Formulae, Procedures & Diagnostics

Essential Formulae

The following formulae cover the calculations most frequently needed when diagnosing and restoring vintage sets. All values use SI units unless noted.

Ohm's Law

The relationship between voltage V, current I, and resistance R:

V = I × R
I = V ÷ R
R = V ÷ I

Where V is in volts, I in amperes, and R in ohms. For a 250V HT rail with a 47kΩ bleeder resistor, current draw is I = 250 ÷ 47,000 = 5.3mA.

Capacitive Reactance

Reactance X_C of a capacitor at frequency f with capacitance C:

X꜀ = 1 ÷ (2π × f × C)

A 0.1µF capacitor at 455kHz — the standard IF — has a reactance of approximately 3.5Ω. Values much higher than this in a signal path indicate a failing component.

Resonant Frequency

The resonant frequency f_r of a tuned circuit with inductance L and capacitance C:

f꜀ = 1 ÷ (2π × √(L × C))

H₂O content in the atmosphere affects coil inductance at high frequencies — a relevant consideration when aligning sets in humid conditions. Temperature coefficients are noted as ppm/°C⁻¹.

Diagnostic Procedures

The following procedures are run from the workshop diagnostic terminal. All commands assume the test rig is connected and the chassis is isolated from the mains.

Signal Injection Test

To inject a test signal at the IF stage and measure output at the speaker terminals:

$ connect --stage IF --freq 455kHz
$ inject --signal sine --level -20dBm
$ measure --point speaker --unit mV

Expected output from a healthy 39-25 is in the range 850mV — 1200mV. A reading below 400mV indicates gain loss in the output stage. A reading of 0mV with signal present at the grid confirms a failed output valve.

Capacitor ESR Sweep

Connect the ESR meter to each capacitor in sequence. The sweep command logs all readings:

$ esr-sweep --chassis 39-25 --log results.csv
Scanning C1...  ESR: 0.8Ω   ✓
Scanning C2...  ESR: 1.2Ω   ✓
Scanning C3...  ESR: 48.3Ω  ✗ FAIL
Scanning C4...  ESR: 2.1Ω   ✓
Scanning C7...  ESR: 31.7Ω  ✗ FAIL

The sweep output above is typical of an unrecapped set. C3 and C7 show ESR values well above the acceptable threshold of 5Ω for electrolytics of this value.

Alignment Sequence

Run the alignment sequence only after all capacitors have been replaced and HT voltages confirmed correct. The sequence must be run in order — do not skip stages.

$ align --stage detector
$ align --stage IF-2
$ align --stage IF-1
$ align --stage RF
$ align --verify --tolerance 2%

If --verify reports tolerance failures, repeat the affected stage and re-verify. Three consecutive failures on the same stage indicate a faulty IF transformer.

Keyboard Reference

The diagnostic terminal supports the following keyboard shortcuts. All shortcuts are active when the terminal window has focus.

Component Marking Conventions

Vintage components use colour band coding. The resistor value formula for a four-band component is:

value = (band1 × 10 + band2) × 10^band3 ± band4%

For a resistor marked brown¹, black⁰, orange³, gold^±5%:

value = (1 × 10 + 0) × 10³ ± 5%
      = 10 × 1000 ± 5%
      = 10,000Ω ± 5%
      = 10kΩ ± 5%

Capacitor markings use a similar three-digit code where the third digit is the multiplier in powers of 10, giving a value in pF. A cap marked 104 is 10 × 10⁴pF = 100,000pF = 100nF = 0.1µF.

Session Output Examples

The following shows typical terminal output from a complete diagnostic session on a newly arrived set:

Wireless Wonder Diagnostic Terminal v2.4
Connected: Philco 39-25 [chassis #WW-2024-0847]
HT voltage: 245V (nominal 250V) ✓
Heater chain: 118V (nominal 117V) ✓

Running ESR sweep...
  C1  0.9Ω  ✓    C2  1.1Ω  ✓    C3  52.4Ω ✗
  C4  49.8Ω ✗    C5  0.7Ω  ✓    C6  0.3Ω  ✓
  C7  28.1Ω ✗

Sweep complete. 3 failures detected.
Recommendation: full recap before alignment.

Session saved to logs/session-2024-11-14.csv

Output like 52.4Ω ✗ on a main filter capacitor is consistent with a dry electrolytic. The set should not be run further until the failed components are replaced — continued use risks damage to the output transformer.