its corners already frayed. The postmark was from yesterday. He squeezed it. Inside were cardboard backing and several sheets of printed paper. No return receipt, no extra fee. The school had accepted it on his behalf; that was the usual practice at County No. 1 High School.

He carried the envelope to the camphor tree behind the teaching building. The shadows of the leaves mottled the ground. Wind passed through the branches with a dry rasp. He tore open the seal.

The first page was the verification schedule: Wednesday, 9:00 a.m., Room 204, third floor, laboratory building. The second page was the materials checklist: ID card, admission ticket, special recommendation form, approved deferred-exam application, two one-inch photos. The third page was an additional note, printed in bold:

On the day of verification, you must bring one piece of project code or a circuit design diagram completed independently by yourself as evidence of practical ability. A design explanation and the calculation process for key parameters must be attached.

Lin Chen read the third page three times.

“Completed independently.” He had no ready-made project in hand. The repair shop ledger contained dozens of fault-repair records, but those were capacitor replacements and resoldering bad joints, not designs built from scratch. What Provincial Institute of Technology wanted was not maintenance history. It was design logic.

He closed his eyes and ran through the circuits he had dealt with: radio intermediate-frequency amplification, cassette-deck preamps, old regulated power supplies. In the end he stopped at a broken tape recorder he had helped the repair-shop owner fix last winter. The owner had said the noise floor was too high, the speech signal hard to make out. Lin Chen had opened it and found that the coupling capacitor in the preamp stage had aged, while power-supply ripple was feeding straight into the signal path. At the time he had not replaced the op-amp. He had only added a first-stage RC passive low-pass filter at the input, pressing the cutoff frequency down to 8 kHz, while also adjusting the ratio of the feedback resistors to reduce the DC gain. The background noise dropped. The voices became clear.

The principle was simple, but he had calculated the parameters himself.

He opened his eyes, put the papers back into the envelope, and turned toward the laboratory building.

The door of Room 407 on the fourth floor opened again. Dust floated up and down in the slanting light of late afternoon. He pulled over a chair, sat down, and took graph paper, a ruler, a pencil, and an eraser from his canvas bag. His left foot was already too swollen to fit into his shoe, so he simply took the shoe off, wrapped his ankle and instep tightly with a clean strip of gauze, and propped it up. The pain had been physically isolated. What remained was only a mechanical heaviness.

He began to draw on the graph paper. Power supply, op-amp, input coupling, RC filter network, feedback loop, output stage. The lines had to be square and straight, the nodes unambiguous. Once the topology was finished, he began listing the parameters.

The cutoff frequency, f_c = 1/(2πRC). Target: 8 kHz. He chose R = 2 kΩ and calculated C ≈ 10 nF. There was no 10 nF part among the standard capacitor values, only 10.3 nF or 9.1 nF. He took 9.1 nF and recalculated: f_c = 8.7 kHz. The error was within tolerance.

The feedback resistor R_f and input resistor R_in determined the gain. The tape recorder microphone output was about 5 mV, and the op-amp saturation voltage was ±12 V. He needed to amplify the signal to about 1 V, a gain of 200. So R_f / R_in = 199. He first chose R_in = 1 kΩ and R_f = 200 kΩ. But a 200 kΩ resistor would contribute too much thermal noise, so he changed to R_in = 2 kΩ and R_f = 390 kΩ, for a gain of 195. Then he recalculated the offset voltage caused by input bias current. The op-amp was an NE5532, with a typical bias current of 200 nA. Offset voltage = 200 nA × 390 kΩ = 78 mV. After DC amplification, the output would carry a 15 V DC offset and go straight into saturation.

He stopped writing.

He had missed the DC-blocking capacitor.

He inserted a 10 μF electrolytic capacitor in series with the feedback loop to block DC and amplify only AC. He recalculated the time constant, confirming that the low-frequency response would not attenuate the speech band. The pencil moved quickly across the page. Formulas, units, reasons for choosing each value—line after line. No ornate terminology, only resistors, capacitors, frequencies, gain, tolerance.

Outside the window, the sky darkened. The streetlights on the field came on. Their dim yellow glow filtered through the glass and fell across the graph paper. He rubbed his eyes and kept writing the design explanation.

Design goal: suppress 50 Hz mains interference and broadband background noise while preserving effective audio signals below 8 kHz. Implementation path: first-stage RC passive low-pass filter + AC negative-feedback amplification. Parameter basis: the effective speech band is 300 Hz–3.4 kHz; leave a twofold margin up to 8 kHz. Tolerance analysis: capacitor tolerance ±10%, resistor tolerance ±5%; the actual cutoff frequency drifts between 7.8 and 9.5 kHz, without affecting core functionality.

After the last line, he set down the pencil. His wrist ached and the skin of his fingertips had been rubbed red by the wood. He lowered his head and looked at his left foot. A little dark yellow tissue fluid had already seeped through the edge of the gauze. He replaced it with a clean strip and wrapped it tight again. His movements were practiced, without pause.

The wall clock pointed to 10:40 at night.

He sorted the sheets of graph paper in order and clipped them into a hard-cover notebook. Beside it lay the special recommendation form, the deferred-exam application, the one-inch photos, and the admission ticket. All the documents were complete. But the timing still was not.

He opened the ledger and flipped to Wednesday’s page.

08:30–10:30 Mock exam venue (County No. 1 High School teaching building) 09:00–12:00 Provincial Institute of Technology verification (provincial capital laboratory building) 10:30 Hand in exam paper 11:00 Bus departs from county passenger station (1.2 km on foot) 13:15 Arrive at provincial capital passenger station 13:30 Transfer to bus for Provincial Institute of Technology 14:00 Arrive at verification site

Under “14:00” he drew a red line. The additional note said: Anyone more than 15 minutes late will be deemed to have forfeited. Verification at Provincial Institute of Technology stopped admitting people after 14:15 at the latest. He had left himself a 15-minute margin. But that was under ideal conditions.

He needed to confirm two things. First: would the Wednesday morning coach from the county passenger station depart on time? Second: after handing in the mock exam paper, could his left foot cover the 1.2 kilometers from the exam room to the passenger station within twenty minutes?

He picked up his pen and wrote on the blank part of the ledger: Variable 1: coach timetable. Variable 2: gait decay rate.

At six o’clock tomorrow morning, he had to go to the station window and verify the schedule. If the bus time had changed or the seats were full, he needed backup routes: share a ride, hire an unlicensed car, or walk to the national highway and flag down a passing coach. Every option came with its own cost and risk.

He closed the ledger and zipped up his canvas bag. He stood. When his left foot touched the floor, the numbness was still there, but his center of gravity had already learned to shift by habit. He locked the door of 407 and slipped the key back into his pocket.

The motion-sensor lights in the corridor blinked on one by one with his footsteps, then went dark again one by one behind him. At the stairwell he stopped, took out the additional note from his bag, and read it once more.

A design explanation and the calculation process for key parameters must be attached.

He suddenly realized that the teachers at the verification site would not just look at the diagram. They would ask questions. Why choose the NE5532 instead of the TL072? Why set the cutoff frequency at 8 kHz instead of 10 kHz? If the input signal amplitude suddenly rose to 50 mV, would the circuit clip and distort?

He ran through the answers in his mind. Bias current, noise density, slew rate, dynamic range. Behind every term stood formulas and measured data. He could not remember every parameter in full, but the logic of the derivation held.

Wind poured in through the stairwell window, carrying the first chill of early autumn. Lin Chen folded the note and tucked it into the inner pocket of his jacket.

Tomorrow there was still morning self-study. The science section of the mock exam was not yet finished. The timetable at the passenger station was not yet confirmed. The gauze on his left foot would have to be changed tomorrow.

He went down the stairs. His footsteps echoed through the empty teaching building. Very light, but every step landed on solid ground.

The ledger was in his bag, the hard cover pressing against his spine. The tolerance was still compressing. The marks on Wednesday’s scale had already come into focus.

He simply had not yet calculated that the old dispatcher at the passenger station would temporarily pull one bus off the line on Wednesday morning. Nor that the proctor at the mock exam venue would collect the papers five minutes early.

But at this moment, Lin Chen only pushed open the door and stepped into the night. The streetlights stretched his shadow long. He looked down at his foot, adjusted his stride a little, and kept walking.

Tomorrow, six o’clock. Passenger station. Variables pending verification.